A FIRST CRYPTOSYSTEM FOR SECURITY OF TWO …web.iitd.ac.in/~rksharma/Research Publications/Journal/deep... · §[email protected]

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Fractals, Vol. 25, No. 1 (2017) 1750011 (28 pages)c© World Scientific Publishing CompanyDOI: 10.1142/S0218348X17500116

A FIRST CRYPTOSYSTEM FOR SECURITYOF TWO-DIMENSIONAL DATA

D. C. MISHRA,∗,‡ HIMANI SHARMA,†,§ R. K. SHARMA∗,¶and NAVEEN KUMAR†,‖

∗Department of MathematicsIndian Institute of TechnologyDelhi-110016, New Delhi, India

†Department of Computer ScienceUniversity of Delhi-110007, New Delhi, India

‡[email protected]§[email protected]

¶[email protected]‖[email protected]

Received October 31, 2015Accepted December 27, 2016Published February 6, 2017

AbstractIn this paper, we present a novel technique for security of two-dimensional data with the helpof cryptography and steganography. The presented approach provides multilayered security oftwo-dimensional data. First layer security was developed by cryptography and second layer bysteganography. The advantage of steganography is that the intended secret message does notattract attention to itself as an object of scrutiny. This paper proposes a novel approach forencryption and decryption of information in the form of Word Data (.doc file), PDF document(.pdf file), Text document, Gray-scale images, and RGB images, etc. by using Vigