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Research Article An Image Steganography Method Hiding Secret Data into Coefficients of Integer Wavelet Transform Using Pixel Value Differencing Approach Avinash K. Gulve 1 and Madhuri S. Joshi 2 1 Government College of Engineering, Aurangabad, Maharashtra 431 005, India 2 Jawaharlal Nehru College of Engineering, Aurangabad, Maharashtra 431 005, India Correspondence should be addressed to Avinash K. Gulve; [email protected] Received 12 November 2014; Accepted 23 December 2014 Academic Editor: Gen Qi Xu Copyright © 2015 A. K. Gulve and M. S. Joshi. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. e image steganography systems use either the spatial domain or the frequency domain to hide the secret information. e proposed technique uses spatial domain technique to hide secret information in the frequency domain. e cover image is transformed using integer wavelet transform to obtain four subbands: LL, LH, HL, and HH. en, the PVD approach is used to hide the secret information in the wavelet coefficients of all the four subbands. For improving the security of the hidden information, the proposed method first modifies the difference between two wavelet coefficients of a pair and then uses the modified difference to hide the information. is makes extraction of secret data from the stego image difficult even if the steganography method fails. e result shows that the proposed technique outperforms other PVD based techniques in terms of security of secret information and hiding capacity of cover image. 1. Introduction Now a day, it is easy to share the information which is in the form of text, image, audio, or video using the Internet as the communication channel. Since Internet is an open channel of communication, there is always a threat of stealing the information. erefore, it is becoming more important to adopt security measures so that the information can be protected from being stolen by malicious user. e security measures include cryptography, steganography, and coding. Steganography involves hiding secret information in a multi- media object such as image, audio, or video in such a way that its existence in these documents cannot be noticed. Digital images are preferred for hiding the secret information. It is relatively easy to place information in digital images because of the availability of sufficient redundant area where valuable information could be placed in an imperceptive way. It is possible to use images, either in the spatial domain or in the frequency domain, to hide secret information. In the spatial domain, the pixel values are used for hiding the secret information and, in the frequency domain, the wavelet coefficients are used for hiding the secret information. e organization of the paper is as follows. A review of necessary background of IWT and PVD based steganography is presented in this section. In Section 2, the proposed method is discussed. In Section 3, the results are discussed while the paper is concluded in Section 4. In the PVD method, as suggested by Wu et al. [1, 2], a gray-valued cover image is partitioned into nonoverlapping blocks composed with two consecutive pixels, and +1 . For each block, difference value is calculated by subtracting from +1 . Since the pixel value ranges from 0 to 255, the difference value also ranges from 255 to 255. erefore, | | ranges from 0 to 255. e block is in smooth area if the difference value | | is small; otherwise, it is in sharply edged area. A range table is designed with contiguous ranges ( where = 1, 2, 3, . . . , ) and the table range is from 0 to 255. e lower and upper boundaries of are denoted by and , respectively. Hence, ∈ [ , ]. e width of is calculated as = + 1. is width is used to estimate Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2015, Article ID 684824, 11 pages http://dx.doi.org/10.1155/2015/684824
12

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Page 1: Research Article An Image Steganography Method Hiding ...downloads.hindawi.com/journals/mpe/2015/684824.pdf · An Image Steganography Method Hiding Secret Data into Coefficients of

Research ArticleAn Image Steganography Method Hiding SecretData into Coefficients of Integer Wavelet TransformUsing Pixel Value Differencing Approach

Avinash K Gulve1 and Madhuri S Joshi2

1Government College of Engineering Aurangabad Maharashtra 431 005 India2Jawaharlal Nehru College of Engineering Aurangabad Maharashtra 431 005 India

Correspondence should be addressed to Avinash K Gulve akgulvegecaacin

Received 12 November 2014 Accepted 23 December 2014

Academic Editor Gen Qi Xu

Copyright copy 2015 A K Gulve and M S Joshi This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The image steganography systems use either the spatial domain or the frequency domain to hide the secret information Theproposed technique uses spatial domain technique to hide secret information in the frequency domain The cover image istransformed using integer wavelet transform to obtain four subbands LL LHHL andHHThen the PVD approach is used to hidethe secret information in the wavelet coefficients of all the four subbands For improving the security of the hidden informationthe proposed method first modifies the difference between two wavelet coefficients of a pair and then uses the modified differenceto hide the informationThis makes extraction of secret data from the stego image difficult even if the steganography method failsThe result shows that the proposed technique outperforms other PVD based techniques in terms of security of secret informationand hiding capacity of cover image

1 Introduction

Now a day it is easy to share the information which is inthe form of text image audio or video using the Internetas the communication channel Since Internet is an openchannel of communication there is always a threat of stealingthe information Therefore it is becoming more importantto adopt security measures so that the information can beprotected from being stolen by malicious user The securitymeasures include cryptography steganography and codingSteganography involves hiding secret information in a multi-media object such as image audio or video in such a way thatits existence in these documents cannot be noticed Digitalimages are preferred for hiding the secret information It isrelatively easy to place information in digital images becauseof the availability of sufficient redundant area where valuableinformation could be placed in an imperceptive way It ispossible to use images either in the spatial domain or in thefrequency domain to hide secret information In the spatialdomain the pixel values are used for hiding the secret

information and in the frequency domain the waveletcoefficients are used for hiding the secret information

The organization of the paper is as follows A review ofnecessary background of IWT andPVDbased steganographyis presented in this section In Section 2 the proposedmethod is discussed In Section 3 the results are discussedwhile the paper is concluded in Section 4

In the PVD method as suggested by Wu et al [1 2] agray-valued cover image is partitioned into nonoverlappingblocks composed with two consecutive pixels119875

119894and119875119894+1

Foreach block difference value 119889

119894is calculated by subtracting

119875119894from 119875

119894+1 Since the pixel value ranges from 0 to 255 the

difference value also ranges from minus255 to 255 Therefore |119889119894|

ranges from 0 to 255 The block is in smooth area if thedifference value |119889

119894| is small otherwise it is in sharply edged

area A range table119877 is designedwith 119899 contiguous ranges (119877119896

where 119896 = 1 2 3 119899) and the table range is from 0 to 255The lower and upper boundaries of 119877

119896are denoted by 119897

119896and

119906119896 respectively Hence 119877

119896isin [119897119896 119906119896] The width119882

119896of 119877119896is

calculated as119882119896= 119906119896minus119897119896+ 1Thiswidth119882

119896is used to estimate

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 684824 11 pageshttpdxdoiorg1011552015684824

2 Mathematical Problems in Engineering

the number of bits 119905119894(where 119905

119894= log2119882119896) of secret message

that can be hidden using the difference of two consecutivepixels After hiding 119905

119894bits using the difference 119889

119894 new values

are assigned to119875119894and 119875119894+1

The new difference 1198891015840119894is calculated

by subtracting 119875119894from 119875

119894+1 The new difference 1198891015840

119894stands for

the secret data hidden in the pair During extraction the stegoimage is partitioned into nonoverlapping blocks composedwith two consecutive pixels 119875

119894and 119875

119894+1 Then the difference

value 1198891015840119894for each pair of two consecutive pixels 119875

119894and 119875

119894+1is

calculated Next |1198891015840119894| is used to locate the suitable range 119877

119896

The decimal equivalent of the secret information hidden inthe block is given by |1198891015840

119894| minus 119897119896which is then transformed into

a binary sequence with 119905119894bits

In order to improve the capacity of hiding secret dataand to provide an imperceptible stego image quality a novelsteganographic method based on least-significant-bit (LSB)replacement and pixel-value differencing (PVD) method ispresented by Wu et al [2] The range table is divided intolower level (smooth area) and higher level (edged area) Inthe smooth area 6 bits of the secret data is hidden by LSBmethod while in the higher level secret data is hidden usingthe PVD method

To improve the hiding capacity of the cover image andquality of the stego image another enhanced method isintroduced based on the PVDmethod byChang et al [3 5 6]In this method data is hidden in vertical and diagonal edgesalong with the horizontal edges The cover image is dividedinto the blocks of 2 times 2 pixels Considering 119909 and 119910 to be thepixel locations each 2 times 2 block includes four pixels 119875

(119909119910)

119875(119909+1119910)

119875(119909119910+1)

and 119875(119909+1119910+1)

Pixel 119875(119909119910)

is grouped withthe remaining three pixels in the block to form three pixelpairs These three pairs are named 119875119875

0 1198751198751 and 119875119875

2where

1198751198750= (119875(119909119910) 119875(119909+1119910)) 1198751198751= (119875(119909119910) 119875(119909119910+1)) and 119875119875

2=

(119875(119909119910) 119875(119909+1119910+1)

) respectively After embedding the secretinformation in each pair using PVD approach values of twopixels in each pair get modified Thus the original differencevalue 119889

119894is modified to a new difference value 1198891015840

119894 The new

pixel values in each pair are different from their original onesThat is three different values are obtained for the pixel 119875

(119909119910)

However pixel 119875(119909119910)

can have only one value Thereforeone of the 1198751198751015840

119894is selected as the reference pair to offset the

remaining two pixel values That is two pixel values of thereference pair are used to adjust the pixel values of othertwo pairs and construct a new 2 times 2 block The embeddedsecret data is unaffected because new difference values 1198891015840

119894

are unaltered During extraction the difference value 1198891015840119894is

used to extract the hidden information |1198891015840119894| is used to locate

the suitable range 119877119896 The decimal equivalent of the secret

information hidden in the pair is given by |1198891015840119894| minus 119897119896which is

then transformed into a binary sequence with 119905119894bits

Gulve and Joshi [4] have proposed a steganographymethod to improve the security of the secret informationusing five-pixel pair differencing approachThe cover image ispartitioned into blocks of 2 times 3 pixels to form five pixel pairsThe secret data is embedded in the pairs using the differencevalue of pixels in that pair Instead of hiding 119872 bits in thepair using the difference value bits le 119873 are hidden in thepair where119873 is the average of bits that can be hidden in each

pair of the blockThus in case of failure of the steganographysystem it becomes difficult to estimate exact number of bitshidden in each pair of the block Another level of securityfor the secret information is introduced by converting thesecret information in its gray code form For each pair in theblock the method converts bits of secret information in thegray code form and then embeds these bits in that pair Thusthe security of the secret information is improved withoutinvolving the overhead of encryption and decryption Gulveand Joshi [7] have proposed a steganography method toimprove the security of the secret data embedded in theimage The cover image is divided in the blocks of 2 times 3pixels to form five pairs The location of the common pixel isdecided using the image data For this reason data of last fewrows are used Since the common pixel is changed randomlybased on the image data it is difficult to extract the secret datafrom stego image even if the steganography method fails

Integer wavelet transform maps an integer data set intoanother integer data set Calderbank et al [8] have explainedthe working of integer wavelet transform Haar wavelettransform in its unnormalized version involving pair wiseaverages and differences is written as

1198781119899=11987802119899+ 11987802119899+1

21198891119899= 11987802119899+1minus 11987802119899 (1)

Its inverse is given by

11987802119899= 1198781119899+1198891119899

211987802119899+1= 1198781119899minus1198891119899

2 (2)

Because of division by two this is not integer transformThe integer version can be built by omitting division by twoin 1198781119899

and calculating the sum instead of the average This iscalled 119878 transform [8] Consider the following example

1198781119899= lfloor(11987802119899+ 11987802119899+1)

2rfloor 119889

1119899= 11987802119899+1minus 11987802119899 (3)

It is possible to define 1198781119899

as above because the sum anddifference of two integers are either even or odd Thus it issafe to omit last bit of sum since it is similar to last bit ofdifference The 119878 transform [8] is invertible and it is given by

11987802119899= 1198781119899minus lfloor1198891119899

2rfloor 119878

02119899+1= 1198781119899+ lfloor(1198891119899+ 1)

2rfloor

(4)A different way of writing Haar transform using ldquoliftingrdquo

steps leads to natural generalizations It is possible to writeHaar and 119878 transform using lifting schemes [8]

First compute the difference and then use the differencein second step to compute the average

1198891119899= 11987802119899+1minus 11987802119899

1198781119899= 11987802119899+1198891119899

2 (5)

The inverse transform can be calculated in two stepsFirst recover the even samples from the average and differ-ence and recover the odd samples from even and difference[8] It is given by the following equations

11987802119899= 1198781119899minus1198891119899

211987802119899+1= 1198891119899+ 11987802119899 (6)

Mathematical Problems in Engineering 3

It is possible to write integer transform by truncating thedivision

1198891119899= 11987802119899+1minus 11987802119899

1198781119899= 11987802119899+ lfloor1198891119899

2rfloor (7)

Lifting can be used to compute the inverse transformTheequations follow from reversing the order and changing thesign of the forward transform [8]

11987802119899= 1198781119899minus lfloor1198891119899

2rfloor 119878

02119899+1= 1198891119899+ 11987802119899 (8)

Ramalingam et al [9] have elaborated the process ofseparating four subbands using Haar IWT The first stageIWT is given by

H = 119862119900minus 119862119890

L = 119862119890+ lfloor

H2rfloor

(9)

where 119862119900represents pixels in odd column and 119862

119890represents

pixels in even column In the next stage the IWT coefficientsare calculated using high pass and low pass filter banks Thisprocess creates four subbands low-low (LL) low-high (LH)high-low (HL) and high-high (HH) The second stage IWTis given by

LH = Lodd minus Leven

LL = Leven + [LH2]

HH = Hodd minusHeven

HH = Heven + [HL2]

(10)

where Hodd represents H bandrsquos odd row Lodd represents Lbandrsquos odd row Heven represents H bandrsquos even row and Levenrepresents L bandrsquos even row [9]

Ghasemi et al [10 11] have proposed a novel steganogra-phy scheme based on integer wavelet transform and geneticalgorithm The scheme embeds data in integer wavelettransform coefficients by using a mapping function basedon genetic algorithm The methods use wavelet transformcoefficients to embed secret data into the four subbandsof two-dimensional wavelet transform Genetic algorithm isused to find themapping functionA chromosome is encodedas an array of 64 genes containing permutations 1 to 64that point to pixel numbers in each block OPAP is used tominimize the error between cover and stego image

Xuan et al [12] have suggested a lossless data hidingmethod for digital images using integer wavelet transformand threshold embedding technique CDF (22) integerwavelet transform is used to obtain the wavelet coefficientsHistogrammodification is applied to prevent possible under-flowoverflow of pixel values A predefined threshold value 119879is used to embed data in the wavelet coefficients

El Safy et al [13] have suggested an adaptive stegano-graphic model which combines adaptive hiding capacity

function that hides secret data in the integer wavelet coef-ficients of the cover image with the optimum pixel adjust-ment (OPA) algorithm Histogram modification is appliedto prevent possible underflowoverflow of pixel values Thecover image is divided into 8 times 8 nonoverlapping blocksEach block is transformed using 2D Haar integer wavelettransform to obtain four subbands LLI LHI HLI andHHI Hiding capacity of each coefficient is determined andthe data is embedded in the coefficients A pseudorandomnumber generation function is used to select the waveletcoefficients for increasing the security of the hidden dataTheOPAalgorithm is applied after embedding secretmessageto minimize the embedding error The extraction procedureis a blind process since it requires only the secret key fromthe receiver The secret key is used to identify the waveletcoefficients Secret message bits are extracted from eachselected wavelet coefficient

Archana et al [14] have proposed a method for hidingsecret information in the discrete wavelet transform coeffi-cients using GA and OPAP algorithm to provide optimumhiding capacity The four subbands LL HL LH and HH areused for hiding the data Hiding capacity function ismodifiedby using different ranges for k for the LH HL and HHsubbands where its values range from 1 to 4 The length L ofmessage bits to be hidden in wavelet coefficient is determinedby using hiding capacity function

Al-Asmari et al [15] have proposed a method using dis-crete wavelet transform and pixel value differencing approachto hide the information Using the discrete wavelet transformthe cover image is decomposed to obtain the four subbands(LL HL LH and HH) Then the LSB method is used tohide secret information in the LL subband by hiding two bitsof secret information in each coefficient The PVD approachis used to hide the information in the remaining threesubbands For hiding the information two consecutive pixelsin the vertical direction are grouped to form a pair Themethod gives high performance in terms of capacity humanvisual quality and PSNR

2 Proposed Method

The proposed method hides secret information in the grayscale images It uses spatial domain technique to hide secretinformation in the frequency domain In the frequencydomain the image is decomposed into four subbands usinginteger wavelet transform and then the spatial domaintechnique is used to hide secret information in the waveletcoefficients of the four subbands

The cover image is transformed using 2D Haar integerwavelet transform to obtain four subbands LL LH HL andHHThe proposed method embeds data in the coefficients offour subbands by using the pixel value differencing approach

21 Preprocessing The gray scale image is read as a 2D arrayof size [119872119873] Histogram modification [12ndash15] is applied toprevent the possible overflowunderflow of pixel values Thisproblem occurs when the pixel values of the cover image areclose to 255 or 0 because they may exceed 255 or fall below 0

4 Mathematical Problems in Engineering

LL HL

LH HH

Figure 1 Arrangements of wavelet coefficients

Figure 2 The image lenatiff after performing Harr transform

during inverse integer wavelet transformThe problem can besolved by mapping the lowest 15 gray scale levels to the value15 and the highest 15 gray scale levels to the value 240 If thepixel values exceed the boundaries during the inverse wavelettransform the image is not suitable for hiding secret dataThe image is transformed using 2D Haar wavelet transformto obtain four subbands LL LH HL and HH of size [11987221198732] each All the four subbands are used to hide the secretinformationThe 2D array of size [119872119873] is again constructedby arranging the four subbands as shown in Figure 1

Figure 2 shows the arrangement of four subbands of theimage lenatiff after transforming it using 2D Harr integerwavelet transform

A 2D array obtained by arranging the wavelet coefficientsof four subbands is shown as follows

(

112 230 150 sdot sdot sdot minus45 minus120 80

130 159 172 sdot sdot sdot minus37 minus89 minus72

sdot sdot sdot sdot sdot sdot sdot sdot sdot

sdot sdot sdot sdot sdot sdot sdot sdot sdot

minus30 minus59 minus72 sdot sdot sdot minus37 minus89 minus72

) (11)

The difference operation in Haar transform may cause someof the wavelet coefficients in HL LH and HH subbands tohave negative values

Since some of the wavelet coefficients have negativevalues the 2D array shown in (11) cannot be used for hid-ing secret information using the pixel value differencingapproach Hence absolute values are used for the coefficient

with negative values to create a new 2D array with positiveelements as follows

(

112 230 150 sdot sdot sdot 45 120 80

130 159 172 sdot sdot sdot 37 89 72

sdot sdot sdot sdot sdot sdot sdot sdot sdot

sdot sdot sdot sdot sdot sdot sdot sdot sdot

30 59 72 sdot sdot sdot 37 89 72

) (12)

After hiding the secret information in the 2D array shownin (12) inverse wavelet transform is performed to obtainthe stego image To obtain good quality of stego image theoriginal sign of each wavelet coefficient as shown in (11) isrequired Hence the 2D array shown in (11) is used to createa sign matrix of the size [119872119873] having elements with values1 or minus1 The sign matrix so created is shown as follows

(

1 1 1 sdot sdot sdot minus1 minus1 1

1 1 1 sdot sdot sdot minus1 minus1 minus1

sdot sdot sdot sdot sdot sdot sdot sdot sdot

sdot sdot sdot sdot sdot sdot sdot sdot sdot

minus1 minus1 minus1 sdot sdot sdot minus1 minus1 minus1

) (13)

The wavelet coefficients having positive values are repre-sented by 1 whereas wavelet coefficients having negativevalues are represented by minus1 in the sign matrix

22 Embedding Process For hiding the data in the 2D arraythe method suggested by Gulve [4 7] is used In the methodproposed byChang [3] a block of 2times 2 pixels is used to form 3pairs which are then used to hide the secret informationTheproposed method uses the block of 2 times 3 wavelet coefficientsThe introduction of 2 wavelet coefficients in the 2 times 2 blockforms two extra pairs For a 512 times 512 image it is possible toform 196608 pairs using the approach suggested by Chang [3]whereas using the proposed approach 217600 pairs can beformed A greater number of pairs provide extra space forhiding the secret information Thus the proposed methodimproves the hiding capacity of the cover image

Thedifference between twowavelet coefficients in the pairis used to hide the secret information If the difference valueis directly used to hide the information it is easy to retrievethe embedded information in case the steganography systemfails To enhance the security of the secret information theproposed algorithm modifies the difference between the twowavelet coefficients in the pair and this modified differenceis used to hide the secret information This imposes extralayer of security making harder extraction of original secretinformation from stego image using the difference valuesdirectly [4 7]

The arrangement of wavelet coefficients into nonover-lapping blocks of 2 times 3 wavelet coefficients is shown inFigure 3 As shown in Figure 3 each 2 times 3 block includes sixwavelet coefficients 119875

(119909119910) 119875(119909119910+1)

119875(119909119910+2)

119875(119909+1119910)

119875(119909+1119910+1)

and 119875

(119909+1119910+2) where 119909 and 119910 are the locations of wavelet

coefficients Five pairs are formed by grouping the commonwavelet coefficient PX

1with the remaining five wavelet

Mathematical Problems in Engineering 5

PX0

PX3

PX1

PX4

PX2

PX5

P(xy) P(xy+1)P(xy+2)

P(x+1y) P(x+1y+1) P(x+1y+2)

Figure 3 Pixel block

coefficients PX0 PX2 PX3 PX4 and PX

5 The five pairs 119875119875

119894

where 119894 = 0 1 2 3 4 are as shown below

1198751198750= (119875(119909119910+1) 119875(119909119910))

1198751198751= (119875(119909119910+1) 119875(119909119910+2))

1198751198752= (119875(119909119910+1) 119875(119909+1119910))

1198751198753= (119875(119909119910+1) 119875(119909+1119910+1)

)

1198751198754= (119875(119909119910+1) 119875(119909+1119910+2)

)

(14)

The difference value 119889119894is calculated for each pair 119875119875

119894by

subtracting the common wavelet coefficient PX1from the

other wavelet coefficient in that pair This difference value isused to identify the corresponding range 119877

119896119894from the range

table119877The range table is designed with ranges [0ndash7] [8ndash15][16ndash31] [32ndash63] [64ndash127] and [128ndash255] The width 119882

119896119894

of range 119877119896119894

is used to determine the number of bits 119905119894(119905119894=

log2119882119896119894) that can be hidden in each pair where 119894 = 0 1 2 3 4

This 119905119894is then used to calculate the average value (119873) of

number of bits possible to be hidden in each pair of the blockThe average value119873 is used to calculate the revised difference119877119889119894as 119877119889119894is remainder (119889

1198942119873) so that 119877119889

119894le 2119873 where 119889

119894is

the original differenceThe offset difference OD119894is calculated

as |119889119894|minus |119877119889

119894| for each pair in the blockThe revised difference

|119877119889119894| is then used to determine the number of bits 119905

119894for each

pair in the block Thus if the original difference value |119889119894|

allows 119872 bits to be hidden in the pair then the proposedapproach hides bits le 119873 in that pair [4 7]

After embedding 119905119894bits of the message in the pair new

difference 1198891015840119894is calculated as OD

119894+119897119896119894+119887where 119897

119896119894represents

lower boundary of the range 119877119896119894

in the range table 119877 and 119887represents the decimal equivalent of 119905

119894message bits hidden in

that pairEmbedding 119905

119894bits in the pair modifies the values of

both the wavelet coefficients in the pair The new valuesof wavelet coefficients in each pair are different from theiroriginal values Since new value is assigned to commonwavelet coefficient PX

1in each pair five different values are

obtained for the common wavelet coefficient PX1 However

the common wavelet coefficient PX1can have only one value

in each bock This requires values of other five waveletcoefficients PX

0 PX2 PX3 PX4 and PX

5to be adjusted such

that the new difference 1198891015840119894remains unchanged Therefore

the pair having new values of wavelet coefficients close totheir original values is selected as the reference pair To find

the reference pair the difference 119898 between 119889119894and 1198891015840

119894is

calculated Small value of |119898| indicates that the newdifferencevalue 1198891015840

119894is close to the original difference value 119889

119894 Thus

for the pair with minimum |119898| the new values of waveletcoefficients are close to their original values So the pair withminimum |119898| is selected as the reference pair The values ofthe two wavelet coefficients in the reference pair are used toadjust the values of wavelet coefficients in other pairs andconstruct a new 2times3 blockThe embedded secret informationin newly constructed block is unaffected because differencevalues for the pairs are unaltered [4 7]

During the extraction process average value (119873) iscalculated using the same process adopted during embeddingof the secret messageThe average value119873 is used to calculatethe revised difference 1198771198891015840

119894as 1198771198891015840

119894is remainder (119889

1198942119873) Suit-

able range 119877119896119894 is identified using this revised difference Thesecretmessage is extracted in the decimal formby subtracting119897119896from |1198771198891015840

119894| Secret message is then converted into a binary

stream with 119905119894(119905119894= log2119882119896119894) bits [4 7]

The process of hiding secret information in the coverimage is described below [4 7]

(1) Create the 2D array as shown in (12) by preprocessingthe gray scale cover image

(2) Partition the array into nonoverlapping blocks of 2times3wavelet coefficients and group wavelet coefficient PX

1

with the remaining wavelet coefficients in the block toform five pairs

(3) Calculate the difference values 119889119894for the five pairs in

each block

1198890= 119875(119909119910)minus 119875(119909119910+1)

1198891= 119875(119909119910+2)minus 119875(119909119910+1)

1198892= 119875(119909+1119910)minus 119875(119909119910+1)

1198893= 119875(119909+1119910+1)

minus 119875(119909119910+1)

1198894= 119875(119909+1119910+2)

minus 119875(119909119910+1)

(15)

(4) Use |119889119894| where 119894 = 0 1 2 3 4 to locate suitable range

119877119896in the designed range table Use this range to

calculate number of bits 119905119894that can be hidden in each

pair 119875119875119894 Then calculate the average bits using

avg = lfloor(sum4

119894=0119905119894

5)rfloor (16)

(5) Calculate the revised difference |119877119889119894| where 119894 =

0 1 2 3 4 as119877119889119894is remainder (119889

1198942avg) so that119877119889

119894lt=

2avg

(6) Calculate the difference OD119894as OD

119894= |119889119894| minus |119877119889

119894| for

each pair

(7) Use |119877119889119894|where 119894 = 0 1 2 3 4 to locate suitable range

119877119896in the designed range table

6 Mathematical Problems in Engineering

(8) Compute the number of bits 119905119894that can be embedded

in each pair using the corresponding range given by119877119896 The value 119905

119894can be estimated from the width 119908

119896

of 119877119896 which is given by 119905

119894= log2119908119896where width119908

119896=

119906119896minus119897119896+1 and119906

119896and 119897119896are upper and lower boundaries

of the range 119877119896

(9) Read 119905119894bits from the binary secret data

(10) Calculate the new difference value 1198891015840119894given by

1198891015840

119894= OD

119894+ 119897119896119894+ 119887119894 if 119889

119894ge 0

1198891015840

119894= minus (OD

119894+ 119897119896119894+ 119887119894) if 119889

119894lt 0

(17)

(11) Modify the values of wavelet coefficients in the pair119875119875119894using

(1198751015840

119899 1198751015840

119899+1) = (119875

119899minus lceil119898

2rceil 119875119899+1+ lfloor119898

2rfloor) (18)

where 119875119899and 119875

119899+1represent two wavelet coefficients

in the pair 119875119875119894and 119898 is obtained by subtracting 119889

119894

from 1198891015840119894

(12) Select the pair with minimum |119898| as the optimalreference pair and use this pair to adjust the values ofwavelet coefficients of the other four pairs The valueof the common wavelet coefficient is given by 1198751015840

119899of

the reference pair Modify value of another waveletcoefficient 1198751015840

119899+1of remaining four pairs such that

the new difference 1198891015840119894will remain unchanged Thus

new values are assigned to remaining four waveletcoefficients in the block

(13) Check the new values of wavelet coefficients for fall-off boundaries that is check whether all the valuesare within the range from 0 to 255 If not modify thevalues preserving the difference between the values oftwo wavelet coefficients of each pair in the block

(a) Find out the smallest of all the wavelet coeffi-cients If the smallest is less than 0 then add|smallest| in all the wavelet coefficients in thatblock

(b) Find out the largest of all the wavelet coeffi-cients If the largest is greater than 255 subtractlargest minus 255 from all the wavelet coefficients inthat block

(c) If fall-off boundary problems still exist thecover image is not suitable for hiding secretinformation

(14) Now reconstruct the block from all pairs with modi-fied values of wavelet coefficients

(15) Repeat steps (2) through (14) until the secret informa-tion is embedded in the cover image

23 Postprocessing After the embedding process is overoriginal signs are assigned to the elements of 2D array usingthe sign matrix created during preprocessing phase This is

accomplished by one to one comparison of elements of 2Darray with the elements of 2D sign matrix The 2D array isthen split to obtain the four subbands Using inverse 2DHaarinteger wavelet transform the four subbands are combined toobtain the stego image of size [119872119873] All the pixel values ofthe stego image in the range from 0 to 255 indicate that secretdata is safely hidden and can be extracted accurately

24 Extraction Process The extraction process is blind Itdoes not require the existence of cover image for extractinghidden secret data from the stego image The stego image ispreprocessed to obtain the 2D array as shown in (12) Theprocess of extraction of secret information from the stegoimage is described below [4 7]

(1) Create the 2D array as shown in (12) by preprocessingthe gray scale stego image

(2) Partition the array into nonoverlapping blocks of 2times 3wavelet coefficients and group wavelet coefficient PX

1

with the remaining wavelet coefficients in the block toform five pairs Keep the partition order the same asthat of the embedding

(3) Calculate the difference values 119889119894for the five pairs in

each block

1198890= 119875(119909119910)minus 119875(119909119910+1)

1198891= 119875(119909119910+2)minus 119875(119909119910+1)

1198892= 119875(119909+1119910)minus 119875(119909119910+1)

1198893= 119875(119909+1119910+1)

minus 119875(119909119910+1)

1198894= 119875(119909+1119910+2)

minus 119875(119909119910+1)

(19)

(4) Use |119889119894| where 119894 = 0 1 2 3 4 to locate suitable range

119877119896in the designed range table Use this range to

calculate number of bits 119905119894 which is hidden in each

pair 119875119875119894 Then calculate the average bits using (16)

(5) Calculate revised difference |1198771198891015840

119894| where

119894 = 0 1 2 3 4 as 1198771198891015840119894is remainder (119889

1198942avg)

(6) Use |1198771198891015840119894| where 119894 = 0 1 2 3 4 to locate suitable 119877

119896in

the designed range table(7) After 119877

119896is located 119897

119896is subtracted from |1198771198891015840

119894| and

1198871015840

119894is obtained in decimal form A binary sequence is

generated from 1198871015840119894with 119905

119894bits where 119905

119894= log2119908119896

Repeat steps (2) through (7) until embedded message isextracted

3 Results

A set of gray scale TIFF images is used for the experimenta-tion This set consists of standard images as well as imagestaken from the camera The standard images are obtainedfrom the ldquothe USC-SIPI image database (httpsipiuscedudatabase)rdquo The images taken from Canon A45 camera

Mathematical Problems in Engineering 7

Table 1 Comparison of hiding capacity (in bytes)

Cover image PVD method [1] TPVD method [3] Gulversquos method [4] Proposed methodCapacity PSNR Capacity PSNR Capacity PSNR Capacity PSNR

Lena 50960 4179 75836 3889 81305 4286 81326 3984Baboon 56291 3790 82407 3393 81766 4199 82933 3962Peppers 50685 4173 75579 3850 81326 4280 81387 4029

Cover imageLenatiff

(a)

Stego-imageLennatiff

(b)

BaboontiffCover image

(c)

BaboontiffStego-image

(d)

Figure 4 Cover and stego images

in JPG format are converted into gray scale tiff format Thetext files are used as secret data Since the proposed algo-rithm use PVD approach to hide information in waveletcoefficients the data hiding capacity and PSNR values ofthe proposed method are compared with PVD method [1]TPVD [3] method and Gulversquos method [4] The comparisonis shown in Table 1The proposedmethod provides increasedhiding capacity and improved PSNR values as comparedto PVD and TPVD method Although the PSNR is less as

compared to Gulversquos [4] method there is an improvement inthe security of secret data

The average payload of the proposed system is sim248 bppThe performance of the proposed method is analyzed usingPSNR Universal Quality Index (119876) and Structural SimilarityIndex Measure (SSIM) 119876 and SSIM are full reference imagequality assessment models and require the cover image tobe available [16 17] Table 2 shows the PSNR values MSEUniversal Quality Index (119876) and Structural Similarity Index

8 Mathematical Problems in Engineering

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Cover image

Lennatiff

(a)

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Stego image

Lennatiff

(b)

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Cover image

Baboontiff

(c)

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Stego imageBaboontiff

(d)

Figure 5 Histograms of cover and stego images

Measure (SSIM) for different images obtained using proposedmethod The PSNR values are above the threshold of 36 dB[18] even after using more than 95 of the hiding capacity ofthe cover image Also Universal Quality Index (119876) values [16]and Structural Similarity Index Measure (SSIM) values [17]are close to 1 which proves that the stego images are visuallyindistinguishable from original cover images

Figure 4 shows the cover image and the correspondingstego images obtained using the proposed method As thefigures show distortions resulted from embedding are imper-ceptible to human vision

Figure 5 shows the histogramof the cover and stego imageobtained using the proposed method From the figure it canbe observed that the shape of the histogram is preserved

The cover image data is subtracted from stego imageand plotted as histogram Figure 6 shows the pixel differencehistogram From the figure it can be observed that there aremore numbers of bins which are close to 0 as compared to

bins which are away from 0 Also the step pattern is notobserved in the figure This confirms that the method isrobust against histogram analysis attack

Histogram of cover image is represented as [ℎ0 ℎ1

ℎ255] whereas histogram of stego image is represented as

[ℎ1015840

0 ℎ1015840

1 ℎ

1015840

255] The change in histogram [19] is measured

by

119863ℎ=

255

sum

119898=1

10038161003816100381610038161003816ℎ1015840

119898minus ℎ119898

10038161003816100381610038161003816 (20)

The proposed method can hide at least 3 bits in eachpair considering the smallest width of the subrange to be 8Figure 7 shows the comparison of the value of 119863

ℎof the 3

bit LSB replacement method and the proposed method withdifferent size of secret data embedded in the cover imageLenatiff It can be observed that difference in histogram forthe proposed method is less than that of 3 bit LSB method

Mathematical Problems in Engineering 9

0 5 10 15 200

05

1

15

2

25

3

Difference values

Occ

urre

nce f

requ

ency

minus20 minus15 minus10 minus5

times104

Cover imageLennatiff

(a)

0 10 20 300

05

1

15

2

25

3

35

Difference values

Occ

urre

nce f

requ

ency

minus30 minus20 minus10

times104

Cover imageBaboontiff

(b)

Figure 6 Difference histogram

Table 2 Hiding capacity PSNR MSE and 119876 index

Coverimage

Resolution of coverimage

Hidingcapacity(Kb)

ofhidingcapacity

Messagefile size(Kb)

PSNR MSE 119876 SSIM

Baboon 256 times 256 1992 3065 195 3987 6684 0959 0965Lena 256 times 256 1994 3068 195 3991 6633 0899 0937Elaine 512 times 512 7942 309 787 4001 6482 0890 0956Baboon 512 times 512 8099 3068 787 3962 7089 0961 0979Lena 512 times 512 7947 3068 787 3984 6740 0806 0953Tank 512 times 512 7941 309 787 3986 6700 0896 0954Peppers 512 times 512 7948 3022 787 4029 6074 0800 0932Barbara 512 times 512 8035 3055 787 3970 6961 0857 0964Boat 512 times 512 7964 3075 787 3990 6652 0883 0962Grass 1024 times 1024 31932 3115 317 3951 7274 0979 0998

The output images are tested under the 119877119878 steganalysis[20] It is observed from Figure 8 that the difference between119877119872

and 119877minus119872

and 119878119872

and 119878minus119872

is very small The rules 119877119872cong

119877minus119872

and 119878119872cong 119878minus119872

are satisfied for the output images Thisproves that the proposed method is secure against 119877119878 attack

4 Conclusion

In steganography hiding capacity of cover image quality ofstego image and security of secret data are three importantfactors There is always a trade-off between data hidingcapacity of cover image and security of secret data Theproposed algorithm provides improvements in the datahiding capacity as well as security of the secret data ascompared to PVD [1] and TPVD [3] methods AlthoughGulversquos [4] method provides better PSNR values as comparedto proposedmethod the proposedmethod improves security

of secret information The secret information is securelyhidden in the coefficients of integer wavelet transform Forthe implementation purpose the four subbands obtainedafter decomposing the cover image by integer wavelet trans-form are arranged as shown in Figure 1 But it is possible toarrange the four subbands in 4 = 24 different ways therebyimproving the security of the steganography system sincethe exact arrangement of four subbands will be known tosender and receiver only The algorithm revises the originaldifference between two wavelet coefficients in the pair andthis revised difference is used for hiding the data in that pairThis makes estimation of exact number of bits hidden in thepair difficult Image steganography techniques hiding textualinformation require 100 accuracy for successful retrieval ofhidden information from stego image If the steganographymethod fails correct estimation of number of bits hidden forsome of the pairs will be a challenge for the invader Thus

10 Mathematical Problems in Engineering

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

10 20 30 40 50 60 70 80

Hist

ogra

m d

iffer

ence

Size of hidden message (KB)

LSBProposed

Figure 7 Histograms comparison of 3 bit LSB substitution andproposed method (Lenatiff)

0

01

02

03

04

10 20 30 40 50 60 70 79

Ratio

of R

S

Message size (KB)

RM SM

RminusMSminusM

Figure 8 119877119878 diagram

one more level of security is imposed to secure the secretinformation

The PSNR values produced by the algorithm are close to395 which are well above the threshold of 36 dB after usingfull hiding capacity of the cover image This proves that thestego images are of good quality Results also show that thedifference between cover image and stego image cannot benoticed by human visual system (HVS)

Considering the fact that there is currently no steganogra-phy system that can resist all the steganalysis attacks the bestway to provide security to the secret data and to eliminate theattack of comparing the original image with the stego image

is to freshly create an image and destroy it after generating thestego image

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D-CWu andW-H Tsai ldquoA steganographic method for imagesby pixel-value differencingrdquo Pattern Recognition Letters vol 24no 9-10 pp 1613ndash1626 2003

[2] H C Wu N I Wu C S Tsai and M-S Hwang ldquoImagesteganographic scheme based on pixel-value differencing andLSB replacementmethodsrdquo IEE ProceedingsmdashVision Image andSignal Processing vol 152 no 5 pp 611ndash615 2005

[3] K-C Chang P S Huang T-M Tu and C-P Chang ldquoAdaptiveimage steganographic scheme based on tri-way pixel-value dif-ferencingrdquo in Proceedings of the IEEE International Conferenceon Systems Man and Cybernetics (SMC rsquo07) pp 1165ndash1170Montreal Canada October 2007

[4] A K Gulve andM S Joshi ldquoAn image steganography algorithmwith five pixel pair differencing and gray code conversionrdquoInternational Journal of Image Graphics and Signal Processingvol 6 no 3 pp 12ndash20 2014

[5] K-C Chang C-P Chang P S Huang and T-M Tu ldquoA novelimage steganographic method using tri-way pixel-value differ-encingrdquo Journal of Multimedia vol 3 no 2 pp 37ndash44 2008

[6] K C Chang P S Huang T M Tu and C P Chang ldquoImagesteganographic scheme using tri-way pixel-value differencingand adaptive rulesrdquo in Proceedings of the IEEE InternationalConference on Intelligent Information Hiding and MultimediaSignal Processing pp 449ndash452 Kaohsiung Taiwan 2007

[7] A K Gulve and M S Joshi ldquoA secured image steganographyalgorithm with five pixel pair differencing by selecting thecommon pixel randomlyrdquo in Proceedings of the 3rd InternationalConference on Computational Intelligence and Information Tech-nology (CIIT rsquo13) pp 55ndash61 Elseveir Mumbai India 2013

[8] A R Calderbank I Daubechies W Sweldens and B-L YeoldquoWavelet transforms that map integers to integersrdquo Applied andComputational Harmonic Analysis vol 5 no 3 pp 332ndash3691998

[9] B Ramalingam R Amirtharajan and J B B Rayappan ldquoStegoon FPGA an IWT approachrdquoThe Scientific World Journal vol2014 Article ID 192512 9 pages 2014

[10] E Ghasemi J Shanbehzadeh and B ZahirAzami ldquoA stegano-graphic method based on Integer Wavelet Transform andGenetic Algorithmrdquo in Proceedings of the International Confer-ence on Communications and Signal Processing (ICCSP rsquo11) pp42ndash45 Calicut India February 2011

[11] E Ghasemi J Shanbehzadeh and N Fassihi ldquoHigh capacityimage steganography using wavelet transform and geneticalgorithmrdquo in Proceedings of the International Multi Conferenceof Engineers and Computer Scientists (IMECS rsquo11) pp 495ndash498Hong Kong March 2011

[12] G Xuan Y Q Shi C Yang Y Zheng D Zou and P ChaildquoLossless data hiding using integer wavelet transform andthreshold embedding techniquerdquo in Proceedings of the IEEEInternational Conference on Multimedia and Expo (ICME rsquo05)pp 1520ndash1523 IEEE Amsterdam The Netherlands July 2005

Mathematical Problems in Engineering 11

[13] R O El Safy H H Zayed and A El Dessouki ldquoAn adaptivesteganographic technique based on integer wavelet transformrdquoin Proceedings of the International Conference on Networkingand Media Convergence (ICNM rsquo09) pp 111ndash117 Cairo EgyptMarch 2009

[14] S Archana A Judice and K P Kaliyamurthie ldquoA novelapproach on image steganographic methods for optimum hid-ing capacityrdquo International Journal of Engineering and ComputerScience vol 2 no 2 pp 378ndash385 2013

[15] A K Al-Asmari M A Al-Qodah and A S Salama ldquoWavelet-pixel value differencing technique for digital images data hid-ingrdquo in Proceedings of the IEEE International Conference onSystem Engineering and Technology (ICSET rsquo11) pp 15ndash18 June2011

[16] Z Wang and A C Bovik ldquoA universal image quality indexrdquoIEEE Signal Processing Letters vol 9 no 3 pp 81ndash84 2002

[17] ZWang A C Bovik H R Sheikh and E P Simoncelli ldquoImagequality assessment from error visibility to structural similarityrdquoIEEE Transactions on Image Processing vol 13 no 4 pp 600ndash612 2004

[18] N I Wu andM S Hwang ldquoData hiding current status and keyissuesrdquo International Journal of Network Security vol 4 no 1pp 1ndash9 2007

[19] X Zhang and S Wang ldquoEfficient data hiding with histogram-preserving propertyrdquo Telecommunication Systems vol 49 no 2pp 179ndash185 2012

[20] J FridrichMGoljan andRDu ldquoDetecting LSB steganographyin color and gray-scale imagesrdquo IEEEMultimediaMagazine vol8 no 4 pp 22ndash28 2001

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Discrete Dynamics in Nature and Society

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Page 2: Research Article An Image Steganography Method Hiding ...downloads.hindawi.com/journals/mpe/2015/684824.pdf · An Image Steganography Method Hiding Secret Data into Coefficients of

2 Mathematical Problems in Engineering

the number of bits 119905119894(where 119905

119894= log2119882119896) of secret message

that can be hidden using the difference of two consecutivepixels After hiding 119905

119894bits using the difference 119889

119894 new values

are assigned to119875119894and 119875119894+1

The new difference 1198891015840119894is calculated

by subtracting 119875119894from 119875

119894+1 The new difference 1198891015840

119894stands for

the secret data hidden in the pair During extraction the stegoimage is partitioned into nonoverlapping blocks composedwith two consecutive pixels 119875

119894and 119875

119894+1 Then the difference

value 1198891015840119894for each pair of two consecutive pixels 119875

119894and 119875

119894+1is

calculated Next |1198891015840119894| is used to locate the suitable range 119877

119896

The decimal equivalent of the secret information hidden inthe block is given by |1198891015840

119894| minus 119897119896which is then transformed into

a binary sequence with 119905119894bits

In order to improve the capacity of hiding secret dataand to provide an imperceptible stego image quality a novelsteganographic method based on least-significant-bit (LSB)replacement and pixel-value differencing (PVD) method ispresented by Wu et al [2] The range table is divided intolower level (smooth area) and higher level (edged area) Inthe smooth area 6 bits of the secret data is hidden by LSBmethod while in the higher level secret data is hidden usingthe PVD method

To improve the hiding capacity of the cover image andquality of the stego image another enhanced method isintroduced based on the PVDmethod byChang et al [3 5 6]In this method data is hidden in vertical and diagonal edgesalong with the horizontal edges The cover image is dividedinto the blocks of 2 times 2 pixels Considering 119909 and 119910 to be thepixel locations each 2 times 2 block includes four pixels 119875

(119909119910)

119875(119909+1119910)

119875(119909119910+1)

and 119875(119909+1119910+1)

Pixel 119875(119909119910)

is grouped withthe remaining three pixels in the block to form three pixelpairs These three pairs are named 119875119875

0 1198751198751 and 119875119875

2where

1198751198750= (119875(119909119910) 119875(119909+1119910)) 1198751198751= (119875(119909119910) 119875(119909119910+1)) and 119875119875

2=

(119875(119909119910) 119875(119909+1119910+1)

) respectively After embedding the secretinformation in each pair using PVD approach values of twopixels in each pair get modified Thus the original differencevalue 119889

119894is modified to a new difference value 1198891015840

119894 The new

pixel values in each pair are different from their original onesThat is three different values are obtained for the pixel 119875

(119909119910)

However pixel 119875(119909119910)

can have only one value Thereforeone of the 1198751198751015840

119894is selected as the reference pair to offset the

remaining two pixel values That is two pixel values of thereference pair are used to adjust the pixel values of othertwo pairs and construct a new 2 times 2 block The embeddedsecret data is unaffected because new difference values 1198891015840

119894

are unaltered During extraction the difference value 1198891015840119894is

used to extract the hidden information |1198891015840119894| is used to locate

the suitable range 119877119896 The decimal equivalent of the secret

information hidden in the pair is given by |1198891015840119894| minus 119897119896which is

then transformed into a binary sequence with 119905119894bits

Gulve and Joshi [4] have proposed a steganographymethod to improve the security of the secret informationusing five-pixel pair differencing approachThe cover image ispartitioned into blocks of 2 times 3 pixels to form five pixel pairsThe secret data is embedded in the pairs using the differencevalue of pixels in that pair Instead of hiding 119872 bits in thepair using the difference value bits le 119873 are hidden in thepair where119873 is the average of bits that can be hidden in each

pair of the blockThus in case of failure of the steganographysystem it becomes difficult to estimate exact number of bitshidden in each pair of the block Another level of securityfor the secret information is introduced by converting thesecret information in its gray code form For each pair in theblock the method converts bits of secret information in thegray code form and then embeds these bits in that pair Thusthe security of the secret information is improved withoutinvolving the overhead of encryption and decryption Gulveand Joshi [7] have proposed a steganography method toimprove the security of the secret data embedded in theimage The cover image is divided in the blocks of 2 times 3pixels to form five pairs The location of the common pixel isdecided using the image data For this reason data of last fewrows are used Since the common pixel is changed randomlybased on the image data it is difficult to extract the secret datafrom stego image even if the steganography method fails

Integer wavelet transform maps an integer data set intoanother integer data set Calderbank et al [8] have explainedthe working of integer wavelet transform Haar wavelettransform in its unnormalized version involving pair wiseaverages and differences is written as

1198781119899=11987802119899+ 11987802119899+1

21198891119899= 11987802119899+1minus 11987802119899 (1)

Its inverse is given by

11987802119899= 1198781119899+1198891119899

211987802119899+1= 1198781119899minus1198891119899

2 (2)

Because of division by two this is not integer transformThe integer version can be built by omitting division by twoin 1198781119899

and calculating the sum instead of the average This iscalled 119878 transform [8] Consider the following example

1198781119899= lfloor(11987802119899+ 11987802119899+1)

2rfloor 119889

1119899= 11987802119899+1minus 11987802119899 (3)

It is possible to define 1198781119899

as above because the sum anddifference of two integers are either even or odd Thus it issafe to omit last bit of sum since it is similar to last bit ofdifference The 119878 transform [8] is invertible and it is given by

11987802119899= 1198781119899minus lfloor1198891119899

2rfloor 119878

02119899+1= 1198781119899+ lfloor(1198891119899+ 1)

2rfloor

(4)A different way of writing Haar transform using ldquoliftingrdquo

steps leads to natural generalizations It is possible to writeHaar and 119878 transform using lifting schemes [8]

First compute the difference and then use the differencein second step to compute the average

1198891119899= 11987802119899+1minus 11987802119899

1198781119899= 11987802119899+1198891119899

2 (5)

The inverse transform can be calculated in two stepsFirst recover the even samples from the average and differ-ence and recover the odd samples from even and difference[8] It is given by the following equations

11987802119899= 1198781119899minus1198891119899

211987802119899+1= 1198891119899+ 11987802119899 (6)

Mathematical Problems in Engineering 3

It is possible to write integer transform by truncating thedivision

1198891119899= 11987802119899+1minus 11987802119899

1198781119899= 11987802119899+ lfloor1198891119899

2rfloor (7)

Lifting can be used to compute the inverse transformTheequations follow from reversing the order and changing thesign of the forward transform [8]

11987802119899= 1198781119899minus lfloor1198891119899

2rfloor 119878

02119899+1= 1198891119899+ 11987802119899 (8)

Ramalingam et al [9] have elaborated the process ofseparating four subbands using Haar IWT The first stageIWT is given by

H = 119862119900minus 119862119890

L = 119862119890+ lfloor

H2rfloor

(9)

where 119862119900represents pixels in odd column and 119862

119890represents

pixels in even column In the next stage the IWT coefficientsare calculated using high pass and low pass filter banks Thisprocess creates four subbands low-low (LL) low-high (LH)high-low (HL) and high-high (HH) The second stage IWTis given by

LH = Lodd minus Leven

LL = Leven + [LH2]

HH = Hodd minusHeven

HH = Heven + [HL2]

(10)

where Hodd represents H bandrsquos odd row Lodd represents Lbandrsquos odd row Heven represents H bandrsquos even row and Levenrepresents L bandrsquos even row [9]

Ghasemi et al [10 11] have proposed a novel steganogra-phy scheme based on integer wavelet transform and geneticalgorithm The scheme embeds data in integer wavelettransform coefficients by using a mapping function basedon genetic algorithm The methods use wavelet transformcoefficients to embed secret data into the four subbandsof two-dimensional wavelet transform Genetic algorithm isused to find themapping functionA chromosome is encodedas an array of 64 genes containing permutations 1 to 64that point to pixel numbers in each block OPAP is used tominimize the error between cover and stego image

Xuan et al [12] have suggested a lossless data hidingmethod for digital images using integer wavelet transformand threshold embedding technique CDF (22) integerwavelet transform is used to obtain the wavelet coefficientsHistogrammodification is applied to prevent possible under-flowoverflow of pixel values A predefined threshold value 119879is used to embed data in the wavelet coefficients

El Safy et al [13] have suggested an adaptive stegano-graphic model which combines adaptive hiding capacity

function that hides secret data in the integer wavelet coef-ficients of the cover image with the optimum pixel adjust-ment (OPA) algorithm Histogram modification is appliedto prevent possible underflowoverflow of pixel values Thecover image is divided into 8 times 8 nonoverlapping blocksEach block is transformed using 2D Haar integer wavelettransform to obtain four subbands LLI LHI HLI andHHI Hiding capacity of each coefficient is determined andthe data is embedded in the coefficients A pseudorandomnumber generation function is used to select the waveletcoefficients for increasing the security of the hidden dataTheOPAalgorithm is applied after embedding secretmessageto minimize the embedding error The extraction procedureis a blind process since it requires only the secret key fromthe receiver The secret key is used to identify the waveletcoefficients Secret message bits are extracted from eachselected wavelet coefficient

Archana et al [14] have proposed a method for hidingsecret information in the discrete wavelet transform coeffi-cients using GA and OPAP algorithm to provide optimumhiding capacity The four subbands LL HL LH and HH areused for hiding the data Hiding capacity function ismodifiedby using different ranges for k for the LH HL and HHsubbands where its values range from 1 to 4 The length L ofmessage bits to be hidden in wavelet coefficient is determinedby using hiding capacity function

Al-Asmari et al [15] have proposed a method using dis-crete wavelet transform and pixel value differencing approachto hide the information Using the discrete wavelet transformthe cover image is decomposed to obtain the four subbands(LL HL LH and HH) Then the LSB method is used tohide secret information in the LL subband by hiding two bitsof secret information in each coefficient The PVD approachis used to hide the information in the remaining threesubbands For hiding the information two consecutive pixelsin the vertical direction are grouped to form a pair Themethod gives high performance in terms of capacity humanvisual quality and PSNR

2 Proposed Method

The proposed method hides secret information in the grayscale images It uses spatial domain technique to hide secretinformation in the frequency domain In the frequencydomain the image is decomposed into four subbands usinginteger wavelet transform and then the spatial domaintechnique is used to hide secret information in the waveletcoefficients of the four subbands

The cover image is transformed using 2D Haar integerwavelet transform to obtain four subbands LL LH HL andHHThe proposed method embeds data in the coefficients offour subbands by using the pixel value differencing approach

21 Preprocessing The gray scale image is read as a 2D arrayof size [119872119873] Histogram modification [12ndash15] is applied toprevent the possible overflowunderflow of pixel values Thisproblem occurs when the pixel values of the cover image areclose to 255 or 0 because they may exceed 255 or fall below 0

4 Mathematical Problems in Engineering

LL HL

LH HH

Figure 1 Arrangements of wavelet coefficients

Figure 2 The image lenatiff after performing Harr transform

during inverse integer wavelet transformThe problem can besolved by mapping the lowest 15 gray scale levels to the value15 and the highest 15 gray scale levels to the value 240 If thepixel values exceed the boundaries during the inverse wavelettransform the image is not suitable for hiding secret dataThe image is transformed using 2D Haar wavelet transformto obtain four subbands LL LH HL and HH of size [11987221198732] each All the four subbands are used to hide the secretinformationThe 2D array of size [119872119873] is again constructedby arranging the four subbands as shown in Figure 1

Figure 2 shows the arrangement of four subbands of theimage lenatiff after transforming it using 2D Harr integerwavelet transform

A 2D array obtained by arranging the wavelet coefficientsof four subbands is shown as follows

(

112 230 150 sdot sdot sdot minus45 minus120 80

130 159 172 sdot sdot sdot minus37 minus89 minus72

sdot sdot sdot sdot sdot sdot sdot sdot sdot

sdot sdot sdot sdot sdot sdot sdot sdot sdot

minus30 minus59 minus72 sdot sdot sdot minus37 minus89 minus72

) (11)

The difference operation in Haar transform may cause someof the wavelet coefficients in HL LH and HH subbands tohave negative values

Since some of the wavelet coefficients have negativevalues the 2D array shown in (11) cannot be used for hid-ing secret information using the pixel value differencingapproach Hence absolute values are used for the coefficient

with negative values to create a new 2D array with positiveelements as follows

(

112 230 150 sdot sdot sdot 45 120 80

130 159 172 sdot sdot sdot 37 89 72

sdot sdot sdot sdot sdot sdot sdot sdot sdot

sdot sdot sdot sdot sdot sdot sdot sdot sdot

30 59 72 sdot sdot sdot 37 89 72

) (12)

After hiding the secret information in the 2D array shownin (12) inverse wavelet transform is performed to obtainthe stego image To obtain good quality of stego image theoriginal sign of each wavelet coefficient as shown in (11) isrequired Hence the 2D array shown in (11) is used to createa sign matrix of the size [119872119873] having elements with values1 or minus1 The sign matrix so created is shown as follows

(

1 1 1 sdot sdot sdot minus1 minus1 1

1 1 1 sdot sdot sdot minus1 minus1 minus1

sdot sdot sdot sdot sdot sdot sdot sdot sdot

sdot sdot sdot sdot sdot sdot sdot sdot sdot

minus1 minus1 minus1 sdot sdot sdot minus1 minus1 minus1

) (13)

The wavelet coefficients having positive values are repre-sented by 1 whereas wavelet coefficients having negativevalues are represented by minus1 in the sign matrix

22 Embedding Process For hiding the data in the 2D arraythe method suggested by Gulve [4 7] is used In the methodproposed byChang [3] a block of 2times 2 pixels is used to form 3pairs which are then used to hide the secret informationTheproposed method uses the block of 2 times 3 wavelet coefficientsThe introduction of 2 wavelet coefficients in the 2 times 2 blockforms two extra pairs For a 512 times 512 image it is possible toform 196608 pairs using the approach suggested by Chang [3]whereas using the proposed approach 217600 pairs can beformed A greater number of pairs provide extra space forhiding the secret information Thus the proposed methodimproves the hiding capacity of the cover image

Thedifference between twowavelet coefficients in the pairis used to hide the secret information If the difference valueis directly used to hide the information it is easy to retrievethe embedded information in case the steganography systemfails To enhance the security of the secret information theproposed algorithm modifies the difference between the twowavelet coefficients in the pair and this modified differenceis used to hide the secret information This imposes extralayer of security making harder extraction of original secretinformation from stego image using the difference valuesdirectly [4 7]

The arrangement of wavelet coefficients into nonover-lapping blocks of 2 times 3 wavelet coefficients is shown inFigure 3 As shown in Figure 3 each 2 times 3 block includes sixwavelet coefficients 119875

(119909119910) 119875(119909119910+1)

119875(119909119910+2)

119875(119909+1119910)

119875(119909+1119910+1)

and 119875

(119909+1119910+2) where 119909 and 119910 are the locations of wavelet

coefficients Five pairs are formed by grouping the commonwavelet coefficient PX

1with the remaining five wavelet

Mathematical Problems in Engineering 5

PX0

PX3

PX1

PX4

PX2

PX5

P(xy) P(xy+1)P(xy+2)

P(x+1y) P(x+1y+1) P(x+1y+2)

Figure 3 Pixel block

coefficients PX0 PX2 PX3 PX4 and PX

5 The five pairs 119875119875

119894

where 119894 = 0 1 2 3 4 are as shown below

1198751198750= (119875(119909119910+1) 119875(119909119910))

1198751198751= (119875(119909119910+1) 119875(119909119910+2))

1198751198752= (119875(119909119910+1) 119875(119909+1119910))

1198751198753= (119875(119909119910+1) 119875(119909+1119910+1)

)

1198751198754= (119875(119909119910+1) 119875(119909+1119910+2)

)

(14)

The difference value 119889119894is calculated for each pair 119875119875

119894by

subtracting the common wavelet coefficient PX1from the

other wavelet coefficient in that pair This difference value isused to identify the corresponding range 119877

119896119894from the range

table119877The range table is designed with ranges [0ndash7] [8ndash15][16ndash31] [32ndash63] [64ndash127] and [128ndash255] The width 119882

119896119894

of range 119877119896119894

is used to determine the number of bits 119905119894(119905119894=

log2119882119896119894) that can be hidden in each pair where 119894 = 0 1 2 3 4

This 119905119894is then used to calculate the average value (119873) of

number of bits possible to be hidden in each pair of the blockThe average value119873 is used to calculate the revised difference119877119889119894as 119877119889119894is remainder (119889

1198942119873) so that 119877119889

119894le 2119873 where 119889

119894is

the original differenceThe offset difference OD119894is calculated

as |119889119894|minus |119877119889

119894| for each pair in the blockThe revised difference

|119877119889119894| is then used to determine the number of bits 119905

119894for each

pair in the block Thus if the original difference value |119889119894|

allows 119872 bits to be hidden in the pair then the proposedapproach hides bits le 119873 in that pair [4 7]

After embedding 119905119894bits of the message in the pair new

difference 1198891015840119894is calculated as OD

119894+119897119896119894+119887where 119897

119896119894represents

lower boundary of the range 119877119896119894

in the range table 119877 and 119887represents the decimal equivalent of 119905

119894message bits hidden in

that pairEmbedding 119905

119894bits in the pair modifies the values of

both the wavelet coefficients in the pair The new valuesof wavelet coefficients in each pair are different from theiroriginal values Since new value is assigned to commonwavelet coefficient PX

1in each pair five different values are

obtained for the common wavelet coefficient PX1 However

the common wavelet coefficient PX1can have only one value

in each bock This requires values of other five waveletcoefficients PX

0 PX2 PX3 PX4 and PX

5to be adjusted such

that the new difference 1198891015840119894remains unchanged Therefore

the pair having new values of wavelet coefficients close totheir original values is selected as the reference pair To find

the reference pair the difference 119898 between 119889119894and 1198891015840

119894is

calculated Small value of |119898| indicates that the newdifferencevalue 1198891015840

119894is close to the original difference value 119889

119894 Thus

for the pair with minimum |119898| the new values of waveletcoefficients are close to their original values So the pair withminimum |119898| is selected as the reference pair The values ofthe two wavelet coefficients in the reference pair are used toadjust the values of wavelet coefficients in other pairs andconstruct a new 2times3 blockThe embedded secret informationin newly constructed block is unaffected because differencevalues for the pairs are unaltered [4 7]

During the extraction process average value (119873) iscalculated using the same process adopted during embeddingof the secret messageThe average value119873 is used to calculatethe revised difference 1198771198891015840

119894as 1198771198891015840

119894is remainder (119889

1198942119873) Suit-

able range 119877119896119894 is identified using this revised difference Thesecretmessage is extracted in the decimal formby subtracting119897119896from |1198771198891015840

119894| Secret message is then converted into a binary

stream with 119905119894(119905119894= log2119882119896119894) bits [4 7]

The process of hiding secret information in the coverimage is described below [4 7]

(1) Create the 2D array as shown in (12) by preprocessingthe gray scale cover image

(2) Partition the array into nonoverlapping blocks of 2times3wavelet coefficients and group wavelet coefficient PX

1

with the remaining wavelet coefficients in the block toform five pairs

(3) Calculate the difference values 119889119894for the five pairs in

each block

1198890= 119875(119909119910)minus 119875(119909119910+1)

1198891= 119875(119909119910+2)minus 119875(119909119910+1)

1198892= 119875(119909+1119910)minus 119875(119909119910+1)

1198893= 119875(119909+1119910+1)

minus 119875(119909119910+1)

1198894= 119875(119909+1119910+2)

minus 119875(119909119910+1)

(15)

(4) Use |119889119894| where 119894 = 0 1 2 3 4 to locate suitable range

119877119896in the designed range table Use this range to

calculate number of bits 119905119894that can be hidden in each

pair 119875119875119894 Then calculate the average bits using

avg = lfloor(sum4

119894=0119905119894

5)rfloor (16)

(5) Calculate the revised difference |119877119889119894| where 119894 =

0 1 2 3 4 as119877119889119894is remainder (119889

1198942avg) so that119877119889

119894lt=

2avg

(6) Calculate the difference OD119894as OD

119894= |119889119894| minus |119877119889

119894| for

each pair

(7) Use |119877119889119894|where 119894 = 0 1 2 3 4 to locate suitable range

119877119896in the designed range table

6 Mathematical Problems in Engineering

(8) Compute the number of bits 119905119894that can be embedded

in each pair using the corresponding range given by119877119896 The value 119905

119894can be estimated from the width 119908

119896

of 119877119896 which is given by 119905

119894= log2119908119896where width119908

119896=

119906119896minus119897119896+1 and119906

119896and 119897119896are upper and lower boundaries

of the range 119877119896

(9) Read 119905119894bits from the binary secret data

(10) Calculate the new difference value 1198891015840119894given by

1198891015840

119894= OD

119894+ 119897119896119894+ 119887119894 if 119889

119894ge 0

1198891015840

119894= minus (OD

119894+ 119897119896119894+ 119887119894) if 119889

119894lt 0

(17)

(11) Modify the values of wavelet coefficients in the pair119875119875119894using

(1198751015840

119899 1198751015840

119899+1) = (119875

119899minus lceil119898

2rceil 119875119899+1+ lfloor119898

2rfloor) (18)

where 119875119899and 119875

119899+1represent two wavelet coefficients

in the pair 119875119875119894and 119898 is obtained by subtracting 119889

119894

from 1198891015840119894

(12) Select the pair with minimum |119898| as the optimalreference pair and use this pair to adjust the values ofwavelet coefficients of the other four pairs The valueof the common wavelet coefficient is given by 1198751015840

119899of

the reference pair Modify value of another waveletcoefficient 1198751015840

119899+1of remaining four pairs such that

the new difference 1198891015840119894will remain unchanged Thus

new values are assigned to remaining four waveletcoefficients in the block

(13) Check the new values of wavelet coefficients for fall-off boundaries that is check whether all the valuesare within the range from 0 to 255 If not modify thevalues preserving the difference between the values oftwo wavelet coefficients of each pair in the block

(a) Find out the smallest of all the wavelet coeffi-cients If the smallest is less than 0 then add|smallest| in all the wavelet coefficients in thatblock

(b) Find out the largest of all the wavelet coeffi-cients If the largest is greater than 255 subtractlargest minus 255 from all the wavelet coefficients inthat block

(c) If fall-off boundary problems still exist thecover image is not suitable for hiding secretinformation

(14) Now reconstruct the block from all pairs with modi-fied values of wavelet coefficients

(15) Repeat steps (2) through (14) until the secret informa-tion is embedded in the cover image

23 Postprocessing After the embedding process is overoriginal signs are assigned to the elements of 2D array usingthe sign matrix created during preprocessing phase This is

accomplished by one to one comparison of elements of 2Darray with the elements of 2D sign matrix The 2D array isthen split to obtain the four subbands Using inverse 2DHaarinteger wavelet transform the four subbands are combined toobtain the stego image of size [119872119873] All the pixel values ofthe stego image in the range from 0 to 255 indicate that secretdata is safely hidden and can be extracted accurately

24 Extraction Process The extraction process is blind Itdoes not require the existence of cover image for extractinghidden secret data from the stego image The stego image ispreprocessed to obtain the 2D array as shown in (12) Theprocess of extraction of secret information from the stegoimage is described below [4 7]

(1) Create the 2D array as shown in (12) by preprocessingthe gray scale stego image

(2) Partition the array into nonoverlapping blocks of 2times 3wavelet coefficients and group wavelet coefficient PX

1

with the remaining wavelet coefficients in the block toform five pairs Keep the partition order the same asthat of the embedding

(3) Calculate the difference values 119889119894for the five pairs in

each block

1198890= 119875(119909119910)minus 119875(119909119910+1)

1198891= 119875(119909119910+2)minus 119875(119909119910+1)

1198892= 119875(119909+1119910)minus 119875(119909119910+1)

1198893= 119875(119909+1119910+1)

minus 119875(119909119910+1)

1198894= 119875(119909+1119910+2)

minus 119875(119909119910+1)

(19)

(4) Use |119889119894| where 119894 = 0 1 2 3 4 to locate suitable range

119877119896in the designed range table Use this range to

calculate number of bits 119905119894 which is hidden in each

pair 119875119875119894 Then calculate the average bits using (16)

(5) Calculate revised difference |1198771198891015840

119894| where

119894 = 0 1 2 3 4 as 1198771198891015840119894is remainder (119889

1198942avg)

(6) Use |1198771198891015840119894| where 119894 = 0 1 2 3 4 to locate suitable 119877

119896in

the designed range table(7) After 119877

119896is located 119897

119896is subtracted from |1198771198891015840

119894| and

1198871015840

119894is obtained in decimal form A binary sequence is

generated from 1198871015840119894with 119905

119894bits where 119905

119894= log2119908119896

Repeat steps (2) through (7) until embedded message isextracted

3 Results

A set of gray scale TIFF images is used for the experimenta-tion This set consists of standard images as well as imagestaken from the camera The standard images are obtainedfrom the ldquothe USC-SIPI image database (httpsipiuscedudatabase)rdquo The images taken from Canon A45 camera

Mathematical Problems in Engineering 7

Table 1 Comparison of hiding capacity (in bytes)

Cover image PVD method [1] TPVD method [3] Gulversquos method [4] Proposed methodCapacity PSNR Capacity PSNR Capacity PSNR Capacity PSNR

Lena 50960 4179 75836 3889 81305 4286 81326 3984Baboon 56291 3790 82407 3393 81766 4199 82933 3962Peppers 50685 4173 75579 3850 81326 4280 81387 4029

Cover imageLenatiff

(a)

Stego-imageLennatiff

(b)

BaboontiffCover image

(c)

BaboontiffStego-image

(d)

Figure 4 Cover and stego images

in JPG format are converted into gray scale tiff format Thetext files are used as secret data Since the proposed algo-rithm use PVD approach to hide information in waveletcoefficients the data hiding capacity and PSNR values ofthe proposed method are compared with PVD method [1]TPVD [3] method and Gulversquos method [4] The comparisonis shown in Table 1The proposedmethod provides increasedhiding capacity and improved PSNR values as comparedto PVD and TPVD method Although the PSNR is less as

compared to Gulversquos [4] method there is an improvement inthe security of secret data

The average payload of the proposed system is sim248 bppThe performance of the proposed method is analyzed usingPSNR Universal Quality Index (119876) and Structural SimilarityIndex Measure (SSIM) 119876 and SSIM are full reference imagequality assessment models and require the cover image tobe available [16 17] Table 2 shows the PSNR values MSEUniversal Quality Index (119876) and Structural Similarity Index

8 Mathematical Problems in Engineering

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Cover image

Lennatiff

(a)

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Stego image

Lennatiff

(b)

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Cover image

Baboontiff

(c)

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Stego imageBaboontiff

(d)

Figure 5 Histograms of cover and stego images

Measure (SSIM) for different images obtained using proposedmethod The PSNR values are above the threshold of 36 dB[18] even after using more than 95 of the hiding capacity ofthe cover image Also Universal Quality Index (119876) values [16]and Structural Similarity Index Measure (SSIM) values [17]are close to 1 which proves that the stego images are visuallyindistinguishable from original cover images

Figure 4 shows the cover image and the correspondingstego images obtained using the proposed method As thefigures show distortions resulted from embedding are imper-ceptible to human vision

Figure 5 shows the histogramof the cover and stego imageobtained using the proposed method From the figure it canbe observed that the shape of the histogram is preserved

The cover image data is subtracted from stego imageand plotted as histogram Figure 6 shows the pixel differencehistogram From the figure it can be observed that there aremore numbers of bins which are close to 0 as compared to

bins which are away from 0 Also the step pattern is notobserved in the figure This confirms that the method isrobust against histogram analysis attack

Histogram of cover image is represented as [ℎ0 ℎ1

ℎ255] whereas histogram of stego image is represented as

[ℎ1015840

0 ℎ1015840

1 ℎ

1015840

255] The change in histogram [19] is measured

by

119863ℎ=

255

sum

119898=1

10038161003816100381610038161003816ℎ1015840

119898minus ℎ119898

10038161003816100381610038161003816 (20)

The proposed method can hide at least 3 bits in eachpair considering the smallest width of the subrange to be 8Figure 7 shows the comparison of the value of 119863

ℎof the 3

bit LSB replacement method and the proposed method withdifferent size of secret data embedded in the cover imageLenatiff It can be observed that difference in histogram forthe proposed method is less than that of 3 bit LSB method

Mathematical Problems in Engineering 9

0 5 10 15 200

05

1

15

2

25

3

Difference values

Occ

urre

nce f

requ

ency

minus20 minus15 minus10 minus5

times104

Cover imageLennatiff

(a)

0 10 20 300

05

1

15

2

25

3

35

Difference values

Occ

urre

nce f

requ

ency

minus30 minus20 minus10

times104

Cover imageBaboontiff

(b)

Figure 6 Difference histogram

Table 2 Hiding capacity PSNR MSE and 119876 index

Coverimage

Resolution of coverimage

Hidingcapacity(Kb)

ofhidingcapacity

Messagefile size(Kb)

PSNR MSE 119876 SSIM

Baboon 256 times 256 1992 3065 195 3987 6684 0959 0965Lena 256 times 256 1994 3068 195 3991 6633 0899 0937Elaine 512 times 512 7942 309 787 4001 6482 0890 0956Baboon 512 times 512 8099 3068 787 3962 7089 0961 0979Lena 512 times 512 7947 3068 787 3984 6740 0806 0953Tank 512 times 512 7941 309 787 3986 6700 0896 0954Peppers 512 times 512 7948 3022 787 4029 6074 0800 0932Barbara 512 times 512 8035 3055 787 3970 6961 0857 0964Boat 512 times 512 7964 3075 787 3990 6652 0883 0962Grass 1024 times 1024 31932 3115 317 3951 7274 0979 0998

The output images are tested under the 119877119878 steganalysis[20] It is observed from Figure 8 that the difference between119877119872

and 119877minus119872

and 119878119872

and 119878minus119872

is very small The rules 119877119872cong

119877minus119872

and 119878119872cong 119878minus119872

are satisfied for the output images Thisproves that the proposed method is secure against 119877119878 attack

4 Conclusion

In steganography hiding capacity of cover image quality ofstego image and security of secret data are three importantfactors There is always a trade-off between data hidingcapacity of cover image and security of secret data Theproposed algorithm provides improvements in the datahiding capacity as well as security of the secret data ascompared to PVD [1] and TPVD [3] methods AlthoughGulversquos [4] method provides better PSNR values as comparedto proposedmethod the proposedmethod improves security

of secret information The secret information is securelyhidden in the coefficients of integer wavelet transform Forthe implementation purpose the four subbands obtainedafter decomposing the cover image by integer wavelet trans-form are arranged as shown in Figure 1 But it is possible toarrange the four subbands in 4 = 24 different ways therebyimproving the security of the steganography system sincethe exact arrangement of four subbands will be known tosender and receiver only The algorithm revises the originaldifference between two wavelet coefficients in the pair andthis revised difference is used for hiding the data in that pairThis makes estimation of exact number of bits hidden in thepair difficult Image steganography techniques hiding textualinformation require 100 accuracy for successful retrieval ofhidden information from stego image If the steganographymethod fails correct estimation of number of bits hidden forsome of the pairs will be a challenge for the invader Thus

10 Mathematical Problems in Engineering

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

10 20 30 40 50 60 70 80

Hist

ogra

m d

iffer

ence

Size of hidden message (KB)

LSBProposed

Figure 7 Histograms comparison of 3 bit LSB substitution andproposed method (Lenatiff)

0

01

02

03

04

10 20 30 40 50 60 70 79

Ratio

of R

S

Message size (KB)

RM SM

RminusMSminusM

Figure 8 119877119878 diagram

one more level of security is imposed to secure the secretinformation

The PSNR values produced by the algorithm are close to395 which are well above the threshold of 36 dB after usingfull hiding capacity of the cover image This proves that thestego images are of good quality Results also show that thedifference between cover image and stego image cannot benoticed by human visual system (HVS)

Considering the fact that there is currently no steganogra-phy system that can resist all the steganalysis attacks the bestway to provide security to the secret data and to eliminate theattack of comparing the original image with the stego image

is to freshly create an image and destroy it after generating thestego image

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D-CWu andW-H Tsai ldquoA steganographic method for imagesby pixel-value differencingrdquo Pattern Recognition Letters vol 24no 9-10 pp 1613ndash1626 2003

[2] H C Wu N I Wu C S Tsai and M-S Hwang ldquoImagesteganographic scheme based on pixel-value differencing andLSB replacementmethodsrdquo IEE ProceedingsmdashVision Image andSignal Processing vol 152 no 5 pp 611ndash615 2005

[3] K-C Chang P S Huang T-M Tu and C-P Chang ldquoAdaptiveimage steganographic scheme based on tri-way pixel-value dif-ferencingrdquo in Proceedings of the IEEE International Conferenceon Systems Man and Cybernetics (SMC rsquo07) pp 1165ndash1170Montreal Canada October 2007

[4] A K Gulve andM S Joshi ldquoAn image steganography algorithmwith five pixel pair differencing and gray code conversionrdquoInternational Journal of Image Graphics and Signal Processingvol 6 no 3 pp 12ndash20 2014

[5] K-C Chang C-P Chang P S Huang and T-M Tu ldquoA novelimage steganographic method using tri-way pixel-value differ-encingrdquo Journal of Multimedia vol 3 no 2 pp 37ndash44 2008

[6] K C Chang P S Huang T M Tu and C P Chang ldquoImagesteganographic scheme using tri-way pixel-value differencingand adaptive rulesrdquo in Proceedings of the IEEE InternationalConference on Intelligent Information Hiding and MultimediaSignal Processing pp 449ndash452 Kaohsiung Taiwan 2007

[7] A K Gulve and M S Joshi ldquoA secured image steganographyalgorithm with five pixel pair differencing by selecting thecommon pixel randomlyrdquo in Proceedings of the 3rd InternationalConference on Computational Intelligence and Information Tech-nology (CIIT rsquo13) pp 55ndash61 Elseveir Mumbai India 2013

[8] A R Calderbank I Daubechies W Sweldens and B-L YeoldquoWavelet transforms that map integers to integersrdquo Applied andComputational Harmonic Analysis vol 5 no 3 pp 332ndash3691998

[9] B Ramalingam R Amirtharajan and J B B Rayappan ldquoStegoon FPGA an IWT approachrdquoThe Scientific World Journal vol2014 Article ID 192512 9 pages 2014

[10] E Ghasemi J Shanbehzadeh and B ZahirAzami ldquoA stegano-graphic method based on Integer Wavelet Transform andGenetic Algorithmrdquo in Proceedings of the International Confer-ence on Communications and Signal Processing (ICCSP rsquo11) pp42ndash45 Calicut India February 2011

[11] E Ghasemi J Shanbehzadeh and N Fassihi ldquoHigh capacityimage steganography using wavelet transform and geneticalgorithmrdquo in Proceedings of the International Multi Conferenceof Engineers and Computer Scientists (IMECS rsquo11) pp 495ndash498Hong Kong March 2011

[12] G Xuan Y Q Shi C Yang Y Zheng D Zou and P ChaildquoLossless data hiding using integer wavelet transform andthreshold embedding techniquerdquo in Proceedings of the IEEEInternational Conference on Multimedia and Expo (ICME rsquo05)pp 1520ndash1523 IEEE Amsterdam The Netherlands July 2005

Mathematical Problems in Engineering 11

[13] R O El Safy H H Zayed and A El Dessouki ldquoAn adaptivesteganographic technique based on integer wavelet transformrdquoin Proceedings of the International Conference on Networkingand Media Convergence (ICNM rsquo09) pp 111ndash117 Cairo EgyptMarch 2009

[14] S Archana A Judice and K P Kaliyamurthie ldquoA novelapproach on image steganographic methods for optimum hid-ing capacityrdquo International Journal of Engineering and ComputerScience vol 2 no 2 pp 378ndash385 2013

[15] A K Al-Asmari M A Al-Qodah and A S Salama ldquoWavelet-pixel value differencing technique for digital images data hid-ingrdquo in Proceedings of the IEEE International Conference onSystem Engineering and Technology (ICSET rsquo11) pp 15ndash18 June2011

[16] Z Wang and A C Bovik ldquoA universal image quality indexrdquoIEEE Signal Processing Letters vol 9 no 3 pp 81ndash84 2002

[17] ZWang A C Bovik H R Sheikh and E P Simoncelli ldquoImagequality assessment from error visibility to structural similarityrdquoIEEE Transactions on Image Processing vol 13 no 4 pp 600ndash612 2004

[18] N I Wu andM S Hwang ldquoData hiding current status and keyissuesrdquo International Journal of Network Security vol 4 no 1pp 1ndash9 2007

[19] X Zhang and S Wang ldquoEfficient data hiding with histogram-preserving propertyrdquo Telecommunication Systems vol 49 no 2pp 179ndash185 2012

[20] J FridrichMGoljan andRDu ldquoDetecting LSB steganographyin color and gray-scale imagesrdquo IEEEMultimediaMagazine vol8 no 4 pp 22ndash28 2001

Submit your manuscripts athttpwwwhindawicom

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Page 3: Research Article An Image Steganography Method Hiding ...downloads.hindawi.com/journals/mpe/2015/684824.pdf · An Image Steganography Method Hiding Secret Data into Coefficients of

Mathematical Problems in Engineering 3

It is possible to write integer transform by truncating thedivision

1198891119899= 11987802119899+1minus 11987802119899

1198781119899= 11987802119899+ lfloor1198891119899

2rfloor (7)

Lifting can be used to compute the inverse transformTheequations follow from reversing the order and changing thesign of the forward transform [8]

11987802119899= 1198781119899minus lfloor1198891119899

2rfloor 119878

02119899+1= 1198891119899+ 11987802119899 (8)

Ramalingam et al [9] have elaborated the process ofseparating four subbands using Haar IWT The first stageIWT is given by

H = 119862119900minus 119862119890

L = 119862119890+ lfloor

H2rfloor

(9)

where 119862119900represents pixels in odd column and 119862

119890represents

pixels in even column In the next stage the IWT coefficientsare calculated using high pass and low pass filter banks Thisprocess creates four subbands low-low (LL) low-high (LH)high-low (HL) and high-high (HH) The second stage IWTis given by

LH = Lodd minus Leven

LL = Leven + [LH2]

HH = Hodd minusHeven

HH = Heven + [HL2]

(10)

where Hodd represents H bandrsquos odd row Lodd represents Lbandrsquos odd row Heven represents H bandrsquos even row and Levenrepresents L bandrsquos even row [9]

Ghasemi et al [10 11] have proposed a novel steganogra-phy scheme based on integer wavelet transform and geneticalgorithm The scheme embeds data in integer wavelettransform coefficients by using a mapping function basedon genetic algorithm The methods use wavelet transformcoefficients to embed secret data into the four subbandsof two-dimensional wavelet transform Genetic algorithm isused to find themapping functionA chromosome is encodedas an array of 64 genes containing permutations 1 to 64that point to pixel numbers in each block OPAP is used tominimize the error between cover and stego image

Xuan et al [12] have suggested a lossless data hidingmethod for digital images using integer wavelet transformand threshold embedding technique CDF (22) integerwavelet transform is used to obtain the wavelet coefficientsHistogrammodification is applied to prevent possible under-flowoverflow of pixel values A predefined threshold value 119879is used to embed data in the wavelet coefficients

El Safy et al [13] have suggested an adaptive stegano-graphic model which combines adaptive hiding capacity

function that hides secret data in the integer wavelet coef-ficients of the cover image with the optimum pixel adjust-ment (OPA) algorithm Histogram modification is appliedto prevent possible underflowoverflow of pixel values Thecover image is divided into 8 times 8 nonoverlapping blocksEach block is transformed using 2D Haar integer wavelettransform to obtain four subbands LLI LHI HLI andHHI Hiding capacity of each coefficient is determined andthe data is embedded in the coefficients A pseudorandomnumber generation function is used to select the waveletcoefficients for increasing the security of the hidden dataTheOPAalgorithm is applied after embedding secretmessageto minimize the embedding error The extraction procedureis a blind process since it requires only the secret key fromthe receiver The secret key is used to identify the waveletcoefficients Secret message bits are extracted from eachselected wavelet coefficient

Archana et al [14] have proposed a method for hidingsecret information in the discrete wavelet transform coeffi-cients using GA and OPAP algorithm to provide optimumhiding capacity The four subbands LL HL LH and HH areused for hiding the data Hiding capacity function ismodifiedby using different ranges for k for the LH HL and HHsubbands where its values range from 1 to 4 The length L ofmessage bits to be hidden in wavelet coefficient is determinedby using hiding capacity function

Al-Asmari et al [15] have proposed a method using dis-crete wavelet transform and pixel value differencing approachto hide the information Using the discrete wavelet transformthe cover image is decomposed to obtain the four subbands(LL HL LH and HH) Then the LSB method is used tohide secret information in the LL subband by hiding two bitsof secret information in each coefficient The PVD approachis used to hide the information in the remaining threesubbands For hiding the information two consecutive pixelsin the vertical direction are grouped to form a pair Themethod gives high performance in terms of capacity humanvisual quality and PSNR

2 Proposed Method

The proposed method hides secret information in the grayscale images It uses spatial domain technique to hide secretinformation in the frequency domain In the frequencydomain the image is decomposed into four subbands usinginteger wavelet transform and then the spatial domaintechnique is used to hide secret information in the waveletcoefficients of the four subbands

The cover image is transformed using 2D Haar integerwavelet transform to obtain four subbands LL LH HL andHHThe proposed method embeds data in the coefficients offour subbands by using the pixel value differencing approach

21 Preprocessing The gray scale image is read as a 2D arrayof size [119872119873] Histogram modification [12ndash15] is applied toprevent the possible overflowunderflow of pixel values Thisproblem occurs when the pixel values of the cover image areclose to 255 or 0 because they may exceed 255 or fall below 0

4 Mathematical Problems in Engineering

LL HL

LH HH

Figure 1 Arrangements of wavelet coefficients

Figure 2 The image lenatiff after performing Harr transform

during inverse integer wavelet transformThe problem can besolved by mapping the lowest 15 gray scale levels to the value15 and the highest 15 gray scale levels to the value 240 If thepixel values exceed the boundaries during the inverse wavelettransform the image is not suitable for hiding secret dataThe image is transformed using 2D Haar wavelet transformto obtain four subbands LL LH HL and HH of size [11987221198732] each All the four subbands are used to hide the secretinformationThe 2D array of size [119872119873] is again constructedby arranging the four subbands as shown in Figure 1

Figure 2 shows the arrangement of four subbands of theimage lenatiff after transforming it using 2D Harr integerwavelet transform

A 2D array obtained by arranging the wavelet coefficientsof four subbands is shown as follows

(

112 230 150 sdot sdot sdot minus45 minus120 80

130 159 172 sdot sdot sdot minus37 minus89 minus72

sdot sdot sdot sdot sdot sdot sdot sdot sdot

sdot sdot sdot sdot sdot sdot sdot sdot sdot

minus30 minus59 minus72 sdot sdot sdot minus37 minus89 minus72

) (11)

The difference operation in Haar transform may cause someof the wavelet coefficients in HL LH and HH subbands tohave negative values

Since some of the wavelet coefficients have negativevalues the 2D array shown in (11) cannot be used for hid-ing secret information using the pixel value differencingapproach Hence absolute values are used for the coefficient

with negative values to create a new 2D array with positiveelements as follows

(

112 230 150 sdot sdot sdot 45 120 80

130 159 172 sdot sdot sdot 37 89 72

sdot sdot sdot sdot sdot sdot sdot sdot sdot

sdot sdot sdot sdot sdot sdot sdot sdot sdot

30 59 72 sdot sdot sdot 37 89 72

) (12)

After hiding the secret information in the 2D array shownin (12) inverse wavelet transform is performed to obtainthe stego image To obtain good quality of stego image theoriginal sign of each wavelet coefficient as shown in (11) isrequired Hence the 2D array shown in (11) is used to createa sign matrix of the size [119872119873] having elements with values1 or minus1 The sign matrix so created is shown as follows

(

1 1 1 sdot sdot sdot minus1 minus1 1

1 1 1 sdot sdot sdot minus1 minus1 minus1

sdot sdot sdot sdot sdot sdot sdot sdot sdot

sdot sdot sdot sdot sdot sdot sdot sdot sdot

minus1 minus1 minus1 sdot sdot sdot minus1 minus1 minus1

) (13)

The wavelet coefficients having positive values are repre-sented by 1 whereas wavelet coefficients having negativevalues are represented by minus1 in the sign matrix

22 Embedding Process For hiding the data in the 2D arraythe method suggested by Gulve [4 7] is used In the methodproposed byChang [3] a block of 2times 2 pixels is used to form 3pairs which are then used to hide the secret informationTheproposed method uses the block of 2 times 3 wavelet coefficientsThe introduction of 2 wavelet coefficients in the 2 times 2 blockforms two extra pairs For a 512 times 512 image it is possible toform 196608 pairs using the approach suggested by Chang [3]whereas using the proposed approach 217600 pairs can beformed A greater number of pairs provide extra space forhiding the secret information Thus the proposed methodimproves the hiding capacity of the cover image

Thedifference between twowavelet coefficients in the pairis used to hide the secret information If the difference valueis directly used to hide the information it is easy to retrievethe embedded information in case the steganography systemfails To enhance the security of the secret information theproposed algorithm modifies the difference between the twowavelet coefficients in the pair and this modified differenceis used to hide the secret information This imposes extralayer of security making harder extraction of original secretinformation from stego image using the difference valuesdirectly [4 7]

The arrangement of wavelet coefficients into nonover-lapping blocks of 2 times 3 wavelet coefficients is shown inFigure 3 As shown in Figure 3 each 2 times 3 block includes sixwavelet coefficients 119875

(119909119910) 119875(119909119910+1)

119875(119909119910+2)

119875(119909+1119910)

119875(119909+1119910+1)

and 119875

(119909+1119910+2) where 119909 and 119910 are the locations of wavelet

coefficients Five pairs are formed by grouping the commonwavelet coefficient PX

1with the remaining five wavelet

Mathematical Problems in Engineering 5

PX0

PX3

PX1

PX4

PX2

PX5

P(xy) P(xy+1)P(xy+2)

P(x+1y) P(x+1y+1) P(x+1y+2)

Figure 3 Pixel block

coefficients PX0 PX2 PX3 PX4 and PX

5 The five pairs 119875119875

119894

where 119894 = 0 1 2 3 4 are as shown below

1198751198750= (119875(119909119910+1) 119875(119909119910))

1198751198751= (119875(119909119910+1) 119875(119909119910+2))

1198751198752= (119875(119909119910+1) 119875(119909+1119910))

1198751198753= (119875(119909119910+1) 119875(119909+1119910+1)

)

1198751198754= (119875(119909119910+1) 119875(119909+1119910+2)

)

(14)

The difference value 119889119894is calculated for each pair 119875119875

119894by

subtracting the common wavelet coefficient PX1from the

other wavelet coefficient in that pair This difference value isused to identify the corresponding range 119877

119896119894from the range

table119877The range table is designed with ranges [0ndash7] [8ndash15][16ndash31] [32ndash63] [64ndash127] and [128ndash255] The width 119882

119896119894

of range 119877119896119894

is used to determine the number of bits 119905119894(119905119894=

log2119882119896119894) that can be hidden in each pair where 119894 = 0 1 2 3 4

This 119905119894is then used to calculate the average value (119873) of

number of bits possible to be hidden in each pair of the blockThe average value119873 is used to calculate the revised difference119877119889119894as 119877119889119894is remainder (119889

1198942119873) so that 119877119889

119894le 2119873 where 119889

119894is

the original differenceThe offset difference OD119894is calculated

as |119889119894|minus |119877119889

119894| for each pair in the blockThe revised difference

|119877119889119894| is then used to determine the number of bits 119905

119894for each

pair in the block Thus if the original difference value |119889119894|

allows 119872 bits to be hidden in the pair then the proposedapproach hides bits le 119873 in that pair [4 7]

After embedding 119905119894bits of the message in the pair new

difference 1198891015840119894is calculated as OD

119894+119897119896119894+119887where 119897

119896119894represents

lower boundary of the range 119877119896119894

in the range table 119877 and 119887represents the decimal equivalent of 119905

119894message bits hidden in

that pairEmbedding 119905

119894bits in the pair modifies the values of

both the wavelet coefficients in the pair The new valuesof wavelet coefficients in each pair are different from theiroriginal values Since new value is assigned to commonwavelet coefficient PX

1in each pair five different values are

obtained for the common wavelet coefficient PX1 However

the common wavelet coefficient PX1can have only one value

in each bock This requires values of other five waveletcoefficients PX

0 PX2 PX3 PX4 and PX

5to be adjusted such

that the new difference 1198891015840119894remains unchanged Therefore

the pair having new values of wavelet coefficients close totheir original values is selected as the reference pair To find

the reference pair the difference 119898 between 119889119894and 1198891015840

119894is

calculated Small value of |119898| indicates that the newdifferencevalue 1198891015840

119894is close to the original difference value 119889

119894 Thus

for the pair with minimum |119898| the new values of waveletcoefficients are close to their original values So the pair withminimum |119898| is selected as the reference pair The values ofthe two wavelet coefficients in the reference pair are used toadjust the values of wavelet coefficients in other pairs andconstruct a new 2times3 blockThe embedded secret informationin newly constructed block is unaffected because differencevalues for the pairs are unaltered [4 7]

During the extraction process average value (119873) iscalculated using the same process adopted during embeddingof the secret messageThe average value119873 is used to calculatethe revised difference 1198771198891015840

119894as 1198771198891015840

119894is remainder (119889

1198942119873) Suit-

able range 119877119896119894 is identified using this revised difference Thesecretmessage is extracted in the decimal formby subtracting119897119896from |1198771198891015840

119894| Secret message is then converted into a binary

stream with 119905119894(119905119894= log2119882119896119894) bits [4 7]

The process of hiding secret information in the coverimage is described below [4 7]

(1) Create the 2D array as shown in (12) by preprocessingthe gray scale cover image

(2) Partition the array into nonoverlapping blocks of 2times3wavelet coefficients and group wavelet coefficient PX

1

with the remaining wavelet coefficients in the block toform five pairs

(3) Calculate the difference values 119889119894for the five pairs in

each block

1198890= 119875(119909119910)minus 119875(119909119910+1)

1198891= 119875(119909119910+2)minus 119875(119909119910+1)

1198892= 119875(119909+1119910)minus 119875(119909119910+1)

1198893= 119875(119909+1119910+1)

minus 119875(119909119910+1)

1198894= 119875(119909+1119910+2)

minus 119875(119909119910+1)

(15)

(4) Use |119889119894| where 119894 = 0 1 2 3 4 to locate suitable range

119877119896in the designed range table Use this range to

calculate number of bits 119905119894that can be hidden in each

pair 119875119875119894 Then calculate the average bits using

avg = lfloor(sum4

119894=0119905119894

5)rfloor (16)

(5) Calculate the revised difference |119877119889119894| where 119894 =

0 1 2 3 4 as119877119889119894is remainder (119889

1198942avg) so that119877119889

119894lt=

2avg

(6) Calculate the difference OD119894as OD

119894= |119889119894| minus |119877119889

119894| for

each pair

(7) Use |119877119889119894|where 119894 = 0 1 2 3 4 to locate suitable range

119877119896in the designed range table

6 Mathematical Problems in Engineering

(8) Compute the number of bits 119905119894that can be embedded

in each pair using the corresponding range given by119877119896 The value 119905

119894can be estimated from the width 119908

119896

of 119877119896 which is given by 119905

119894= log2119908119896where width119908

119896=

119906119896minus119897119896+1 and119906

119896and 119897119896are upper and lower boundaries

of the range 119877119896

(9) Read 119905119894bits from the binary secret data

(10) Calculate the new difference value 1198891015840119894given by

1198891015840

119894= OD

119894+ 119897119896119894+ 119887119894 if 119889

119894ge 0

1198891015840

119894= minus (OD

119894+ 119897119896119894+ 119887119894) if 119889

119894lt 0

(17)

(11) Modify the values of wavelet coefficients in the pair119875119875119894using

(1198751015840

119899 1198751015840

119899+1) = (119875

119899minus lceil119898

2rceil 119875119899+1+ lfloor119898

2rfloor) (18)

where 119875119899and 119875

119899+1represent two wavelet coefficients

in the pair 119875119875119894and 119898 is obtained by subtracting 119889

119894

from 1198891015840119894

(12) Select the pair with minimum |119898| as the optimalreference pair and use this pair to adjust the values ofwavelet coefficients of the other four pairs The valueof the common wavelet coefficient is given by 1198751015840

119899of

the reference pair Modify value of another waveletcoefficient 1198751015840

119899+1of remaining four pairs such that

the new difference 1198891015840119894will remain unchanged Thus

new values are assigned to remaining four waveletcoefficients in the block

(13) Check the new values of wavelet coefficients for fall-off boundaries that is check whether all the valuesare within the range from 0 to 255 If not modify thevalues preserving the difference between the values oftwo wavelet coefficients of each pair in the block

(a) Find out the smallest of all the wavelet coeffi-cients If the smallest is less than 0 then add|smallest| in all the wavelet coefficients in thatblock

(b) Find out the largest of all the wavelet coeffi-cients If the largest is greater than 255 subtractlargest minus 255 from all the wavelet coefficients inthat block

(c) If fall-off boundary problems still exist thecover image is not suitable for hiding secretinformation

(14) Now reconstruct the block from all pairs with modi-fied values of wavelet coefficients

(15) Repeat steps (2) through (14) until the secret informa-tion is embedded in the cover image

23 Postprocessing After the embedding process is overoriginal signs are assigned to the elements of 2D array usingthe sign matrix created during preprocessing phase This is

accomplished by one to one comparison of elements of 2Darray with the elements of 2D sign matrix The 2D array isthen split to obtain the four subbands Using inverse 2DHaarinteger wavelet transform the four subbands are combined toobtain the stego image of size [119872119873] All the pixel values ofthe stego image in the range from 0 to 255 indicate that secretdata is safely hidden and can be extracted accurately

24 Extraction Process The extraction process is blind Itdoes not require the existence of cover image for extractinghidden secret data from the stego image The stego image ispreprocessed to obtain the 2D array as shown in (12) Theprocess of extraction of secret information from the stegoimage is described below [4 7]

(1) Create the 2D array as shown in (12) by preprocessingthe gray scale stego image

(2) Partition the array into nonoverlapping blocks of 2times 3wavelet coefficients and group wavelet coefficient PX

1

with the remaining wavelet coefficients in the block toform five pairs Keep the partition order the same asthat of the embedding

(3) Calculate the difference values 119889119894for the five pairs in

each block

1198890= 119875(119909119910)minus 119875(119909119910+1)

1198891= 119875(119909119910+2)minus 119875(119909119910+1)

1198892= 119875(119909+1119910)minus 119875(119909119910+1)

1198893= 119875(119909+1119910+1)

minus 119875(119909119910+1)

1198894= 119875(119909+1119910+2)

minus 119875(119909119910+1)

(19)

(4) Use |119889119894| where 119894 = 0 1 2 3 4 to locate suitable range

119877119896in the designed range table Use this range to

calculate number of bits 119905119894 which is hidden in each

pair 119875119875119894 Then calculate the average bits using (16)

(5) Calculate revised difference |1198771198891015840

119894| where

119894 = 0 1 2 3 4 as 1198771198891015840119894is remainder (119889

1198942avg)

(6) Use |1198771198891015840119894| where 119894 = 0 1 2 3 4 to locate suitable 119877

119896in

the designed range table(7) After 119877

119896is located 119897

119896is subtracted from |1198771198891015840

119894| and

1198871015840

119894is obtained in decimal form A binary sequence is

generated from 1198871015840119894with 119905

119894bits where 119905

119894= log2119908119896

Repeat steps (2) through (7) until embedded message isextracted

3 Results

A set of gray scale TIFF images is used for the experimenta-tion This set consists of standard images as well as imagestaken from the camera The standard images are obtainedfrom the ldquothe USC-SIPI image database (httpsipiuscedudatabase)rdquo The images taken from Canon A45 camera

Mathematical Problems in Engineering 7

Table 1 Comparison of hiding capacity (in bytes)

Cover image PVD method [1] TPVD method [3] Gulversquos method [4] Proposed methodCapacity PSNR Capacity PSNR Capacity PSNR Capacity PSNR

Lena 50960 4179 75836 3889 81305 4286 81326 3984Baboon 56291 3790 82407 3393 81766 4199 82933 3962Peppers 50685 4173 75579 3850 81326 4280 81387 4029

Cover imageLenatiff

(a)

Stego-imageLennatiff

(b)

BaboontiffCover image

(c)

BaboontiffStego-image

(d)

Figure 4 Cover and stego images

in JPG format are converted into gray scale tiff format Thetext files are used as secret data Since the proposed algo-rithm use PVD approach to hide information in waveletcoefficients the data hiding capacity and PSNR values ofthe proposed method are compared with PVD method [1]TPVD [3] method and Gulversquos method [4] The comparisonis shown in Table 1The proposedmethod provides increasedhiding capacity and improved PSNR values as comparedto PVD and TPVD method Although the PSNR is less as

compared to Gulversquos [4] method there is an improvement inthe security of secret data

The average payload of the proposed system is sim248 bppThe performance of the proposed method is analyzed usingPSNR Universal Quality Index (119876) and Structural SimilarityIndex Measure (SSIM) 119876 and SSIM are full reference imagequality assessment models and require the cover image tobe available [16 17] Table 2 shows the PSNR values MSEUniversal Quality Index (119876) and Structural Similarity Index

8 Mathematical Problems in Engineering

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Cover image

Lennatiff

(a)

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Stego image

Lennatiff

(b)

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Cover image

Baboontiff

(c)

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Stego imageBaboontiff

(d)

Figure 5 Histograms of cover and stego images

Measure (SSIM) for different images obtained using proposedmethod The PSNR values are above the threshold of 36 dB[18] even after using more than 95 of the hiding capacity ofthe cover image Also Universal Quality Index (119876) values [16]and Structural Similarity Index Measure (SSIM) values [17]are close to 1 which proves that the stego images are visuallyindistinguishable from original cover images

Figure 4 shows the cover image and the correspondingstego images obtained using the proposed method As thefigures show distortions resulted from embedding are imper-ceptible to human vision

Figure 5 shows the histogramof the cover and stego imageobtained using the proposed method From the figure it canbe observed that the shape of the histogram is preserved

The cover image data is subtracted from stego imageand plotted as histogram Figure 6 shows the pixel differencehistogram From the figure it can be observed that there aremore numbers of bins which are close to 0 as compared to

bins which are away from 0 Also the step pattern is notobserved in the figure This confirms that the method isrobust against histogram analysis attack

Histogram of cover image is represented as [ℎ0 ℎ1

ℎ255] whereas histogram of stego image is represented as

[ℎ1015840

0 ℎ1015840

1 ℎ

1015840

255] The change in histogram [19] is measured

by

119863ℎ=

255

sum

119898=1

10038161003816100381610038161003816ℎ1015840

119898minus ℎ119898

10038161003816100381610038161003816 (20)

The proposed method can hide at least 3 bits in eachpair considering the smallest width of the subrange to be 8Figure 7 shows the comparison of the value of 119863

ℎof the 3

bit LSB replacement method and the proposed method withdifferent size of secret data embedded in the cover imageLenatiff It can be observed that difference in histogram forthe proposed method is less than that of 3 bit LSB method

Mathematical Problems in Engineering 9

0 5 10 15 200

05

1

15

2

25

3

Difference values

Occ

urre

nce f

requ

ency

minus20 minus15 minus10 minus5

times104

Cover imageLennatiff

(a)

0 10 20 300

05

1

15

2

25

3

35

Difference values

Occ

urre

nce f

requ

ency

minus30 minus20 minus10

times104

Cover imageBaboontiff

(b)

Figure 6 Difference histogram

Table 2 Hiding capacity PSNR MSE and 119876 index

Coverimage

Resolution of coverimage

Hidingcapacity(Kb)

ofhidingcapacity

Messagefile size(Kb)

PSNR MSE 119876 SSIM

Baboon 256 times 256 1992 3065 195 3987 6684 0959 0965Lena 256 times 256 1994 3068 195 3991 6633 0899 0937Elaine 512 times 512 7942 309 787 4001 6482 0890 0956Baboon 512 times 512 8099 3068 787 3962 7089 0961 0979Lena 512 times 512 7947 3068 787 3984 6740 0806 0953Tank 512 times 512 7941 309 787 3986 6700 0896 0954Peppers 512 times 512 7948 3022 787 4029 6074 0800 0932Barbara 512 times 512 8035 3055 787 3970 6961 0857 0964Boat 512 times 512 7964 3075 787 3990 6652 0883 0962Grass 1024 times 1024 31932 3115 317 3951 7274 0979 0998

The output images are tested under the 119877119878 steganalysis[20] It is observed from Figure 8 that the difference between119877119872

and 119877minus119872

and 119878119872

and 119878minus119872

is very small The rules 119877119872cong

119877minus119872

and 119878119872cong 119878minus119872

are satisfied for the output images Thisproves that the proposed method is secure against 119877119878 attack

4 Conclusion

In steganography hiding capacity of cover image quality ofstego image and security of secret data are three importantfactors There is always a trade-off between data hidingcapacity of cover image and security of secret data Theproposed algorithm provides improvements in the datahiding capacity as well as security of the secret data ascompared to PVD [1] and TPVD [3] methods AlthoughGulversquos [4] method provides better PSNR values as comparedto proposedmethod the proposedmethod improves security

of secret information The secret information is securelyhidden in the coefficients of integer wavelet transform Forthe implementation purpose the four subbands obtainedafter decomposing the cover image by integer wavelet trans-form are arranged as shown in Figure 1 But it is possible toarrange the four subbands in 4 = 24 different ways therebyimproving the security of the steganography system sincethe exact arrangement of four subbands will be known tosender and receiver only The algorithm revises the originaldifference between two wavelet coefficients in the pair andthis revised difference is used for hiding the data in that pairThis makes estimation of exact number of bits hidden in thepair difficult Image steganography techniques hiding textualinformation require 100 accuracy for successful retrieval ofhidden information from stego image If the steganographymethod fails correct estimation of number of bits hidden forsome of the pairs will be a challenge for the invader Thus

10 Mathematical Problems in Engineering

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

10 20 30 40 50 60 70 80

Hist

ogra

m d

iffer

ence

Size of hidden message (KB)

LSBProposed

Figure 7 Histograms comparison of 3 bit LSB substitution andproposed method (Lenatiff)

0

01

02

03

04

10 20 30 40 50 60 70 79

Ratio

of R

S

Message size (KB)

RM SM

RminusMSminusM

Figure 8 119877119878 diagram

one more level of security is imposed to secure the secretinformation

The PSNR values produced by the algorithm are close to395 which are well above the threshold of 36 dB after usingfull hiding capacity of the cover image This proves that thestego images are of good quality Results also show that thedifference between cover image and stego image cannot benoticed by human visual system (HVS)

Considering the fact that there is currently no steganogra-phy system that can resist all the steganalysis attacks the bestway to provide security to the secret data and to eliminate theattack of comparing the original image with the stego image

is to freshly create an image and destroy it after generating thestego image

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D-CWu andW-H Tsai ldquoA steganographic method for imagesby pixel-value differencingrdquo Pattern Recognition Letters vol 24no 9-10 pp 1613ndash1626 2003

[2] H C Wu N I Wu C S Tsai and M-S Hwang ldquoImagesteganographic scheme based on pixel-value differencing andLSB replacementmethodsrdquo IEE ProceedingsmdashVision Image andSignal Processing vol 152 no 5 pp 611ndash615 2005

[3] K-C Chang P S Huang T-M Tu and C-P Chang ldquoAdaptiveimage steganographic scheme based on tri-way pixel-value dif-ferencingrdquo in Proceedings of the IEEE International Conferenceon Systems Man and Cybernetics (SMC rsquo07) pp 1165ndash1170Montreal Canada October 2007

[4] A K Gulve andM S Joshi ldquoAn image steganography algorithmwith five pixel pair differencing and gray code conversionrdquoInternational Journal of Image Graphics and Signal Processingvol 6 no 3 pp 12ndash20 2014

[5] K-C Chang C-P Chang P S Huang and T-M Tu ldquoA novelimage steganographic method using tri-way pixel-value differ-encingrdquo Journal of Multimedia vol 3 no 2 pp 37ndash44 2008

[6] K C Chang P S Huang T M Tu and C P Chang ldquoImagesteganographic scheme using tri-way pixel-value differencingand adaptive rulesrdquo in Proceedings of the IEEE InternationalConference on Intelligent Information Hiding and MultimediaSignal Processing pp 449ndash452 Kaohsiung Taiwan 2007

[7] A K Gulve and M S Joshi ldquoA secured image steganographyalgorithm with five pixel pair differencing by selecting thecommon pixel randomlyrdquo in Proceedings of the 3rd InternationalConference on Computational Intelligence and Information Tech-nology (CIIT rsquo13) pp 55ndash61 Elseveir Mumbai India 2013

[8] A R Calderbank I Daubechies W Sweldens and B-L YeoldquoWavelet transforms that map integers to integersrdquo Applied andComputational Harmonic Analysis vol 5 no 3 pp 332ndash3691998

[9] B Ramalingam R Amirtharajan and J B B Rayappan ldquoStegoon FPGA an IWT approachrdquoThe Scientific World Journal vol2014 Article ID 192512 9 pages 2014

[10] E Ghasemi J Shanbehzadeh and B ZahirAzami ldquoA stegano-graphic method based on Integer Wavelet Transform andGenetic Algorithmrdquo in Proceedings of the International Confer-ence on Communications and Signal Processing (ICCSP rsquo11) pp42ndash45 Calicut India February 2011

[11] E Ghasemi J Shanbehzadeh and N Fassihi ldquoHigh capacityimage steganography using wavelet transform and geneticalgorithmrdquo in Proceedings of the International Multi Conferenceof Engineers and Computer Scientists (IMECS rsquo11) pp 495ndash498Hong Kong March 2011

[12] G Xuan Y Q Shi C Yang Y Zheng D Zou and P ChaildquoLossless data hiding using integer wavelet transform andthreshold embedding techniquerdquo in Proceedings of the IEEEInternational Conference on Multimedia and Expo (ICME rsquo05)pp 1520ndash1523 IEEE Amsterdam The Netherlands July 2005

Mathematical Problems in Engineering 11

[13] R O El Safy H H Zayed and A El Dessouki ldquoAn adaptivesteganographic technique based on integer wavelet transformrdquoin Proceedings of the International Conference on Networkingand Media Convergence (ICNM rsquo09) pp 111ndash117 Cairo EgyptMarch 2009

[14] S Archana A Judice and K P Kaliyamurthie ldquoA novelapproach on image steganographic methods for optimum hid-ing capacityrdquo International Journal of Engineering and ComputerScience vol 2 no 2 pp 378ndash385 2013

[15] A K Al-Asmari M A Al-Qodah and A S Salama ldquoWavelet-pixel value differencing technique for digital images data hid-ingrdquo in Proceedings of the IEEE International Conference onSystem Engineering and Technology (ICSET rsquo11) pp 15ndash18 June2011

[16] Z Wang and A C Bovik ldquoA universal image quality indexrdquoIEEE Signal Processing Letters vol 9 no 3 pp 81ndash84 2002

[17] ZWang A C Bovik H R Sheikh and E P Simoncelli ldquoImagequality assessment from error visibility to structural similarityrdquoIEEE Transactions on Image Processing vol 13 no 4 pp 600ndash612 2004

[18] N I Wu andM S Hwang ldquoData hiding current status and keyissuesrdquo International Journal of Network Security vol 4 no 1pp 1ndash9 2007

[19] X Zhang and S Wang ldquoEfficient data hiding with histogram-preserving propertyrdquo Telecommunication Systems vol 49 no 2pp 179ndash185 2012

[20] J FridrichMGoljan andRDu ldquoDetecting LSB steganographyin color and gray-scale imagesrdquo IEEEMultimediaMagazine vol8 no 4 pp 22ndash28 2001

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Complex AnalysisJournal of

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OptimizationJournal of

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Operations ResearchAdvances in

Journal of

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Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Page 4: Research Article An Image Steganography Method Hiding ...downloads.hindawi.com/journals/mpe/2015/684824.pdf · An Image Steganography Method Hiding Secret Data into Coefficients of

4 Mathematical Problems in Engineering

LL HL

LH HH

Figure 1 Arrangements of wavelet coefficients

Figure 2 The image lenatiff after performing Harr transform

during inverse integer wavelet transformThe problem can besolved by mapping the lowest 15 gray scale levels to the value15 and the highest 15 gray scale levels to the value 240 If thepixel values exceed the boundaries during the inverse wavelettransform the image is not suitable for hiding secret dataThe image is transformed using 2D Haar wavelet transformto obtain four subbands LL LH HL and HH of size [11987221198732] each All the four subbands are used to hide the secretinformationThe 2D array of size [119872119873] is again constructedby arranging the four subbands as shown in Figure 1

Figure 2 shows the arrangement of four subbands of theimage lenatiff after transforming it using 2D Harr integerwavelet transform

A 2D array obtained by arranging the wavelet coefficientsof four subbands is shown as follows

(

112 230 150 sdot sdot sdot minus45 minus120 80

130 159 172 sdot sdot sdot minus37 minus89 minus72

sdot sdot sdot sdot sdot sdot sdot sdot sdot

sdot sdot sdot sdot sdot sdot sdot sdot sdot

minus30 minus59 minus72 sdot sdot sdot minus37 minus89 minus72

) (11)

The difference operation in Haar transform may cause someof the wavelet coefficients in HL LH and HH subbands tohave negative values

Since some of the wavelet coefficients have negativevalues the 2D array shown in (11) cannot be used for hid-ing secret information using the pixel value differencingapproach Hence absolute values are used for the coefficient

with negative values to create a new 2D array with positiveelements as follows

(

112 230 150 sdot sdot sdot 45 120 80

130 159 172 sdot sdot sdot 37 89 72

sdot sdot sdot sdot sdot sdot sdot sdot sdot

sdot sdot sdot sdot sdot sdot sdot sdot sdot

30 59 72 sdot sdot sdot 37 89 72

) (12)

After hiding the secret information in the 2D array shownin (12) inverse wavelet transform is performed to obtainthe stego image To obtain good quality of stego image theoriginal sign of each wavelet coefficient as shown in (11) isrequired Hence the 2D array shown in (11) is used to createa sign matrix of the size [119872119873] having elements with values1 or minus1 The sign matrix so created is shown as follows

(

1 1 1 sdot sdot sdot minus1 minus1 1

1 1 1 sdot sdot sdot minus1 minus1 minus1

sdot sdot sdot sdot sdot sdot sdot sdot sdot

sdot sdot sdot sdot sdot sdot sdot sdot sdot

minus1 minus1 minus1 sdot sdot sdot minus1 minus1 minus1

) (13)

The wavelet coefficients having positive values are repre-sented by 1 whereas wavelet coefficients having negativevalues are represented by minus1 in the sign matrix

22 Embedding Process For hiding the data in the 2D arraythe method suggested by Gulve [4 7] is used In the methodproposed byChang [3] a block of 2times 2 pixels is used to form 3pairs which are then used to hide the secret informationTheproposed method uses the block of 2 times 3 wavelet coefficientsThe introduction of 2 wavelet coefficients in the 2 times 2 blockforms two extra pairs For a 512 times 512 image it is possible toform 196608 pairs using the approach suggested by Chang [3]whereas using the proposed approach 217600 pairs can beformed A greater number of pairs provide extra space forhiding the secret information Thus the proposed methodimproves the hiding capacity of the cover image

Thedifference between twowavelet coefficients in the pairis used to hide the secret information If the difference valueis directly used to hide the information it is easy to retrievethe embedded information in case the steganography systemfails To enhance the security of the secret information theproposed algorithm modifies the difference between the twowavelet coefficients in the pair and this modified differenceis used to hide the secret information This imposes extralayer of security making harder extraction of original secretinformation from stego image using the difference valuesdirectly [4 7]

The arrangement of wavelet coefficients into nonover-lapping blocks of 2 times 3 wavelet coefficients is shown inFigure 3 As shown in Figure 3 each 2 times 3 block includes sixwavelet coefficients 119875

(119909119910) 119875(119909119910+1)

119875(119909119910+2)

119875(119909+1119910)

119875(119909+1119910+1)

and 119875

(119909+1119910+2) where 119909 and 119910 are the locations of wavelet

coefficients Five pairs are formed by grouping the commonwavelet coefficient PX

1with the remaining five wavelet

Mathematical Problems in Engineering 5

PX0

PX3

PX1

PX4

PX2

PX5

P(xy) P(xy+1)P(xy+2)

P(x+1y) P(x+1y+1) P(x+1y+2)

Figure 3 Pixel block

coefficients PX0 PX2 PX3 PX4 and PX

5 The five pairs 119875119875

119894

where 119894 = 0 1 2 3 4 are as shown below

1198751198750= (119875(119909119910+1) 119875(119909119910))

1198751198751= (119875(119909119910+1) 119875(119909119910+2))

1198751198752= (119875(119909119910+1) 119875(119909+1119910))

1198751198753= (119875(119909119910+1) 119875(119909+1119910+1)

)

1198751198754= (119875(119909119910+1) 119875(119909+1119910+2)

)

(14)

The difference value 119889119894is calculated for each pair 119875119875

119894by

subtracting the common wavelet coefficient PX1from the

other wavelet coefficient in that pair This difference value isused to identify the corresponding range 119877

119896119894from the range

table119877The range table is designed with ranges [0ndash7] [8ndash15][16ndash31] [32ndash63] [64ndash127] and [128ndash255] The width 119882

119896119894

of range 119877119896119894

is used to determine the number of bits 119905119894(119905119894=

log2119882119896119894) that can be hidden in each pair where 119894 = 0 1 2 3 4

This 119905119894is then used to calculate the average value (119873) of

number of bits possible to be hidden in each pair of the blockThe average value119873 is used to calculate the revised difference119877119889119894as 119877119889119894is remainder (119889

1198942119873) so that 119877119889

119894le 2119873 where 119889

119894is

the original differenceThe offset difference OD119894is calculated

as |119889119894|minus |119877119889

119894| for each pair in the blockThe revised difference

|119877119889119894| is then used to determine the number of bits 119905

119894for each

pair in the block Thus if the original difference value |119889119894|

allows 119872 bits to be hidden in the pair then the proposedapproach hides bits le 119873 in that pair [4 7]

After embedding 119905119894bits of the message in the pair new

difference 1198891015840119894is calculated as OD

119894+119897119896119894+119887where 119897

119896119894represents

lower boundary of the range 119877119896119894

in the range table 119877 and 119887represents the decimal equivalent of 119905

119894message bits hidden in

that pairEmbedding 119905

119894bits in the pair modifies the values of

both the wavelet coefficients in the pair The new valuesof wavelet coefficients in each pair are different from theiroriginal values Since new value is assigned to commonwavelet coefficient PX

1in each pair five different values are

obtained for the common wavelet coefficient PX1 However

the common wavelet coefficient PX1can have only one value

in each bock This requires values of other five waveletcoefficients PX

0 PX2 PX3 PX4 and PX

5to be adjusted such

that the new difference 1198891015840119894remains unchanged Therefore

the pair having new values of wavelet coefficients close totheir original values is selected as the reference pair To find

the reference pair the difference 119898 between 119889119894and 1198891015840

119894is

calculated Small value of |119898| indicates that the newdifferencevalue 1198891015840

119894is close to the original difference value 119889

119894 Thus

for the pair with minimum |119898| the new values of waveletcoefficients are close to their original values So the pair withminimum |119898| is selected as the reference pair The values ofthe two wavelet coefficients in the reference pair are used toadjust the values of wavelet coefficients in other pairs andconstruct a new 2times3 blockThe embedded secret informationin newly constructed block is unaffected because differencevalues for the pairs are unaltered [4 7]

During the extraction process average value (119873) iscalculated using the same process adopted during embeddingof the secret messageThe average value119873 is used to calculatethe revised difference 1198771198891015840

119894as 1198771198891015840

119894is remainder (119889

1198942119873) Suit-

able range 119877119896119894 is identified using this revised difference Thesecretmessage is extracted in the decimal formby subtracting119897119896from |1198771198891015840

119894| Secret message is then converted into a binary

stream with 119905119894(119905119894= log2119882119896119894) bits [4 7]

The process of hiding secret information in the coverimage is described below [4 7]

(1) Create the 2D array as shown in (12) by preprocessingthe gray scale cover image

(2) Partition the array into nonoverlapping blocks of 2times3wavelet coefficients and group wavelet coefficient PX

1

with the remaining wavelet coefficients in the block toform five pairs

(3) Calculate the difference values 119889119894for the five pairs in

each block

1198890= 119875(119909119910)minus 119875(119909119910+1)

1198891= 119875(119909119910+2)minus 119875(119909119910+1)

1198892= 119875(119909+1119910)minus 119875(119909119910+1)

1198893= 119875(119909+1119910+1)

minus 119875(119909119910+1)

1198894= 119875(119909+1119910+2)

minus 119875(119909119910+1)

(15)

(4) Use |119889119894| where 119894 = 0 1 2 3 4 to locate suitable range

119877119896in the designed range table Use this range to

calculate number of bits 119905119894that can be hidden in each

pair 119875119875119894 Then calculate the average bits using

avg = lfloor(sum4

119894=0119905119894

5)rfloor (16)

(5) Calculate the revised difference |119877119889119894| where 119894 =

0 1 2 3 4 as119877119889119894is remainder (119889

1198942avg) so that119877119889

119894lt=

2avg

(6) Calculate the difference OD119894as OD

119894= |119889119894| minus |119877119889

119894| for

each pair

(7) Use |119877119889119894|where 119894 = 0 1 2 3 4 to locate suitable range

119877119896in the designed range table

6 Mathematical Problems in Engineering

(8) Compute the number of bits 119905119894that can be embedded

in each pair using the corresponding range given by119877119896 The value 119905

119894can be estimated from the width 119908

119896

of 119877119896 which is given by 119905

119894= log2119908119896where width119908

119896=

119906119896minus119897119896+1 and119906

119896and 119897119896are upper and lower boundaries

of the range 119877119896

(9) Read 119905119894bits from the binary secret data

(10) Calculate the new difference value 1198891015840119894given by

1198891015840

119894= OD

119894+ 119897119896119894+ 119887119894 if 119889

119894ge 0

1198891015840

119894= minus (OD

119894+ 119897119896119894+ 119887119894) if 119889

119894lt 0

(17)

(11) Modify the values of wavelet coefficients in the pair119875119875119894using

(1198751015840

119899 1198751015840

119899+1) = (119875

119899minus lceil119898

2rceil 119875119899+1+ lfloor119898

2rfloor) (18)

where 119875119899and 119875

119899+1represent two wavelet coefficients

in the pair 119875119875119894and 119898 is obtained by subtracting 119889

119894

from 1198891015840119894

(12) Select the pair with minimum |119898| as the optimalreference pair and use this pair to adjust the values ofwavelet coefficients of the other four pairs The valueof the common wavelet coefficient is given by 1198751015840

119899of

the reference pair Modify value of another waveletcoefficient 1198751015840

119899+1of remaining four pairs such that

the new difference 1198891015840119894will remain unchanged Thus

new values are assigned to remaining four waveletcoefficients in the block

(13) Check the new values of wavelet coefficients for fall-off boundaries that is check whether all the valuesare within the range from 0 to 255 If not modify thevalues preserving the difference between the values oftwo wavelet coefficients of each pair in the block

(a) Find out the smallest of all the wavelet coeffi-cients If the smallest is less than 0 then add|smallest| in all the wavelet coefficients in thatblock

(b) Find out the largest of all the wavelet coeffi-cients If the largest is greater than 255 subtractlargest minus 255 from all the wavelet coefficients inthat block

(c) If fall-off boundary problems still exist thecover image is not suitable for hiding secretinformation

(14) Now reconstruct the block from all pairs with modi-fied values of wavelet coefficients

(15) Repeat steps (2) through (14) until the secret informa-tion is embedded in the cover image

23 Postprocessing After the embedding process is overoriginal signs are assigned to the elements of 2D array usingthe sign matrix created during preprocessing phase This is

accomplished by one to one comparison of elements of 2Darray with the elements of 2D sign matrix The 2D array isthen split to obtain the four subbands Using inverse 2DHaarinteger wavelet transform the four subbands are combined toobtain the stego image of size [119872119873] All the pixel values ofthe stego image in the range from 0 to 255 indicate that secretdata is safely hidden and can be extracted accurately

24 Extraction Process The extraction process is blind Itdoes not require the existence of cover image for extractinghidden secret data from the stego image The stego image ispreprocessed to obtain the 2D array as shown in (12) Theprocess of extraction of secret information from the stegoimage is described below [4 7]

(1) Create the 2D array as shown in (12) by preprocessingthe gray scale stego image

(2) Partition the array into nonoverlapping blocks of 2times 3wavelet coefficients and group wavelet coefficient PX

1

with the remaining wavelet coefficients in the block toform five pairs Keep the partition order the same asthat of the embedding

(3) Calculate the difference values 119889119894for the five pairs in

each block

1198890= 119875(119909119910)minus 119875(119909119910+1)

1198891= 119875(119909119910+2)minus 119875(119909119910+1)

1198892= 119875(119909+1119910)minus 119875(119909119910+1)

1198893= 119875(119909+1119910+1)

minus 119875(119909119910+1)

1198894= 119875(119909+1119910+2)

minus 119875(119909119910+1)

(19)

(4) Use |119889119894| where 119894 = 0 1 2 3 4 to locate suitable range

119877119896in the designed range table Use this range to

calculate number of bits 119905119894 which is hidden in each

pair 119875119875119894 Then calculate the average bits using (16)

(5) Calculate revised difference |1198771198891015840

119894| where

119894 = 0 1 2 3 4 as 1198771198891015840119894is remainder (119889

1198942avg)

(6) Use |1198771198891015840119894| where 119894 = 0 1 2 3 4 to locate suitable 119877

119896in

the designed range table(7) After 119877

119896is located 119897

119896is subtracted from |1198771198891015840

119894| and

1198871015840

119894is obtained in decimal form A binary sequence is

generated from 1198871015840119894with 119905

119894bits where 119905

119894= log2119908119896

Repeat steps (2) through (7) until embedded message isextracted

3 Results

A set of gray scale TIFF images is used for the experimenta-tion This set consists of standard images as well as imagestaken from the camera The standard images are obtainedfrom the ldquothe USC-SIPI image database (httpsipiuscedudatabase)rdquo The images taken from Canon A45 camera

Mathematical Problems in Engineering 7

Table 1 Comparison of hiding capacity (in bytes)

Cover image PVD method [1] TPVD method [3] Gulversquos method [4] Proposed methodCapacity PSNR Capacity PSNR Capacity PSNR Capacity PSNR

Lena 50960 4179 75836 3889 81305 4286 81326 3984Baboon 56291 3790 82407 3393 81766 4199 82933 3962Peppers 50685 4173 75579 3850 81326 4280 81387 4029

Cover imageLenatiff

(a)

Stego-imageLennatiff

(b)

BaboontiffCover image

(c)

BaboontiffStego-image

(d)

Figure 4 Cover and stego images

in JPG format are converted into gray scale tiff format Thetext files are used as secret data Since the proposed algo-rithm use PVD approach to hide information in waveletcoefficients the data hiding capacity and PSNR values ofthe proposed method are compared with PVD method [1]TPVD [3] method and Gulversquos method [4] The comparisonis shown in Table 1The proposedmethod provides increasedhiding capacity and improved PSNR values as comparedto PVD and TPVD method Although the PSNR is less as

compared to Gulversquos [4] method there is an improvement inthe security of secret data

The average payload of the proposed system is sim248 bppThe performance of the proposed method is analyzed usingPSNR Universal Quality Index (119876) and Structural SimilarityIndex Measure (SSIM) 119876 and SSIM are full reference imagequality assessment models and require the cover image tobe available [16 17] Table 2 shows the PSNR values MSEUniversal Quality Index (119876) and Structural Similarity Index

8 Mathematical Problems in Engineering

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Cover image

Lennatiff

(a)

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Stego image

Lennatiff

(b)

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Cover image

Baboontiff

(c)

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Stego imageBaboontiff

(d)

Figure 5 Histograms of cover and stego images

Measure (SSIM) for different images obtained using proposedmethod The PSNR values are above the threshold of 36 dB[18] even after using more than 95 of the hiding capacity ofthe cover image Also Universal Quality Index (119876) values [16]and Structural Similarity Index Measure (SSIM) values [17]are close to 1 which proves that the stego images are visuallyindistinguishable from original cover images

Figure 4 shows the cover image and the correspondingstego images obtained using the proposed method As thefigures show distortions resulted from embedding are imper-ceptible to human vision

Figure 5 shows the histogramof the cover and stego imageobtained using the proposed method From the figure it canbe observed that the shape of the histogram is preserved

The cover image data is subtracted from stego imageand plotted as histogram Figure 6 shows the pixel differencehistogram From the figure it can be observed that there aremore numbers of bins which are close to 0 as compared to

bins which are away from 0 Also the step pattern is notobserved in the figure This confirms that the method isrobust against histogram analysis attack

Histogram of cover image is represented as [ℎ0 ℎ1

ℎ255] whereas histogram of stego image is represented as

[ℎ1015840

0 ℎ1015840

1 ℎ

1015840

255] The change in histogram [19] is measured

by

119863ℎ=

255

sum

119898=1

10038161003816100381610038161003816ℎ1015840

119898minus ℎ119898

10038161003816100381610038161003816 (20)

The proposed method can hide at least 3 bits in eachpair considering the smallest width of the subrange to be 8Figure 7 shows the comparison of the value of 119863

ℎof the 3

bit LSB replacement method and the proposed method withdifferent size of secret data embedded in the cover imageLenatiff It can be observed that difference in histogram forthe proposed method is less than that of 3 bit LSB method

Mathematical Problems in Engineering 9

0 5 10 15 200

05

1

15

2

25

3

Difference values

Occ

urre

nce f

requ

ency

minus20 minus15 minus10 minus5

times104

Cover imageLennatiff

(a)

0 10 20 300

05

1

15

2

25

3

35

Difference values

Occ

urre

nce f

requ

ency

minus30 minus20 minus10

times104

Cover imageBaboontiff

(b)

Figure 6 Difference histogram

Table 2 Hiding capacity PSNR MSE and 119876 index

Coverimage

Resolution of coverimage

Hidingcapacity(Kb)

ofhidingcapacity

Messagefile size(Kb)

PSNR MSE 119876 SSIM

Baboon 256 times 256 1992 3065 195 3987 6684 0959 0965Lena 256 times 256 1994 3068 195 3991 6633 0899 0937Elaine 512 times 512 7942 309 787 4001 6482 0890 0956Baboon 512 times 512 8099 3068 787 3962 7089 0961 0979Lena 512 times 512 7947 3068 787 3984 6740 0806 0953Tank 512 times 512 7941 309 787 3986 6700 0896 0954Peppers 512 times 512 7948 3022 787 4029 6074 0800 0932Barbara 512 times 512 8035 3055 787 3970 6961 0857 0964Boat 512 times 512 7964 3075 787 3990 6652 0883 0962Grass 1024 times 1024 31932 3115 317 3951 7274 0979 0998

The output images are tested under the 119877119878 steganalysis[20] It is observed from Figure 8 that the difference between119877119872

and 119877minus119872

and 119878119872

and 119878minus119872

is very small The rules 119877119872cong

119877minus119872

and 119878119872cong 119878minus119872

are satisfied for the output images Thisproves that the proposed method is secure against 119877119878 attack

4 Conclusion

In steganography hiding capacity of cover image quality ofstego image and security of secret data are three importantfactors There is always a trade-off between data hidingcapacity of cover image and security of secret data Theproposed algorithm provides improvements in the datahiding capacity as well as security of the secret data ascompared to PVD [1] and TPVD [3] methods AlthoughGulversquos [4] method provides better PSNR values as comparedto proposedmethod the proposedmethod improves security

of secret information The secret information is securelyhidden in the coefficients of integer wavelet transform Forthe implementation purpose the four subbands obtainedafter decomposing the cover image by integer wavelet trans-form are arranged as shown in Figure 1 But it is possible toarrange the four subbands in 4 = 24 different ways therebyimproving the security of the steganography system sincethe exact arrangement of four subbands will be known tosender and receiver only The algorithm revises the originaldifference between two wavelet coefficients in the pair andthis revised difference is used for hiding the data in that pairThis makes estimation of exact number of bits hidden in thepair difficult Image steganography techniques hiding textualinformation require 100 accuracy for successful retrieval ofhidden information from stego image If the steganographymethod fails correct estimation of number of bits hidden forsome of the pairs will be a challenge for the invader Thus

10 Mathematical Problems in Engineering

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

10 20 30 40 50 60 70 80

Hist

ogra

m d

iffer

ence

Size of hidden message (KB)

LSBProposed

Figure 7 Histograms comparison of 3 bit LSB substitution andproposed method (Lenatiff)

0

01

02

03

04

10 20 30 40 50 60 70 79

Ratio

of R

S

Message size (KB)

RM SM

RminusMSminusM

Figure 8 119877119878 diagram

one more level of security is imposed to secure the secretinformation

The PSNR values produced by the algorithm are close to395 which are well above the threshold of 36 dB after usingfull hiding capacity of the cover image This proves that thestego images are of good quality Results also show that thedifference between cover image and stego image cannot benoticed by human visual system (HVS)

Considering the fact that there is currently no steganogra-phy system that can resist all the steganalysis attacks the bestway to provide security to the secret data and to eliminate theattack of comparing the original image with the stego image

is to freshly create an image and destroy it after generating thestego image

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D-CWu andW-H Tsai ldquoA steganographic method for imagesby pixel-value differencingrdquo Pattern Recognition Letters vol 24no 9-10 pp 1613ndash1626 2003

[2] H C Wu N I Wu C S Tsai and M-S Hwang ldquoImagesteganographic scheme based on pixel-value differencing andLSB replacementmethodsrdquo IEE ProceedingsmdashVision Image andSignal Processing vol 152 no 5 pp 611ndash615 2005

[3] K-C Chang P S Huang T-M Tu and C-P Chang ldquoAdaptiveimage steganographic scheme based on tri-way pixel-value dif-ferencingrdquo in Proceedings of the IEEE International Conferenceon Systems Man and Cybernetics (SMC rsquo07) pp 1165ndash1170Montreal Canada October 2007

[4] A K Gulve andM S Joshi ldquoAn image steganography algorithmwith five pixel pair differencing and gray code conversionrdquoInternational Journal of Image Graphics and Signal Processingvol 6 no 3 pp 12ndash20 2014

[5] K-C Chang C-P Chang P S Huang and T-M Tu ldquoA novelimage steganographic method using tri-way pixel-value differ-encingrdquo Journal of Multimedia vol 3 no 2 pp 37ndash44 2008

[6] K C Chang P S Huang T M Tu and C P Chang ldquoImagesteganographic scheme using tri-way pixel-value differencingand adaptive rulesrdquo in Proceedings of the IEEE InternationalConference on Intelligent Information Hiding and MultimediaSignal Processing pp 449ndash452 Kaohsiung Taiwan 2007

[7] A K Gulve and M S Joshi ldquoA secured image steganographyalgorithm with five pixel pair differencing by selecting thecommon pixel randomlyrdquo in Proceedings of the 3rd InternationalConference on Computational Intelligence and Information Tech-nology (CIIT rsquo13) pp 55ndash61 Elseveir Mumbai India 2013

[8] A R Calderbank I Daubechies W Sweldens and B-L YeoldquoWavelet transforms that map integers to integersrdquo Applied andComputational Harmonic Analysis vol 5 no 3 pp 332ndash3691998

[9] B Ramalingam R Amirtharajan and J B B Rayappan ldquoStegoon FPGA an IWT approachrdquoThe Scientific World Journal vol2014 Article ID 192512 9 pages 2014

[10] E Ghasemi J Shanbehzadeh and B ZahirAzami ldquoA stegano-graphic method based on Integer Wavelet Transform andGenetic Algorithmrdquo in Proceedings of the International Confer-ence on Communications and Signal Processing (ICCSP rsquo11) pp42ndash45 Calicut India February 2011

[11] E Ghasemi J Shanbehzadeh and N Fassihi ldquoHigh capacityimage steganography using wavelet transform and geneticalgorithmrdquo in Proceedings of the International Multi Conferenceof Engineers and Computer Scientists (IMECS rsquo11) pp 495ndash498Hong Kong March 2011

[12] G Xuan Y Q Shi C Yang Y Zheng D Zou and P ChaildquoLossless data hiding using integer wavelet transform andthreshold embedding techniquerdquo in Proceedings of the IEEEInternational Conference on Multimedia and Expo (ICME rsquo05)pp 1520ndash1523 IEEE Amsterdam The Netherlands July 2005

Mathematical Problems in Engineering 11

[13] R O El Safy H H Zayed and A El Dessouki ldquoAn adaptivesteganographic technique based on integer wavelet transformrdquoin Proceedings of the International Conference on Networkingand Media Convergence (ICNM rsquo09) pp 111ndash117 Cairo EgyptMarch 2009

[14] S Archana A Judice and K P Kaliyamurthie ldquoA novelapproach on image steganographic methods for optimum hid-ing capacityrdquo International Journal of Engineering and ComputerScience vol 2 no 2 pp 378ndash385 2013

[15] A K Al-Asmari M A Al-Qodah and A S Salama ldquoWavelet-pixel value differencing technique for digital images data hid-ingrdquo in Proceedings of the IEEE International Conference onSystem Engineering and Technology (ICSET rsquo11) pp 15ndash18 June2011

[16] Z Wang and A C Bovik ldquoA universal image quality indexrdquoIEEE Signal Processing Letters vol 9 no 3 pp 81ndash84 2002

[17] ZWang A C Bovik H R Sheikh and E P Simoncelli ldquoImagequality assessment from error visibility to structural similarityrdquoIEEE Transactions on Image Processing vol 13 no 4 pp 600ndash612 2004

[18] N I Wu andM S Hwang ldquoData hiding current status and keyissuesrdquo International Journal of Network Security vol 4 no 1pp 1ndash9 2007

[19] X Zhang and S Wang ldquoEfficient data hiding with histogram-preserving propertyrdquo Telecommunication Systems vol 49 no 2pp 179ndash185 2012

[20] J FridrichMGoljan andRDu ldquoDetecting LSB steganographyin color and gray-scale imagesrdquo IEEEMultimediaMagazine vol8 no 4 pp 22ndash28 2001

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Page 5: Research Article An Image Steganography Method Hiding ...downloads.hindawi.com/journals/mpe/2015/684824.pdf · An Image Steganography Method Hiding Secret Data into Coefficients of

Mathematical Problems in Engineering 5

PX0

PX3

PX1

PX4

PX2

PX5

P(xy) P(xy+1)P(xy+2)

P(x+1y) P(x+1y+1) P(x+1y+2)

Figure 3 Pixel block

coefficients PX0 PX2 PX3 PX4 and PX

5 The five pairs 119875119875

119894

where 119894 = 0 1 2 3 4 are as shown below

1198751198750= (119875(119909119910+1) 119875(119909119910))

1198751198751= (119875(119909119910+1) 119875(119909119910+2))

1198751198752= (119875(119909119910+1) 119875(119909+1119910))

1198751198753= (119875(119909119910+1) 119875(119909+1119910+1)

)

1198751198754= (119875(119909119910+1) 119875(119909+1119910+2)

)

(14)

The difference value 119889119894is calculated for each pair 119875119875

119894by

subtracting the common wavelet coefficient PX1from the

other wavelet coefficient in that pair This difference value isused to identify the corresponding range 119877

119896119894from the range

table119877The range table is designed with ranges [0ndash7] [8ndash15][16ndash31] [32ndash63] [64ndash127] and [128ndash255] The width 119882

119896119894

of range 119877119896119894

is used to determine the number of bits 119905119894(119905119894=

log2119882119896119894) that can be hidden in each pair where 119894 = 0 1 2 3 4

This 119905119894is then used to calculate the average value (119873) of

number of bits possible to be hidden in each pair of the blockThe average value119873 is used to calculate the revised difference119877119889119894as 119877119889119894is remainder (119889

1198942119873) so that 119877119889

119894le 2119873 where 119889

119894is

the original differenceThe offset difference OD119894is calculated

as |119889119894|minus |119877119889

119894| for each pair in the blockThe revised difference

|119877119889119894| is then used to determine the number of bits 119905

119894for each

pair in the block Thus if the original difference value |119889119894|

allows 119872 bits to be hidden in the pair then the proposedapproach hides bits le 119873 in that pair [4 7]

After embedding 119905119894bits of the message in the pair new

difference 1198891015840119894is calculated as OD

119894+119897119896119894+119887where 119897

119896119894represents

lower boundary of the range 119877119896119894

in the range table 119877 and 119887represents the decimal equivalent of 119905

119894message bits hidden in

that pairEmbedding 119905

119894bits in the pair modifies the values of

both the wavelet coefficients in the pair The new valuesof wavelet coefficients in each pair are different from theiroriginal values Since new value is assigned to commonwavelet coefficient PX

1in each pair five different values are

obtained for the common wavelet coefficient PX1 However

the common wavelet coefficient PX1can have only one value

in each bock This requires values of other five waveletcoefficients PX

0 PX2 PX3 PX4 and PX

5to be adjusted such

that the new difference 1198891015840119894remains unchanged Therefore

the pair having new values of wavelet coefficients close totheir original values is selected as the reference pair To find

the reference pair the difference 119898 between 119889119894and 1198891015840

119894is

calculated Small value of |119898| indicates that the newdifferencevalue 1198891015840

119894is close to the original difference value 119889

119894 Thus

for the pair with minimum |119898| the new values of waveletcoefficients are close to their original values So the pair withminimum |119898| is selected as the reference pair The values ofthe two wavelet coefficients in the reference pair are used toadjust the values of wavelet coefficients in other pairs andconstruct a new 2times3 blockThe embedded secret informationin newly constructed block is unaffected because differencevalues for the pairs are unaltered [4 7]

During the extraction process average value (119873) iscalculated using the same process adopted during embeddingof the secret messageThe average value119873 is used to calculatethe revised difference 1198771198891015840

119894as 1198771198891015840

119894is remainder (119889

1198942119873) Suit-

able range 119877119896119894 is identified using this revised difference Thesecretmessage is extracted in the decimal formby subtracting119897119896from |1198771198891015840

119894| Secret message is then converted into a binary

stream with 119905119894(119905119894= log2119882119896119894) bits [4 7]

The process of hiding secret information in the coverimage is described below [4 7]

(1) Create the 2D array as shown in (12) by preprocessingthe gray scale cover image

(2) Partition the array into nonoverlapping blocks of 2times3wavelet coefficients and group wavelet coefficient PX

1

with the remaining wavelet coefficients in the block toform five pairs

(3) Calculate the difference values 119889119894for the five pairs in

each block

1198890= 119875(119909119910)minus 119875(119909119910+1)

1198891= 119875(119909119910+2)minus 119875(119909119910+1)

1198892= 119875(119909+1119910)minus 119875(119909119910+1)

1198893= 119875(119909+1119910+1)

minus 119875(119909119910+1)

1198894= 119875(119909+1119910+2)

minus 119875(119909119910+1)

(15)

(4) Use |119889119894| where 119894 = 0 1 2 3 4 to locate suitable range

119877119896in the designed range table Use this range to

calculate number of bits 119905119894that can be hidden in each

pair 119875119875119894 Then calculate the average bits using

avg = lfloor(sum4

119894=0119905119894

5)rfloor (16)

(5) Calculate the revised difference |119877119889119894| where 119894 =

0 1 2 3 4 as119877119889119894is remainder (119889

1198942avg) so that119877119889

119894lt=

2avg

(6) Calculate the difference OD119894as OD

119894= |119889119894| minus |119877119889

119894| for

each pair

(7) Use |119877119889119894|where 119894 = 0 1 2 3 4 to locate suitable range

119877119896in the designed range table

6 Mathematical Problems in Engineering

(8) Compute the number of bits 119905119894that can be embedded

in each pair using the corresponding range given by119877119896 The value 119905

119894can be estimated from the width 119908

119896

of 119877119896 which is given by 119905

119894= log2119908119896where width119908

119896=

119906119896minus119897119896+1 and119906

119896and 119897119896are upper and lower boundaries

of the range 119877119896

(9) Read 119905119894bits from the binary secret data

(10) Calculate the new difference value 1198891015840119894given by

1198891015840

119894= OD

119894+ 119897119896119894+ 119887119894 if 119889

119894ge 0

1198891015840

119894= minus (OD

119894+ 119897119896119894+ 119887119894) if 119889

119894lt 0

(17)

(11) Modify the values of wavelet coefficients in the pair119875119875119894using

(1198751015840

119899 1198751015840

119899+1) = (119875

119899minus lceil119898

2rceil 119875119899+1+ lfloor119898

2rfloor) (18)

where 119875119899and 119875

119899+1represent two wavelet coefficients

in the pair 119875119875119894and 119898 is obtained by subtracting 119889

119894

from 1198891015840119894

(12) Select the pair with minimum |119898| as the optimalreference pair and use this pair to adjust the values ofwavelet coefficients of the other four pairs The valueof the common wavelet coefficient is given by 1198751015840

119899of

the reference pair Modify value of another waveletcoefficient 1198751015840

119899+1of remaining four pairs such that

the new difference 1198891015840119894will remain unchanged Thus

new values are assigned to remaining four waveletcoefficients in the block

(13) Check the new values of wavelet coefficients for fall-off boundaries that is check whether all the valuesare within the range from 0 to 255 If not modify thevalues preserving the difference between the values oftwo wavelet coefficients of each pair in the block

(a) Find out the smallest of all the wavelet coeffi-cients If the smallest is less than 0 then add|smallest| in all the wavelet coefficients in thatblock

(b) Find out the largest of all the wavelet coeffi-cients If the largest is greater than 255 subtractlargest minus 255 from all the wavelet coefficients inthat block

(c) If fall-off boundary problems still exist thecover image is not suitable for hiding secretinformation

(14) Now reconstruct the block from all pairs with modi-fied values of wavelet coefficients

(15) Repeat steps (2) through (14) until the secret informa-tion is embedded in the cover image

23 Postprocessing After the embedding process is overoriginal signs are assigned to the elements of 2D array usingthe sign matrix created during preprocessing phase This is

accomplished by one to one comparison of elements of 2Darray with the elements of 2D sign matrix The 2D array isthen split to obtain the four subbands Using inverse 2DHaarinteger wavelet transform the four subbands are combined toobtain the stego image of size [119872119873] All the pixel values ofthe stego image in the range from 0 to 255 indicate that secretdata is safely hidden and can be extracted accurately

24 Extraction Process The extraction process is blind Itdoes not require the existence of cover image for extractinghidden secret data from the stego image The stego image ispreprocessed to obtain the 2D array as shown in (12) Theprocess of extraction of secret information from the stegoimage is described below [4 7]

(1) Create the 2D array as shown in (12) by preprocessingthe gray scale stego image

(2) Partition the array into nonoverlapping blocks of 2times 3wavelet coefficients and group wavelet coefficient PX

1

with the remaining wavelet coefficients in the block toform five pairs Keep the partition order the same asthat of the embedding

(3) Calculate the difference values 119889119894for the five pairs in

each block

1198890= 119875(119909119910)minus 119875(119909119910+1)

1198891= 119875(119909119910+2)minus 119875(119909119910+1)

1198892= 119875(119909+1119910)minus 119875(119909119910+1)

1198893= 119875(119909+1119910+1)

minus 119875(119909119910+1)

1198894= 119875(119909+1119910+2)

minus 119875(119909119910+1)

(19)

(4) Use |119889119894| where 119894 = 0 1 2 3 4 to locate suitable range

119877119896in the designed range table Use this range to

calculate number of bits 119905119894 which is hidden in each

pair 119875119875119894 Then calculate the average bits using (16)

(5) Calculate revised difference |1198771198891015840

119894| where

119894 = 0 1 2 3 4 as 1198771198891015840119894is remainder (119889

1198942avg)

(6) Use |1198771198891015840119894| where 119894 = 0 1 2 3 4 to locate suitable 119877

119896in

the designed range table(7) After 119877

119896is located 119897

119896is subtracted from |1198771198891015840

119894| and

1198871015840

119894is obtained in decimal form A binary sequence is

generated from 1198871015840119894with 119905

119894bits where 119905

119894= log2119908119896

Repeat steps (2) through (7) until embedded message isextracted

3 Results

A set of gray scale TIFF images is used for the experimenta-tion This set consists of standard images as well as imagestaken from the camera The standard images are obtainedfrom the ldquothe USC-SIPI image database (httpsipiuscedudatabase)rdquo The images taken from Canon A45 camera

Mathematical Problems in Engineering 7

Table 1 Comparison of hiding capacity (in bytes)

Cover image PVD method [1] TPVD method [3] Gulversquos method [4] Proposed methodCapacity PSNR Capacity PSNR Capacity PSNR Capacity PSNR

Lena 50960 4179 75836 3889 81305 4286 81326 3984Baboon 56291 3790 82407 3393 81766 4199 82933 3962Peppers 50685 4173 75579 3850 81326 4280 81387 4029

Cover imageLenatiff

(a)

Stego-imageLennatiff

(b)

BaboontiffCover image

(c)

BaboontiffStego-image

(d)

Figure 4 Cover and stego images

in JPG format are converted into gray scale tiff format Thetext files are used as secret data Since the proposed algo-rithm use PVD approach to hide information in waveletcoefficients the data hiding capacity and PSNR values ofthe proposed method are compared with PVD method [1]TPVD [3] method and Gulversquos method [4] The comparisonis shown in Table 1The proposedmethod provides increasedhiding capacity and improved PSNR values as comparedto PVD and TPVD method Although the PSNR is less as

compared to Gulversquos [4] method there is an improvement inthe security of secret data

The average payload of the proposed system is sim248 bppThe performance of the proposed method is analyzed usingPSNR Universal Quality Index (119876) and Structural SimilarityIndex Measure (SSIM) 119876 and SSIM are full reference imagequality assessment models and require the cover image tobe available [16 17] Table 2 shows the PSNR values MSEUniversal Quality Index (119876) and Structural Similarity Index

8 Mathematical Problems in Engineering

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Cover image

Lennatiff

(a)

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Stego image

Lennatiff

(b)

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Cover image

Baboontiff

(c)

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Stego imageBaboontiff

(d)

Figure 5 Histograms of cover and stego images

Measure (SSIM) for different images obtained using proposedmethod The PSNR values are above the threshold of 36 dB[18] even after using more than 95 of the hiding capacity ofthe cover image Also Universal Quality Index (119876) values [16]and Structural Similarity Index Measure (SSIM) values [17]are close to 1 which proves that the stego images are visuallyindistinguishable from original cover images

Figure 4 shows the cover image and the correspondingstego images obtained using the proposed method As thefigures show distortions resulted from embedding are imper-ceptible to human vision

Figure 5 shows the histogramof the cover and stego imageobtained using the proposed method From the figure it canbe observed that the shape of the histogram is preserved

The cover image data is subtracted from stego imageand plotted as histogram Figure 6 shows the pixel differencehistogram From the figure it can be observed that there aremore numbers of bins which are close to 0 as compared to

bins which are away from 0 Also the step pattern is notobserved in the figure This confirms that the method isrobust against histogram analysis attack

Histogram of cover image is represented as [ℎ0 ℎ1

ℎ255] whereas histogram of stego image is represented as

[ℎ1015840

0 ℎ1015840

1 ℎ

1015840

255] The change in histogram [19] is measured

by

119863ℎ=

255

sum

119898=1

10038161003816100381610038161003816ℎ1015840

119898minus ℎ119898

10038161003816100381610038161003816 (20)

The proposed method can hide at least 3 bits in eachpair considering the smallest width of the subrange to be 8Figure 7 shows the comparison of the value of 119863

ℎof the 3

bit LSB replacement method and the proposed method withdifferent size of secret data embedded in the cover imageLenatiff It can be observed that difference in histogram forthe proposed method is less than that of 3 bit LSB method

Mathematical Problems in Engineering 9

0 5 10 15 200

05

1

15

2

25

3

Difference values

Occ

urre

nce f

requ

ency

minus20 minus15 minus10 minus5

times104

Cover imageLennatiff

(a)

0 10 20 300

05

1

15

2

25

3

35

Difference values

Occ

urre

nce f

requ

ency

minus30 minus20 minus10

times104

Cover imageBaboontiff

(b)

Figure 6 Difference histogram

Table 2 Hiding capacity PSNR MSE and 119876 index

Coverimage

Resolution of coverimage

Hidingcapacity(Kb)

ofhidingcapacity

Messagefile size(Kb)

PSNR MSE 119876 SSIM

Baboon 256 times 256 1992 3065 195 3987 6684 0959 0965Lena 256 times 256 1994 3068 195 3991 6633 0899 0937Elaine 512 times 512 7942 309 787 4001 6482 0890 0956Baboon 512 times 512 8099 3068 787 3962 7089 0961 0979Lena 512 times 512 7947 3068 787 3984 6740 0806 0953Tank 512 times 512 7941 309 787 3986 6700 0896 0954Peppers 512 times 512 7948 3022 787 4029 6074 0800 0932Barbara 512 times 512 8035 3055 787 3970 6961 0857 0964Boat 512 times 512 7964 3075 787 3990 6652 0883 0962Grass 1024 times 1024 31932 3115 317 3951 7274 0979 0998

The output images are tested under the 119877119878 steganalysis[20] It is observed from Figure 8 that the difference between119877119872

and 119877minus119872

and 119878119872

and 119878minus119872

is very small The rules 119877119872cong

119877minus119872

and 119878119872cong 119878minus119872

are satisfied for the output images Thisproves that the proposed method is secure against 119877119878 attack

4 Conclusion

In steganography hiding capacity of cover image quality ofstego image and security of secret data are three importantfactors There is always a trade-off between data hidingcapacity of cover image and security of secret data Theproposed algorithm provides improvements in the datahiding capacity as well as security of the secret data ascompared to PVD [1] and TPVD [3] methods AlthoughGulversquos [4] method provides better PSNR values as comparedto proposedmethod the proposedmethod improves security

of secret information The secret information is securelyhidden in the coefficients of integer wavelet transform Forthe implementation purpose the four subbands obtainedafter decomposing the cover image by integer wavelet trans-form are arranged as shown in Figure 1 But it is possible toarrange the four subbands in 4 = 24 different ways therebyimproving the security of the steganography system sincethe exact arrangement of four subbands will be known tosender and receiver only The algorithm revises the originaldifference between two wavelet coefficients in the pair andthis revised difference is used for hiding the data in that pairThis makes estimation of exact number of bits hidden in thepair difficult Image steganography techniques hiding textualinformation require 100 accuracy for successful retrieval ofhidden information from stego image If the steganographymethod fails correct estimation of number of bits hidden forsome of the pairs will be a challenge for the invader Thus

10 Mathematical Problems in Engineering

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

10 20 30 40 50 60 70 80

Hist

ogra

m d

iffer

ence

Size of hidden message (KB)

LSBProposed

Figure 7 Histograms comparison of 3 bit LSB substitution andproposed method (Lenatiff)

0

01

02

03

04

10 20 30 40 50 60 70 79

Ratio

of R

S

Message size (KB)

RM SM

RminusMSminusM

Figure 8 119877119878 diagram

one more level of security is imposed to secure the secretinformation

The PSNR values produced by the algorithm are close to395 which are well above the threshold of 36 dB after usingfull hiding capacity of the cover image This proves that thestego images are of good quality Results also show that thedifference between cover image and stego image cannot benoticed by human visual system (HVS)

Considering the fact that there is currently no steganogra-phy system that can resist all the steganalysis attacks the bestway to provide security to the secret data and to eliminate theattack of comparing the original image with the stego image

is to freshly create an image and destroy it after generating thestego image

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D-CWu andW-H Tsai ldquoA steganographic method for imagesby pixel-value differencingrdquo Pattern Recognition Letters vol 24no 9-10 pp 1613ndash1626 2003

[2] H C Wu N I Wu C S Tsai and M-S Hwang ldquoImagesteganographic scheme based on pixel-value differencing andLSB replacementmethodsrdquo IEE ProceedingsmdashVision Image andSignal Processing vol 152 no 5 pp 611ndash615 2005

[3] K-C Chang P S Huang T-M Tu and C-P Chang ldquoAdaptiveimage steganographic scheme based on tri-way pixel-value dif-ferencingrdquo in Proceedings of the IEEE International Conferenceon Systems Man and Cybernetics (SMC rsquo07) pp 1165ndash1170Montreal Canada October 2007

[4] A K Gulve andM S Joshi ldquoAn image steganography algorithmwith five pixel pair differencing and gray code conversionrdquoInternational Journal of Image Graphics and Signal Processingvol 6 no 3 pp 12ndash20 2014

[5] K-C Chang C-P Chang P S Huang and T-M Tu ldquoA novelimage steganographic method using tri-way pixel-value differ-encingrdquo Journal of Multimedia vol 3 no 2 pp 37ndash44 2008

[6] K C Chang P S Huang T M Tu and C P Chang ldquoImagesteganographic scheme using tri-way pixel-value differencingand adaptive rulesrdquo in Proceedings of the IEEE InternationalConference on Intelligent Information Hiding and MultimediaSignal Processing pp 449ndash452 Kaohsiung Taiwan 2007

[7] A K Gulve and M S Joshi ldquoA secured image steganographyalgorithm with five pixel pair differencing by selecting thecommon pixel randomlyrdquo in Proceedings of the 3rd InternationalConference on Computational Intelligence and Information Tech-nology (CIIT rsquo13) pp 55ndash61 Elseveir Mumbai India 2013

[8] A R Calderbank I Daubechies W Sweldens and B-L YeoldquoWavelet transforms that map integers to integersrdquo Applied andComputational Harmonic Analysis vol 5 no 3 pp 332ndash3691998

[9] B Ramalingam R Amirtharajan and J B B Rayappan ldquoStegoon FPGA an IWT approachrdquoThe Scientific World Journal vol2014 Article ID 192512 9 pages 2014

[10] E Ghasemi J Shanbehzadeh and B ZahirAzami ldquoA stegano-graphic method based on Integer Wavelet Transform andGenetic Algorithmrdquo in Proceedings of the International Confer-ence on Communications and Signal Processing (ICCSP rsquo11) pp42ndash45 Calicut India February 2011

[11] E Ghasemi J Shanbehzadeh and N Fassihi ldquoHigh capacityimage steganography using wavelet transform and geneticalgorithmrdquo in Proceedings of the International Multi Conferenceof Engineers and Computer Scientists (IMECS rsquo11) pp 495ndash498Hong Kong March 2011

[12] G Xuan Y Q Shi C Yang Y Zheng D Zou and P ChaildquoLossless data hiding using integer wavelet transform andthreshold embedding techniquerdquo in Proceedings of the IEEEInternational Conference on Multimedia and Expo (ICME rsquo05)pp 1520ndash1523 IEEE Amsterdam The Netherlands July 2005

Mathematical Problems in Engineering 11

[13] R O El Safy H H Zayed and A El Dessouki ldquoAn adaptivesteganographic technique based on integer wavelet transformrdquoin Proceedings of the International Conference on Networkingand Media Convergence (ICNM rsquo09) pp 111ndash117 Cairo EgyptMarch 2009

[14] S Archana A Judice and K P Kaliyamurthie ldquoA novelapproach on image steganographic methods for optimum hid-ing capacityrdquo International Journal of Engineering and ComputerScience vol 2 no 2 pp 378ndash385 2013

[15] A K Al-Asmari M A Al-Qodah and A S Salama ldquoWavelet-pixel value differencing technique for digital images data hid-ingrdquo in Proceedings of the IEEE International Conference onSystem Engineering and Technology (ICSET rsquo11) pp 15ndash18 June2011

[16] Z Wang and A C Bovik ldquoA universal image quality indexrdquoIEEE Signal Processing Letters vol 9 no 3 pp 81ndash84 2002

[17] ZWang A C Bovik H R Sheikh and E P Simoncelli ldquoImagequality assessment from error visibility to structural similarityrdquoIEEE Transactions on Image Processing vol 13 no 4 pp 600ndash612 2004

[18] N I Wu andM S Hwang ldquoData hiding current status and keyissuesrdquo International Journal of Network Security vol 4 no 1pp 1ndash9 2007

[19] X Zhang and S Wang ldquoEfficient data hiding with histogram-preserving propertyrdquo Telecommunication Systems vol 49 no 2pp 179ndash185 2012

[20] J FridrichMGoljan andRDu ldquoDetecting LSB steganographyin color and gray-scale imagesrdquo IEEEMultimediaMagazine vol8 no 4 pp 22ndash28 2001

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Page 6: Research Article An Image Steganography Method Hiding ...downloads.hindawi.com/journals/mpe/2015/684824.pdf · An Image Steganography Method Hiding Secret Data into Coefficients of

6 Mathematical Problems in Engineering

(8) Compute the number of bits 119905119894that can be embedded

in each pair using the corresponding range given by119877119896 The value 119905

119894can be estimated from the width 119908

119896

of 119877119896 which is given by 119905

119894= log2119908119896where width119908

119896=

119906119896minus119897119896+1 and119906

119896and 119897119896are upper and lower boundaries

of the range 119877119896

(9) Read 119905119894bits from the binary secret data

(10) Calculate the new difference value 1198891015840119894given by

1198891015840

119894= OD

119894+ 119897119896119894+ 119887119894 if 119889

119894ge 0

1198891015840

119894= minus (OD

119894+ 119897119896119894+ 119887119894) if 119889

119894lt 0

(17)

(11) Modify the values of wavelet coefficients in the pair119875119875119894using

(1198751015840

119899 1198751015840

119899+1) = (119875

119899minus lceil119898

2rceil 119875119899+1+ lfloor119898

2rfloor) (18)

where 119875119899and 119875

119899+1represent two wavelet coefficients

in the pair 119875119875119894and 119898 is obtained by subtracting 119889

119894

from 1198891015840119894

(12) Select the pair with minimum |119898| as the optimalreference pair and use this pair to adjust the values ofwavelet coefficients of the other four pairs The valueof the common wavelet coefficient is given by 1198751015840

119899of

the reference pair Modify value of another waveletcoefficient 1198751015840

119899+1of remaining four pairs such that

the new difference 1198891015840119894will remain unchanged Thus

new values are assigned to remaining four waveletcoefficients in the block

(13) Check the new values of wavelet coefficients for fall-off boundaries that is check whether all the valuesare within the range from 0 to 255 If not modify thevalues preserving the difference between the values oftwo wavelet coefficients of each pair in the block

(a) Find out the smallest of all the wavelet coeffi-cients If the smallest is less than 0 then add|smallest| in all the wavelet coefficients in thatblock

(b) Find out the largest of all the wavelet coeffi-cients If the largest is greater than 255 subtractlargest minus 255 from all the wavelet coefficients inthat block

(c) If fall-off boundary problems still exist thecover image is not suitable for hiding secretinformation

(14) Now reconstruct the block from all pairs with modi-fied values of wavelet coefficients

(15) Repeat steps (2) through (14) until the secret informa-tion is embedded in the cover image

23 Postprocessing After the embedding process is overoriginal signs are assigned to the elements of 2D array usingthe sign matrix created during preprocessing phase This is

accomplished by one to one comparison of elements of 2Darray with the elements of 2D sign matrix The 2D array isthen split to obtain the four subbands Using inverse 2DHaarinteger wavelet transform the four subbands are combined toobtain the stego image of size [119872119873] All the pixel values ofthe stego image in the range from 0 to 255 indicate that secretdata is safely hidden and can be extracted accurately

24 Extraction Process The extraction process is blind Itdoes not require the existence of cover image for extractinghidden secret data from the stego image The stego image ispreprocessed to obtain the 2D array as shown in (12) Theprocess of extraction of secret information from the stegoimage is described below [4 7]

(1) Create the 2D array as shown in (12) by preprocessingthe gray scale stego image

(2) Partition the array into nonoverlapping blocks of 2times 3wavelet coefficients and group wavelet coefficient PX

1

with the remaining wavelet coefficients in the block toform five pairs Keep the partition order the same asthat of the embedding

(3) Calculate the difference values 119889119894for the five pairs in

each block

1198890= 119875(119909119910)minus 119875(119909119910+1)

1198891= 119875(119909119910+2)minus 119875(119909119910+1)

1198892= 119875(119909+1119910)minus 119875(119909119910+1)

1198893= 119875(119909+1119910+1)

minus 119875(119909119910+1)

1198894= 119875(119909+1119910+2)

minus 119875(119909119910+1)

(19)

(4) Use |119889119894| where 119894 = 0 1 2 3 4 to locate suitable range

119877119896in the designed range table Use this range to

calculate number of bits 119905119894 which is hidden in each

pair 119875119875119894 Then calculate the average bits using (16)

(5) Calculate revised difference |1198771198891015840

119894| where

119894 = 0 1 2 3 4 as 1198771198891015840119894is remainder (119889

1198942avg)

(6) Use |1198771198891015840119894| where 119894 = 0 1 2 3 4 to locate suitable 119877

119896in

the designed range table(7) After 119877

119896is located 119897

119896is subtracted from |1198771198891015840

119894| and

1198871015840

119894is obtained in decimal form A binary sequence is

generated from 1198871015840119894with 119905

119894bits where 119905

119894= log2119908119896

Repeat steps (2) through (7) until embedded message isextracted

3 Results

A set of gray scale TIFF images is used for the experimenta-tion This set consists of standard images as well as imagestaken from the camera The standard images are obtainedfrom the ldquothe USC-SIPI image database (httpsipiuscedudatabase)rdquo The images taken from Canon A45 camera

Mathematical Problems in Engineering 7

Table 1 Comparison of hiding capacity (in bytes)

Cover image PVD method [1] TPVD method [3] Gulversquos method [4] Proposed methodCapacity PSNR Capacity PSNR Capacity PSNR Capacity PSNR

Lena 50960 4179 75836 3889 81305 4286 81326 3984Baboon 56291 3790 82407 3393 81766 4199 82933 3962Peppers 50685 4173 75579 3850 81326 4280 81387 4029

Cover imageLenatiff

(a)

Stego-imageLennatiff

(b)

BaboontiffCover image

(c)

BaboontiffStego-image

(d)

Figure 4 Cover and stego images

in JPG format are converted into gray scale tiff format Thetext files are used as secret data Since the proposed algo-rithm use PVD approach to hide information in waveletcoefficients the data hiding capacity and PSNR values ofthe proposed method are compared with PVD method [1]TPVD [3] method and Gulversquos method [4] The comparisonis shown in Table 1The proposedmethod provides increasedhiding capacity and improved PSNR values as comparedto PVD and TPVD method Although the PSNR is less as

compared to Gulversquos [4] method there is an improvement inthe security of secret data

The average payload of the proposed system is sim248 bppThe performance of the proposed method is analyzed usingPSNR Universal Quality Index (119876) and Structural SimilarityIndex Measure (SSIM) 119876 and SSIM are full reference imagequality assessment models and require the cover image tobe available [16 17] Table 2 shows the PSNR values MSEUniversal Quality Index (119876) and Structural Similarity Index

8 Mathematical Problems in Engineering

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Cover image

Lennatiff

(a)

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Stego image

Lennatiff

(b)

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Cover image

Baboontiff

(c)

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Stego imageBaboontiff

(d)

Figure 5 Histograms of cover and stego images

Measure (SSIM) for different images obtained using proposedmethod The PSNR values are above the threshold of 36 dB[18] even after using more than 95 of the hiding capacity ofthe cover image Also Universal Quality Index (119876) values [16]and Structural Similarity Index Measure (SSIM) values [17]are close to 1 which proves that the stego images are visuallyindistinguishable from original cover images

Figure 4 shows the cover image and the correspondingstego images obtained using the proposed method As thefigures show distortions resulted from embedding are imper-ceptible to human vision

Figure 5 shows the histogramof the cover and stego imageobtained using the proposed method From the figure it canbe observed that the shape of the histogram is preserved

The cover image data is subtracted from stego imageand plotted as histogram Figure 6 shows the pixel differencehistogram From the figure it can be observed that there aremore numbers of bins which are close to 0 as compared to

bins which are away from 0 Also the step pattern is notobserved in the figure This confirms that the method isrobust against histogram analysis attack

Histogram of cover image is represented as [ℎ0 ℎ1

ℎ255] whereas histogram of stego image is represented as

[ℎ1015840

0 ℎ1015840

1 ℎ

1015840

255] The change in histogram [19] is measured

by

119863ℎ=

255

sum

119898=1

10038161003816100381610038161003816ℎ1015840

119898minus ℎ119898

10038161003816100381610038161003816 (20)

The proposed method can hide at least 3 bits in eachpair considering the smallest width of the subrange to be 8Figure 7 shows the comparison of the value of 119863

ℎof the 3

bit LSB replacement method and the proposed method withdifferent size of secret data embedded in the cover imageLenatiff It can be observed that difference in histogram forthe proposed method is less than that of 3 bit LSB method

Mathematical Problems in Engineering 9

0 5 10 15 200

05

1

15

2

25

3

Difference values

Occ

urre

nce f

requ

ency

minus20 minus15 minus10 minus5

times104

Cover imageLennatiff

(a)

0 10 20 300

05

1

15

2

25

3

35

Difference values

Occ

urre

nce f

requ

ency

minus30 minus20 minus10

times104

Cover imageBaboontiff

(b)

Figure 6 Difference histogram

Table 2 Hiding capacity PSNR MSE and 119876 index

Coverimage

Resolution of coverimage

Hidingcapacity(Kb)

ofhidingcapacity

Messagefile size(Kb)

PSNR MSE 119876 SSIM

Baboon 256 times 256 1992 3065 195 3987 6684 0959 0965Lena 256 times 256 1994 3068 195 3991 6633 0899 0937Elaine 512 times 512 7942 309 787 4001 6482 0890 0956Baboon 512 times 512 8099 3068 787 3962 7089 0961 0979Lena 512 times 512 7947 3068 787 3984 6740 0806 0953Tank 512 times 512 7941 309 787 3986 6700 0896 0954Peppers 512 times 512 7948 3022 787 4029 6074 0800 0932Barbara 512 times 512 8035 3055 787 3970 6961 0857 0964Boat 512 times 512 7964 3075 787 3990 6652 0883 0962Grass 1024 times 1024 31932 3115 317 3951 7274 0979 0998

The output images are tested under the 119877119878 steganalysis[20] It is observed from Figure 8 that the difference between119877119872

and 119877minus119872

and 119878119872

and 119878minus119872

is very small The rules 119877119872cong

119877minus119872

and 119878119872cong 119878minus119872

are satisfied for the output images Thisproves that the proposed method is secure against 119877119878 attack

4 Conclusion

In steganography hiding capacity of cover image quality ofstego image and security of secret data are three importantfactors There is always a trade-off between data hidingcapacity of cover image and security of secret data Theproposed algorithm provides improvements in the datahiding capacity as well as security of the secret data ascompared to PVD [1] and TPVD [3] methods AlthoughGulversquos [4] method provides better PSNR values as comparedto proposedmethod the proposedmethod improves security

of secret information The secret information is securelyhidden in the coefficients of integer wavelet transform Forthe implementation purpose the four subbands obtainedafter decomposing the cover image by integer wavelet trans-form are arranged as shown in Figure 1 But it is possible toarrange the four subbands in 4 = 24 different ways therebyimproving the security of the steganography system sincethe exact arrangement of four subbands will be known tosender and receiver only The algorithm revises the originaldifference between two wavelet coefficients in the pair andthis revised difference is used for hiding the data in that pairThis makes estimation of exact number of bits hidden in thepair difficult Image steganography techniques hiding textualinformation require 100 accuracy for successful retrieval ofhidden information from stego image If the steganographymethod fails correct estimation of number of bits hidden forsome of the pairs will be a challenge for the invader Thus

10 Mathematical Problems in Engineering

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

10 20 30 40 50 60 70 80

Hist

ogra

m d

iffer

ence

Size of hidden message (KB)

LSBProposed

Figure 7 Histograms comparison of 3 bit LSB substitution andproposed method (Lenatiff)

0

01

02

03

04

10 20 30 40 50 60 70 79

Ratio

of R

S

Message size (KB)

RM SM

RminusMSminusM

Figure 8 119877119878 diagram

one more level of security is imposed to secure the secretinformation

The PSNR values produced by the algorithm are close to395 which are well above the threshold of 36 dB after usingfull hiding capacity of the cover image This proves that thestego images are of good quality Results also show that thedifference between cover image and stego image cannot benoticed by human visual system (HVS)

Considering the fact that there is currently no steganogra-phy system that can resist all the steganalysis attacks the bestway to provide security to the secret data and to eliminate theattack of comparing the original image with the stego image

is to freshly create an image and destroy it after generating thestego image

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D-CWu andW-H Tsai ldquoA steganographic method for imagesby pixel-value differencingrdquo Pattern Recognition Letters vol 24no 9-10 pp 1613ndash1626 2003

[2] H C Wu N I Wu C S Tsai and M-S Hwang ldquoImagesteganographic scheme based on pixel-value differencing andLSB replacementmethodsrdquo IEE ProceedingsmdashVision Image andSignal Processing vol 152 no 5 pp 611ndash615 2005

[3] K-C Chang P S Huang T-M Tu and C-P Chang ldquoAdaptiveimage steganographic scheme based on tri-way pixel-value dif-ferencingrdquo in Proceedings of the IEEE International Conferenceon Systems Man and Cybernetics (SMC rsquo07) pp 1165ndash1170Montreal Canada October 2007

[4] A K Gulve andM S Joshi ldquoAn image steganography algorithmwith five pixel pair differencing and gray code conversionrdquoInternational Journal of Image Graphics and Signal Processingvol 6 no 3 pp 12ndash20 2014

[5] K-C Chang C-P Chang P S Huang and T-M Tu ldquoA novelimage steganographic method using tri-way pixel-value differ-encingrdquo Journal of Multimedia vol 3 no 2 pp 37ndash44 2008

[6] K C Chang P S Huang T M Tu and C P Chang ldquoImagesteganographic scheme using tri-way pixel-value differencingand adaptive rulesrdquo in Proceedings of the IEEE InternationalConference on Intelligent Information Hiding and MultimediaSignal Processing pp 449ndash452 Kaohsiung Taiwan 2007

[7] A K Gulve and M S Joshi ldquoA secured image steganographyalgorithm with five pixel pair differencing by selecting thecommon pixel randomlyrdquo in Proceedings of the 3rd InternationalConference on Computational Intelligence and Information Tech-nology (CIIT rsquo13) pp 55ndash61 Elseveir Mumbai India 2013

[8] A R Calderbank I Daubechies W Sweldens and B-L YeoldquoWavelet transforms that map integers to integersrdquo Applied andComputational Harmonic Analysis vol 5 no 3 pp 332ndash3691998

[9] B Ramalingam R Amirtharajan and J B B Rayappan ldquoStegoon FPGA an IWT approachrdquoThe Scientific World Journal vol2014 Article ID 192512 9 pages 2014

[10] E Ghasemi J Shanbehzadeh and B ZahirAzami ldquoA stegano-graphic method based on Integer Wavelet Transform andGenetic Algorithmrdquo in Proceedings of the International Confer-ence on Communications and Signal Processing (ICCSP rsquo11) pp42ndash45 Calicut India February 2011

[11] E Ghasemi J Shanbehzadeh and N Fassihi ldquoHigh capacityimage steganography using wavelet transform and geneticalgorithmrdquo in Proceedings of the International Multi Conferenceof Engineers and Computer Scientists (IMECS rsquo11) pp 495ndash498Hong Kong March 2011

[12] G Xuan Y Q Shi C Yang Y Zheng D Zou and P ChaildquoLossless data hiding using integer wavelet transform andthreshold embedding techniquerdquo in Proceedings of the IEEEInternational Conference on Multimedia and Expo (ICME rsquo05)pp 1520ndash1523 IEEE Amsterdam The Netherlands July 2005

Mathematical Problems in Engineering 11

[13] R O El Safy H H Zayed and A El Dessouki ldquoAn adaptivesteganographic technique based on integer wavelet transformrdquoin Proceedings of the International Conference on Networkingand Media Convergence (ICNM rsquo09) pp 111ndash117 Cairo EgyptMarch 2009

[14] S Archana A Judice and K P Kaliyamurthie ldquoA novelapproach on image steganographic methods for optimum hid-ing capacityrdquo International Journal of Engineering and ComputerScience vol 2 no 2 pp 378ndash385 2013

[15] A K Al-Asmari M A Al-Qodah and A S Salama ldquoWavelet-pixel value differencing technique for digital images data hid-ingrdquo in Proceedings of the IEEE International Conference onSystem Engineering and Technology (ICSET rsquo11) pp 15ndash18 June2011

[16] Z Wang and A C Bovik ldquoA universal image quality indexrdquoIEEE Signal Processing Letters vol 9 no 3 pp 81ndash84 2002

[17] ZWang A C Bovik H R Sheikh and E P Simoncelli ldquoImagequality assessment from error visibility to structural similarityrdquoIEEE Transactions on Image Processing vol 13 no 4 pp 600ndash612 2004

[18] N I Wu andM S Hwang ldquoData hiding current status and keyissuesrdquo International Journal of Network Security vol 4 no 1pp 1ndash9 2007

[19] X Zhang and S Wang ldquoEfficient data hiding with histogram-preserving propertyrdquo Telecommunication Systems vol 49 no 2pp 179ndash185 2012

[20] J FridrichMGoljan andRDu ldquoDetecting LSB steganographyin color and gray-scale imagesrdquo IEEEMultimediaMagazine vol8 no 4 pp 22ndash28 2001

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Page 7: Research Article An Image Steganography Method Hiding ...downloads.hindawi.com/journals/mpe/2015/684824.pdf · An Image Steganography Method Hiding Secret Data into Coefficients of

Mathematical Problems in Engineering 7

Table 1 Comparison of hiding capacity (in bytes)

Cover image PVD method [1] TPVD method [3] Gulversquos method [4] Proposed methodCapacity PSNR Capacity PSNR Capacity PSNR Capacity PSNR

Lena 50960 4179 75836 3889 81305 4286 81326 3984Baboon 56291 3790 82407 3393 81766 4199 82933 3962Peppers 50685 4173 75579 3850 81326 4280 81387 4029

Cover imageLenatiff

(a)

Stego-imageLennatiff

(b)

BaboontiffCover image

(c)

BaboontiffStego-image

(d)

Figure 4 Cover and stego images

in JPG format are converted into gray scale tiff format Thetext files are used as secret data Since the proposed algo-rithm use PVD approach to hide information in waveletcoefficients the data hiding capacity and PSNR values ofthe proposed method are compared with PVD method [1]TPVD [3] method and Gulversquos method [4] The comparisonis shown in Table 1The proposedmethod provides increasedhiding capacity and improved PSNR values as comparedto PVD and TPVD method Although the PSNR is less as

compared to Gulversquos [4] method there is an improvement inthe security of secret data

The average payload of the proposed system is sim248 bppThe performance of the proposed method is analyzed usingPSNR Universal Quality Index (119876) and Structural SimilarityIndex Measure (SSIM) 119876 and SSIM are full reference imagequality assessment models and require the cover image tobe available [16 17] Table 2 shows the PSNR values MSEUniversal Quality Index (119876) and Structural Similarity Index

8 Mathematical Problems in Engineering

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Cover image

Lennatiff

(a)

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Stego image

Lennatiff

(b)

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Cover image

Baboontiff

(c)

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Stego imageBaboontiff

(d)

Figure 5 Histograms of cover and stego images

Measure (SSIM) for different images obtained using proposedmethod The PSNR values are above the threshold of 36 dB[18] even after using more than 95 of the hiding capacity ofthe cover image Also Universal Quality Index (119876) values [16]and Structural Similarity Index Measure (SSIM) values [17]are close to 1 which proves that the stego images are visuallyindistinguishable from original cover images

Figure 4 shows the cover image and the correspondingstego images obtained using the proposed method As thefigures show distortions resulted from embedding are imper-ceptible to human vision

Figure 5 shows the histogramof the cover and stego imageobtained using the proposed method From the figure it canbe observed that the shape of the histogram is preserved

The cover image data is subtracted from stego imageand plotted as histogram Figure 6 shows the pixel differencehistogram From the figure it can be observed that there aremore numbers of bins which are close to 0 as compared to

bins which are away from 0 Also the step pattern is notobserved in the figure This confirms that the method isrobust against histogram analysis attack

Histogram of cover image is represented as [ℎ0 ℎ1

ℎ255] whereas histogram of stego image is represented as

[ℎ1015840

0 ℎ1015840

1 ℎ

1015840

255] The change in histogram [19] is measured

by

119863ℎ=

255

sum

119898=1

10038161003816100381610038161003816ℎ1015840

119898minus ℎ119898

10038161003816100381610038161003816 (20)

The proposed method can hide at least 3 bits in eachpair considering the smallest width of the subrange to be 8Figure 7 shows the comparison of the value of 119863

ℎof the 3

bit LSB replacement method and the proposed method withdifferent size of secret data embedded in the cover imageLenatiff It can be observed that difference in histogram forthe proposed method is less than that of 3 bit LSB method

Mathematical Problems in Engineering 9

0 5 10 15 200

05

1

15

2

25

3

Difference values

Occ

urre

nce f

requ

ency

minus20 minus15 minus10 minus5

times104

Cover imageLennatiff

(a)

0 10 20 300

05

1

15

2

25

3

35

Difference values

Occ

urre

nce f

requ

ency

minus30 minus20 minus10

times104

Cover imageBaboontiff

(b)

Figure 6 Difference histogram

Table 2 Hiding capacity PSNR MSE and 119876 index

Coverimage

Resolution of coverimage

Hidingcapacity(Kb)

ofhidingcapacity

Messagefile size(Kb)

PSNR MSE 119876 SSIM

Baboon 256 times 256 1992 3065 195 3987 6684 0959 0965Lena 256 times 256 1994 3068 195 3991 6633 0899 0937Elaine 512 times 512 7942 309 787 4001 6482 0890 0956Baboon 512 times 512 8099 3068 787 3962 7089 0961 0979Lena 512 times 512 7947 3068 787 3984 6740 0806 0953Tank 512 times 512 7941 309 787 3986 6700 0896 0954Peppers 512 times 512 7948 3022 787 4029 6074 0800 0932Barbara 512 times 512 8035 3055 787 3970 6961 0857 0964Boat 512 times 512 7964 3075 787 3990 6652 0883 0962Grass 1024 times 1024 31932 3115 317 3951 7274 0979 0998

The output images are tested under the 119877119878 steganalysis[20] It is observed from Figure 8 that the difference between119877119872

and 119877minus119872

and 119878119872

and 119878minus119872

is very small The rules 119877119872cong

119877minus119872

and 119878119872cong 119878minus119872

are satisfied for the output images Thisproves that the proposed method is secure against 119877119878 attack

4 Conclusion

In steganography hiding capacity of cover image quality ofstego image and security of secret data are three importantfactors There is always a trade-off between data hidingcapacity of cover image and security of secret data Theproposed algorithm provides improvements in the datahiding capacity as well as security of the secret data ascompared to PVD [1] and TPVD [3] methods AlthoughGulversquos [4] method provides better PSNR values as comparedto proposedmethod the proposedmethod improves security

of secret information The secret information is securelyhidden in the coefficients of integer wavelet transform Forthe implementation purpose the four subbands obtainedafter decomposing the cover image by integer wavelet trans-form are arranged as shown in Figure 1 But it is possible toarrange the four subbands in 4 = 24 different ways therebyimproving the security of the steganography system sincethe exact arrangement of four subbands will be known tosender and receiver only The algorithm revises the originaldifference between two wavelet coefficients in the pair andthis revised difference is used for hiding the data in that pairThis makes estimation of exact number of bits hidden in thepair difficult Image steganography techniques hiding textualinformation require 100 accuracy for successful retrieval ofhidden information from stego image If the steganographymethod fails correct estimation of number of bits hidden forsome of the pairs will be a challenge for the invader Thus

10 Mathematical Problems in Engineering

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

10 20 30 40 50 60 70 80

Hist

ogra

m d

iffer

ence

Size of hidden message (KB)

LSBProposed

Figure 7 Histograms comparison of 3 bit LSB substitution andproposed method (Lenatiff)

0

01

02

03

04

10 20 30 40 50 60 70 79

Ratio

of R

S

Message size (KB)

RM SM

RminusMSminusM

Figure 8 119877119878 diagram

one more level of security is imposed to secure the secretinformation

The PSNR values produced by the algorithm are close to395 which are well above the threshold of 36 dB after usingfull hiding capacity of the cover image This proves that thestego images are of good quality Results also show that thedifference between cover image and stego image cannot benoticed by human visual system (HVS)

Considering the fact that there is currently no steganogra-phy system that can resist all the steganalysis attacks the bestway to provide security to the secret data and to eliminate theattack of comparing the original image with the stego image

is to freshly create an image and destroy it after generating thestego image

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D-CWu andW-H Tsai ldquoA steganographic method for imagesby pixel-value differencingrdquo Pattern Recognition Letters vol 24no 9-10 pp 1613ndash1626 2003

[2] H C Wu N I Wu C S Tsai and M-S Hwang ldquoImagesteganographic scheme based on pixel-value differencing andLSB replacementmethodsrdquo IEE ProceedingsmdashVision Image andSignal Processing vol 152 no 5 pp 611ndash615 2005

[3] K-C Chang P S Huang T-M Tu and C-P Chang ldquoAdaptiveimage steganographic scheme based on tri-way pixel-value dif-ferencingrdquo in Proceedings of the IEEE International Conferenceon Systems Man and Cybernetics (SMC rsquo07) pp 1165ndash1170Montreal Canada October 2007

[4] A K Gulve andM S Joshi ldquoAn image steganography algorithmwith five pixel pair differencing and gray code conversionrdquoInternational Journal of Image Graphics and Signal Processingvol 6 no 3 pp 12ndash20 2014

[5] K-C Chang C-P Chang P S Huang and T-M Tu ldquoA novelimage steganographic method using tri-way pixel-value differ-encingrdquo Journal of Multimedia vol 3 no 2 pp 37ndash44 2008

[6] K C Chang P S Huang T M Tu and C P Chang ldquoImagesteganographic scheme using tri-way pixel-value differencingand adaptive rulesrdquo in Proceedings of the IEEE InternationalConference on Intelligent Information Hiding and MultimediaSignal Processing pp 449ndash452 Kaohsiung Taiwan 2007

[7] A K Gulve and M S Joshi ldquoA secured image steganographyalgorithm with five pixel pair differencing by selecting thecommon pixel randomlyrdquo in Proceedings of the 3rd InternationalConference on Computational Intelligence and Information Tech-nology (CIIT rsquo13) pp 55ndash61 Elseveir Mumbai India 2013

[8] A R Calderbank I Daubechies W Sweldens and B-L YeoldquoWavelet transforms that map integers to integersrdquo Applied andComputational Harmonic Analysis vol 5 no 3 pp 332ndash3691998

[9] B Ramalingam R Amirtharajan and J B B Rayappan ldquoStegoon FPGA an IWT approachrdquoThe Scientific World Journal vol2014 Article ID 192512 9 pages 2014

[10] E Ghasemi J Shanbehzadeh and B ZahirAzami ldquoA stegano-graphic method based on Integer Wavelet Transform andGenetic Algorithmrdquo in Proceedings of the International Confer-ence on Communications and Signal Processing (ICCSP rsquo11) pp42ndash45 Calicut India February 2011

[11] E Ghasemi J Shanbehzadeh and N Fassihi ldquoHigh capacityimage steganography using wavelet transform and geneticalgorithmrdquo in Proceedings of the International Multi Conferenceof Engineers and Computer Scientists (IMECS rsquo11) pp 495ndash498Hong Kong March 2011

[12] G Xuan Y Q Shi C Yang Y Zheng D Zou and P ChaildquoLossless data hiding using integer wavelet transform andthreshold embedding techniquerdquo in Proceedings of the IEEEInternational Conference on Multimedia and Expo (ICME rsquo05)pp 1520ndash1523 IEEE Amsterdam The Netherlands July 2005

Mathematical Problems in Engineering 11

[13] R O El Safy H H Zayed and A El Dessouki ldquoAn adaptivesteganographic technique based on integer wavelet transformrdquoin Proceedings of the International Conference on Networkingand Media Convergence (ICNM rsquo09) pp 111ndash117 Cairo EgyptMarch 2009

[14] S Archana A Judice and K P Kaliyamurthie ldquoA novelapproach on image steganographic methods for optimum hid-ing capacityrdquo International Journal of Engineering and ComputerScience vol 2 no 2 pp 378ndash385 2013

[15] A K Al-Asmari M A Al-Qodah and A S Salama ldquoWavelet-pixel value differencing technique for digital images data hid-ingrdquo in Proceedings of the IEEE International Conference onSystem Engineering and Technology (ICSET rsquo11) pp 15ndash18 June2011

[16] Z Wang and A C Bovik ldquoA universal image quality indexrdquoIEEE Signal Processing Letters vol 9 no 3 pp 81ndash84 2002

[17] ZWang A C Bovik H R Sheikh and E P Simoncelli ldquoImagequality assessment from error visibility to structural similarityrdquoIEEE Transactions on Image Processing vol 13 no 4 pp 600ndash612 2004

[18] N I Wu andM S Hwang ldquoData hiding current status and keyissuesrdquo International Journal of Network Security vol 4 no 1pp 1ndash9 2007

[19] X Zhang and S Wang ldquoEfficient data hiding with histogram-preserving propertyrdquo Telecommunication Systems vol 49 no 2pp 179ndash185 2012

[20] J FridrichMGoljan andRDu ldquoDetecting LSB steganographyin color and gray-scale imagesrdquo IEEEMultimediaMagazine vol8 no 4 pp 22ndash28 2001

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Page 8: Research Article An Image Steganography Method Hiding ...downloads.hindawi.com/journals/mpe/2015/684824.pdf · An Image Steganography Method Hiding Secret Data into Coefficients of

8 Mathematical Problems in Engineering

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Cover image

Lennatiff

(a)

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Stego image

Lennatiff

(b)

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Cover image

Baboontiff

(c)

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Stego imageBaboontiff

(d)

Figure 5 Histograms of cover and stego images

Measure (SSIM) for different images obtained using proposedmethod The PSNR values are above the threshold of 36 dB[18] even after using more than 95 of the hiding capacity ofthe cover image Also Universal Quality Index (119876) values [16]and Structural Similarity Index Measure (SSIM) values [17]are close to 1 which proves that the stego images are visuallyindistinguishable from original cover images

Figure 4 shows the cover image and the correspondingstego images obtained using the proposed method As thefigures show distortions resulted from embedding are imper-ceptible to human vision

Figure 5 shows the histogramof the cover and stego imageobtained using the proposed method From the figure it canbe observed that the shape of the histogram is preserved

The cover image data is subtracted from stego imageand plotted as histogram Figure 6 shows the pixel differencehistogram From the figure it can be observed that there aremore numbers of bins which are close to 0 as compared to

bins which are away from 0 Also the step pattern is notobserved in the figure This confirms that the method isrobust against histogram analysis attack

Histogram of cover image is represented as [ℎ0 ℎ1

ℎ255] whereas histogram of stego image is represented as

[ℎ1015840

0 ℎ1015840

1 ℎ

1015840

255] The change in histogram [19] is measured

by

119863ℎ=

255

sum

119898=1

10038161003816100381610038161003816ℎ1015840

119898minus ℎ119898

10038161003816100381610038161003816 (20)

The proposed method can hide at least 3 bits in eachpair considering the smallest width of the subrange to be 8Figure 7 shows the comparison of the value of 119863

ℎof the 3

bit LSB replacement method and the proposed method withdifferent size of secret data embedded in the cover imageLenatiff It can be observed that difference in histogram forthe proposed method is less than that of 3 bit LSB method

Mathematical Problems in Engineering 9

0 5 10 15 200

05

1

15

2

25

3

Difference values

Occ

urre

nce f

requ

ency

minus20 minus15 minus10 minus5

times104

Cover imageLennatiff

(a)

0 10 20 300

05

1

15

2

25

3

35

Difference values

Occ

urre

nce f

requ

ency

minus30 minus20 minus10

times104

Cover imageBaboontiff

(b)

Figure 6 Difference histogram

Table 2 Hiding capacity PSNR MSE and 119876 index

Coverimage

Resolution of coverimage

Hidingcapacity(Kb)

ofhidingcapacity

Messagefile size(Kb)

PSNR MSE 119876 SSIM

Baboon 256 times 256 1992 3065 195 3987 6684 0959 0965Lena 256 times 256 1994 3068 195 3991 6633 0899 0937Elaine 512 times 512 7942 309 787 4001 6482 0890 0956Baboon 512 times 512 8099 3068 787 3962 7089 0961 0979Lena 512 times 512 7947 3068 787 3984 6740 0806 0953Tank 512 times 512 7941 309 787 3986 6700 0896 0954Peppers 512 times 512 7948 3022 787 4029 6074 0800 0932Barbara 512 times 512 8035 3055 787 3970 6961 0857 0964Boat 512 times 512 7964 3075 787 3990 6652 0883 0962Grass 1024 times 1024 31932 3115 317 3951 7274 0979 0998

The output images are tested under the 119877119878 steganalysis[20] It is observed from Figure 8 that the difference between119877119872

and 119877minus119872

and 119878119872

and 119878minus119872

is very small The rules 119877119872cong

119877minus119872

and 119878119872cong 119878minus119872

are satisfied for the output images Thisproves that the proposed method is secure against 119877119878 attack

4 Conclusion

In steganography hiding capacity of cover image quality ofstego image and security of secret data are three importantfactors There is always a trade-off between data hidingcapacity of cover image and security of secret data Theproposed algorithm provides improvements in the datahiding capacity as well as security of the secret data ascompared to PVD [1] and TPVD [3] methods AlthoughGulversquos [4] method provides better PSNR values as comparedto proposedmethod the proposedmethod improves security

of secret information The secret information is securelyhidden in the coefficients of integer wavelet transform Forthe implementation purpose the four subbands obtainedafter decomposing the cover image by integer wavelet trans-form are arranged as shown in Figure 1 But it is possible toarrange the four subbands in 4 = 24 different ways therebyimproving the security of the steganography system sincethe exact arrangement of four subbands will be known tosender and receiver only The algorithm revises the originaldifference between two wavelet coefficients in the pair andthis revised difference is used for hiding the data in that pairThis makes estimation of exact number of bits hidden in thepair difficult Image steganography techniques hiding textualinformation require 100 accuracy for successful retrieval ofhidden information from stego image If the steganographymethod fails correct estimation of number of bits hidden forsome of the pairs will be a challenge for the invader Thus

10 Mathematical Problems in Engineering

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

10 20 30 40 50 60 70 80

Hist

ogra

m d

iffer

ence

Size of hidden message (KB)

LSBProposed

Figure 7 Histograms comparison of 3 bit LSB substitution andproposed method (Lenatiff)

0

01

02

03

04

10 20 30 40 50 60 70 79

Ratio

of R

S

Message size (KB)

RM SM

RminusMSminusM

Figure 8 119877119878 diagram

one more level of security is imposed to secure the secretinformation

The PSNR values produced by the algorithm are close to395 which are well above the threshold of 36 dB after usingfull hiding capacity of the cover image This proves that thestego images are of good quality Results also show that thedifference between cover image and stego image cannot benoticed by human visual system (HVS)

Considering the fact that there is currently no steganogra-phy system that can resist all the steganalysis attacks the bestway to provide security to the secret data and to eliminate theattack of comparing the original image with the stego image

is to freshly create an image and destroy it after generating thestego image

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D-CWu andW-H Tsai ldquoA steganographic method for imagesby pixel-value differencingrdquo Pattern Recognition Letters vol 24no 9-10 pp 1613ndash1626 2003

[2] H C Wu N I Wu C S Tsai and M-S Hwang ldquoImagesteganographic scheme based on pixel-value differencing andLSB replacementmethodsrdquo IEE ProceedingsmdashVision Image andSignal Processing vol 152 no 5 pp 611ndash615 2005

[3] K-C Chang P S Huang T-M Tu and C-P Chang ldquoAdaptiveimage steganographic scheme based on tri-way pixel-value dif-ferencingrdquo in Proceedings of the IEEE International Conferenceon Systems Man and Cybernetics (SMC rsquo07) pp 1165ndash1170Montreal Canada October 2007

[4] A K Gulve andM S Joshi ldquoAn image steganography algorithmwith five pixel pair differencing and gray code conversionrdquoInternational Journal of Image Graphics and Signal Processingvol 6 no 3 pp 12ndash20 2014

[5] K-C Chang C-P Chang P S Huang and T-M Tu ldquoA novelimage steganographic method using tri-way pixel-value differ-encingrdquo Journal of Multimedia vol 3 no 2 pp 37ndash44 2008

[6] K C Chang P S Huang T M Tu and C P Chang ldquoImagesteganographic scheme using tri-way pixel-value differencingand adaptive rulesrdquo in Proceedings of the IEEE InternationalConference on Intelligent Information Hiding and MultimediaSignal Processing pp 449ndash452 Kaohsiung Taiwan 2007

[7] A K Gulve and M S Joshi ldquoA secured image steganographyalgorithm with five pixel pair differencing by selecting thecommon pixel randomlyrdquo in Proceedings of the 3rd InternationalConference on Computational Intelligence and Information Tech-nology (CIIT rsquo13) pp 55ndash61 Elseveir Mumbai India 2013

[8] A R Calderbank I Daubechies W Sweldens and B-L YeoldquoWavelet transforms that map integers to integersrdquo Applied andComputational Harmonic Analysis vol 5 no 3 pp 332ndash3691998

[9] B Ramalingam R Amirtharajan and J B B Rayappan ldquoStegoon FPGA an IWT approachrdquoThe Scientific World Journal vol2014 Article ID 192512 9 pages 2014

[10] E Ghasemi J Shanbehzadeh and B ZahirAzami ldquoA stegano-graphic method based on Integer Wavelet Transform andGenetic Algorithmrdquo in Proceedings of the International Confer-ence on Communications and Signal Processing (ICCSP rsquo11) pp42ndash45 Calicut India February 2011

[11] E Ghasemi J Shanbehzadeh and N Fassihi ldquoHigh capacityimage steganography using wavelet transform and geneticalgorithmrdquo in Proceedings of the International Multi Conferenceof Engineers and Computer Scientists (IMECS rsquo11) pp 495ndash498Hong Kong March 2011

[12] G Xuan Y Q Shi C Yang Y Zheng D Zou and P ChaildquoLossless data hiding using integer wavelet transform andthreshold embedding techniquerdquo in Proceedings of the IEEEInternational Conference on Multimedia and Expo (ICME rsquo05)pp 1520ndash1523 IEEE Amsterdam The Netherlands July 2005

Mathematical Problems in Engineering 11

[13] R O El Safy H H Zayed and A El Dessouki ldquoAn adaptivesteganographic technique based on integer wavelet transformrdquoin Proceedings of the International Conference on Networkingand Media Convergence (ICNM rsquo09) pp 111ndash117 Cairo EgyptMarch 2009

[14] S Archana A Judice and K P Kaliyamurthie ldquoA novelapproach on image steganographic methods for optimum hid-ing capacityrdquo International Journal of Engineering and ComputerScience vol 2 no 2 pp 378ndash385 2013

[15] A K Al-Asmari M A Al-Qodah and A S Salama ldquoWavelet-pixel value differencing technique for digital images data hid-ingrdquo in Proceedings of the IEEE International Conference onSystem Engineering and Technology (ICSET rsquo11) pp 15ndash18 June2011

[16] Z Wang and A C Bovik ldquoA universal image quality indexrdquoIEEE Signal Processing Letters vol 9 no 3 pp 81ndash84 2002

[17] ZWang A C Bovik H R Sheikh and E P Simoncelli ldquoImagequality assessment from error visibility to structural similarityrdquoIEEE Transactions on Image Processing vol 13 no 4 pp 600ndash612 2004

[18] N I Wu andM S Hwang ldquoData hiding current status and keyissuesrdquo International Journal of Network Security vol 4 no 1pp 1ndash9 2007

[19] X Zhang and S Wang ldquoEfficient data hiding with histogram-preserving propertyrdquo Telecommunication Systems vol 49 no 2pp 179ndash185 2012

[20] J FridrichMGoljan andRDu ldquoDetecting LSB steganographyin color and gray-scale imagesrdquo IEEEMultimediaMagazine vol8 no 4 pp 22ndash28 2001

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Page 9: Research Article An Image Steganography Method Hiding ...downloads.hindawi.com/journals/mpe/2015/684824.pdf · An Image Steganography Method Hiding Secret Data into Coefficients of

Mathematical Problems in Engineering 9

0 5 10 15 200

05

1

15

2

25

3

Difference values

Occ

urre

nce f

requ

ency

minus20 minus15 minus10 minus5

times104

Cover imageLennatiff

(a)

0 10 20 300

05

1

15

2

25

3

35

Difference values

Occ

urre

nce f

requ

ency

minus30 minus20 minus10

times104

Cover imageBaboontiff

(b)

Figure 6 Difference histogram

Table 2 Hiding capacity PSNR MSE and 119876 index

Coverimage

Resolution of coverimage

Hidingcapacity(Kb)

ofhidingcapacity

Messagefile size(Kb)

PSNR MSE 119876 SSIM

Baboon 256 times 256 1992 3065 195 3987 6684 0959 0965Lena 256 times 256 1994 3068 195 3991 6633 0899 0937Elaine 512 times 512 7942 309 787 4001 6482 0890 0956Baboon 512 times 512 8099 3068 787 3962 7089 0961 0979Lena 512 times 512 7947 3068 787 3984 6740 0806 0953Tank 512 times 512 7941 309 787 3986 6700 0896 0954Peppers 512 times 512 7948 3022 787 4029 6074 0800 0932Barbara 512 times 512 8035 3055 787 3970 6961 0857 0964Boat 512 times 512 7964 3075 787 3990 6652 0883 0962Grass 1024 times 1024 31932 3115 317 3951 7274 0979 0998

The output images are tested under the 119877119878 steganalysis[20] It is observed from Figure 8 that the difference between119877119872

and 119877minus119872

and 119878119872

and 119878minus119872

is very small The rules 119877119872cong

119877minus119872

and 119878119872cong 119878minus119872

are satisfied for the output images Thisproves that the proposed method is secure against 119877119878 attack

4 Conclusion

In steganography hiding capacity of cover image quality ofstego image and security of secret data are three importantfactors There is always a trade-off between data hidingcapacity of cover image and security of secret data Theproposed algorithm provides improvements in the datahiding capacity as well as security of the secret data ascompared to PVD [1] and TPVD [3] methods AlthoughGulversquos [4] method provides better PSNR values as comparedto proposedmethod the proposedmethod improves security

of secret information The secret information is securelyhidden in the coefficients of integer wavelet transform Forthe implementation purpose the four subbands obtainedafter decomposing the cover image by integer wavelet trans-form are arranged as shown in Figure 1 But it is possible toarrange the four subbands in 4 = 24 different ways therebyimproving the security of the steganography system sincethe exact arrangement of four subbands will be known tosender and receiver only The algorithm revises the originaldifference between two wavelet coefficients in the pair andthis revised difference is used for hiding the data in that pairThis makes estimation of exact number of bits hidden in thepair difficult Image steganography techniques hiding textualinformation require 100 accuracy for successful retrieval ofhidden information from stego image If the steganographymethod fails correct estimation of number of bits hidden forsome of the pairs will be a challenge for the invader Thus

10 Mathematical Problems in Engineering

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

10 20 30 40 50 60 70 80

Hist

ogra

m d

iffer

ence

Size of hidden message (KB)

LSBProposed

Figure 7 Histograms comparison of 3 bit LSB substitution andproposed method (Lenatiff)

0

01

02

03

04

10 20 30 40 50 60 70 79

Ratio

of R

S

Message size (KB)

RM SM

RminusMSminusM

Figure 8 119877119878 diagram

one more level of security is imposed to secure the secretinformation

The PSNR values produced by the algorithm are close to395 which are well above the threshold of 36 dB after usingfull hiding capacity of the cover image This proves that thestego images are of good quality Results also show that thedifference between cover image and stego image cannot benoticed by human visual system (HVS)

Considering the fact that there is currently no steganogra-phy system that can resist all the steganalysis attacks the bestway to provide security to the secret data and to eliminate theattack of comparing the original image with the stego image

is to freshly create an image and destroy it after generating thestego image

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D-CWu andW-H Tsai ldquoA steganographic method for imagesby pixel-value differencingrdquo Pattern Recognition Letters vol 24no 9-10 pp 1613ndash1626 2003

[2] H C Wu N I Wu C S Tsai and M-S Hwang ldquoImagesteganographic scheme based on pixel-value differencing andLSB replacementmethodsrdquo IEE ProceedingsmdashVision Image andSignal Processing vol 152 no 5 pp 611ndash615 2005

[3] K-C Chang P S Huang T-M Tu and C-P Chang ldquoAdaptiveimage steganographic scheme based on tri-way pixel-value dif-ferencingrdquo in Proceedings of the IEEE International Conferenceon Systems Man and Cybernetics (SMC rsquo07) pp 1165ndash1170Montreal Canada October 2007

[4] A K Gulve andM S Joshi ldquoAn image steganography algorithmwith five pixel pair differencing and gray code conversionrdquoInternational Journal of Image Graphics and Signal Processingvol 6 no 3 pp 12ndash20 2014

[5] K-C Chang C-P Chang P S Huang and T-M Tu ldquoA novelimage steganographic method using tri-way pixel-value differ-encingrdquo Journal of Multimedia vol 3 no 2 pp 37ndash44 2008

[6] K C Chang P S Huang T M Tu and C P Chang ldquoImagesteganographic scheme using tri-way pixel-value differencingand adaptive rulesrdquo in Proceedings of the IEEE InternationalConference on Intelligent Information Hiding and MultimediaSignal Processing pp 449ndash452 Kaohsiung Taiwan 2007

[7] A K Gulve and M S Joshi ldquoA secured image steganographyalgorithm with five pixel pair differencing by selecting thecommon pixel randomlyrdquo in Proceedings of the 3rd InternationalConference on Computational Intelligence and Information Tech-nology (CIIT rsquo13) pp 55ndash61 Elseveir Mumbai India 2013

[8] A R Calderbank I Daubechies W Sweldens and B-L YeoldquoWavelet transforms that map integers to integersrdquo Applied andComputational Harmonic Analysis vol 5 no 3 pp 332ndash3691998

[9] B Ramalingam R Amirtharajan and J B B Rayappan ldquoStegoon FPGA an IWT approachrdquoThe Scientific World Journal vol2014 Article ID 192512 9 pages 2014

[10] E Ghasemi J Shanbehzadeh and B ZahirAzami ldquoA stegano-graphic method based on Integer Wavelet Transform andGenetic Algorithmrdquo in Proceedings of the International Confer-ence on Communications and Signal Processing (ICCSP rsquo11) pp42ndash45 Calicut India February 2011

[11] E Ghasemi J Shanbehzadeh and N Fassihi ldquoHigh capacityimage steganography using wavelet transform and geneticalgorithmrdquo in Proceedings of the International Multi Conferenceof Engineers and Computer Scientists (IMECS rsquo11) pp 495ndash498Hong Kong March 2011

[12] G Xuan Y Q Shi C Yang Y Zheng D Zou and P ChaildquoLossless data hiding using integer wavelet transform andthreshold embedding techniquerdquo in Proceedings of the IEEEInternational Conference on Multimedia and Expo (ICME rsquo05)pp 1520ndash1523 IEEE Amsterdam The Netherlands July 2005

Mathematical Problems in Engineering 11

[13] R O El Safy H H Zayed and A El Dessouki ldquoAn adaptivesteganographic technique based on integer wavelet transformrdquoin Proceedings of the International Conference on Networkingand Media Convergence (ICNM rsquo09) pp 111ndash117 Cairo EgyptMarch 2009

[14] S Archana A Judice and K P Kaliyamurthie ldquoA novelapproach on image steganographic methods for optimum hid-ing capacityrdquo International Journal of Engineering and ComputerScience vol 2 no 2 pp 378ndash385 2013

[15] A K Al-Asmari M A Al-Qodah and A S Salama ldquoWavelet-pixel value differencing technique for digital images data hid-ingrdquo in Proceedings of the IEEE International Conference onSystem Engineering and Technology (ICSET rsquo11) pp 15ndash18 June2011

[16] Z Wang and A C Bovik ldquoA universal image quality indexrdquoIEEE Signal Processing Letters vol 9 no 3 pp 81ndash84 2002

[17] ZWang A C Bovik H R Sheikh and E P Simoncelli ldquoImagequality assessment from error visibility to structural similarityrdquoIEEE Transactions on Image Processing vol 13 no 4 pp 600ndash612 2004

[18] N I Wu andM S Hwang ldquoData hiding current status and keyissuesrdquo International Journal of Network Security vol 4 no 1pp 1ndash9 2007

[19] X Zhang and S Wang ldquoEfficient data hiding with histogram-preserving propertyrdquo Telecommunication Systems vol 49 no 2pp 179ndash185 2012

[20] J FridrichMGoljan andRDu ldquoDetecting LSB steganographyin color and gray-scale imagesrdquo IEEEMultimediaMagazine vol8 no 4 pp 22ndash28 2001

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Page 10: Research Article An Image Steganography Method Hiding ...downloads.hindawi.com/journals/mpe/2015/684824.pdf · An Image Steganography Method Hiding Secret Data into Coefficients of

10 Mathematical Problems in Engineering

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

10 20 30 40 50 60 70 80

Hist

ogra

m d

iffer

ence

Size of hidden message (KB)

LSBProposed

Figure 7 Histograms comparison of 3 bit LSB substitution andproposed method (Lenatiff)

0

01

02

03

04

10 20 30 40 50 60 70 79

Ratio

of R

S

Message size (KB)

RM SM

RminusMSminusM

Figure 8 119877119878 diagram

one more level of security is imposed to secure the secretinformation

The PSNR values produced by the algorithm are close to395 which are well above the threshold of 36 dB after usingfull hiding capacity of the cover image This proves that thestego images are of good quality Results also show that thedifference between cover image and stego image cannot benoticed by human visual system (HVS)

Considering the fact that there is currently no steganogra-phy system that can resist all the steganalysis attacks the bestway to provide security to the secret data and to eliminate theattack of comparing the original image with the stego image

is to freshly create an image and destroy it after generating thestego image

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D-CWu andW-H Tsai ldquoA steganographic method for imagesby pixel-value differencingrdquo Pattern Recognition Letters vol 24no 9-10 pp 1613ndash1626 2003

[2] H C Wu N I Wu C S Tsai and M-S Hwang ldquoImagesteganographic scheme based on pixel-value differencing andLSB replacementmethodsrdquo IEE ProceedingsmdashVision Image andSignal Processing vol 152 no 5 pp 611ndash615 2005

[3] K-C Chang P S Huang T-M Tu and C-P Chang ldquoAdaptiveimage steganographic scheme based on tri-way pixel-value dif-ferencingrdquo in Proceedings of the IEEE International Conferenceon Systems Man and Cybernetics (SMC rsquo07) pp 1165ndash1170Montreal Canada October 2007

[4] A K Gulve andM S Joshi ldquoAn image steganography algorithmwith five pixel pair differencing and gray code conversionrdquoInternational Journal of Image Graphics and Signal Processingvol 6 no 3 pp 12ndash20 2014

[5] K-C Chang C-P Chang P S Huang and T-M Tu ldquoA novelimage steganographic method using tri-way pixel-value differ-encingrdquo Journal of Multimedia vol 3 no 2 pp 37ndash44 2008

[6] K C Chang P S Huang T M Tu and C P Chang ldquoImagesteganographic scheme using tri-way pixel-value differencingand adaptive rulesrdquo in Proceedings of the IEEE InternationalConference on Intelligent Information Hiding and MultimediaSignal Processing pp 449ndash452 Kaohsiung Taiwan 2007

[7] A K Gulve and M S Joshi ldquoA secured image steganographyalgorithm with five pixel pair differencing by selecting thecommon pixel randomlyrdquo in Proceedings of the 3rd InternationalConference on Computational Intelligence and Information Tech-nology (CIIT rsquo13) pp 55ndash61 Elseveir Mumbai India 2013

[8] A R Calderbank I Daubechies W Sweldens and B-L YeoldquoWavelet transforms that map integers to integersrdquo Applied andComputational Harmonic Analysis vol 5 no 3 pp 332ndash3691998

[9] B Ramalingam R Amirtharajan and J B B Rayappan ldquoStegoon FPGA an IWT approachrdquoThe Scientific World Journal vol2014 Article ID 192512 9 pages 2014

[10] E Ghasemi J Shanbehzadeh and B ZahirAzami ldquoA stegano-graphic method based on Integer Wavelet Transform andGenetic Algorithmrdquo in Proceedings of the International Confer-ence on Communications and Signal Processing (ICCSP rsquo11) pp42ndash45 Calicut India February 2011

[11] E Ghasemi J Shanbehzadeh and N Fassihi ldquoHigh capacityimage steganography using wavelet transform and geneticalgorithmrdquo in Proceedings of the International Multi Conferenceof Engineers and Computer Scientists (IMECS rsquo11) pp 495ndash498Hong Kong March 2011

[12] G Xuan Y Q Shi C Yang Y Zheng D Zou and P ChaildquoLossless data hiding using integer wavelet transform andthreshold embedding techniquerdquo in Proceedings of the IEEEInternational Conference on Multimedia and Expo (ICME rsquo05)pp 1520ndash1523 IEEE Amsterdam The Netherlands July 2005

Mathematical Problems in Engineering 11

[13] R O El Safy H H Zayed and A El Dessouki ldquoAn adaptivesteganographic technique based on integer wavelet transformrdquoin Proceedings of the International Conference on Networkingand Media Convergence (ICNM rsquo09) pp 111ndash117 Cairo EgyptMarch 2009

[14] S Archana A Judice and K P Kaliyamurthie ldquoA novelapproach on image steganographic methods for optimum hid-ing capacityrdquo International Journal of Engineering and ComputerScience vol 2 no 2 pp 378ndash385 2013

[15] A K Al-Asmari M A Al-Qodah and A S Salama ldquoWavelet-pixel value differencing technique for digital images data hid-ingrdquo in Proceedings of the IEEE International Conference onSystem Engineering and Technology (ICSET rsquo11) pp 15ndash18 June2011

[16] Z Wang and A C Bovik ldquoA universal image quality indexrdquoIEEE Signal Processing Letters vol 9 no 3 pp 81ndash84 2002

[17] ZWang A C Bovik H R Sheikh and E P Simoncelli ldquoImagequality assessment from error visibility to structural similarityrdquoIEEE Transactions on Image Processing vol 13 no 4 pp 600ndash612 2004

[18] N I Wu andM S Hwang ldquoData hiding current status and keyissuesrdquo International Journal of Network Security vol 4 no 1pp 1ndash9 2007

[19] X Zhang and S Wang ldquoEfficient data hiding with histogram-preserving propertyrdquo Telecommunication Systems vol 49 no 2pp 179ndash185 2012

[20] J FridrichMGoljan andRDu ldquoDetecting LSB steganographyin color and gray-scale imagesrdquo IEEEMultimediaMagazine vol8 no 4 pp 22ndash28 2001

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Page 11: Research Article An Image Steganography Method Hiding ...downloads.hindawi.com/journals/mpe/2015/684824.pdf · An Image Steganography Method Hiding Secret Data into Coefficients of

Mathematical Problems in Engineering 11

[13] R O El Safy H H Zayed and A El Dessouki ldquoAn adaptivesteganographic technique based on integer wavelet transformrdquoin Proceedings of the International Conference on Networkingand Media Convergence (ICNM rsquo09) pp 111ndash117 Cairo EgyptMarch 2009

[14] S Archana A Judice and K P Kaliyamurthie ldquoA novelapproach on image steganographic methods for optimum hid-ing capacityrdquo International Journal of Engineering and ComputerScience vol 2 no 2 pp 378ndash385 2013

[15] A K Al-Asmari M A Al-Qodah and A S Salama ldquoWavelet-pixel value differencing technique for digital images data hid-ingrdquo in Proceedings of the IEEE International Conference onSystem Engineering and Technology (ICSET rsquo11) pp 15ndash18 June2011

[16] Z Wang and A C Bovik ldquoA universal image quality indexrdquoIEEE Signal Processing Letters vol 9 no 3 pp 81ndash84 2002

[17] ZWang A C Bovik H R Sheikh and E P Simoncelli ldquoImagequality assessment from error visibility to structural similarityrdquoIEEE Transactions on Image Processing vol 13 no 4 pp 600ndash612 2004

[18] N I Wu andM S Hwang ldquoData hiding current status and keyissuesrdquo International Journal of Network Security vol 4 no 1pp 1ndash9 2007

[19] X Zhang and S Wang ldquoEfficient data hiding with histogram-preserving propertyrdquo Telecommunication Systems vol 49 no 2pp 179ndash185 2012

[20] J FridrichMGoljan andRDu ldquoDetecting LSB steganographyin color and gray-scale imagesrdquo IEEEMultimediaMagazine vol8 no 4 pp 22ndash28 2001

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Page 12: Research Article An Image Steganography Method Hiding ...downloads.hindawi.com/journals/mpe/2015/684824.pdf · An Image Steganography Method Hiding Secret Data into Coefficients of

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of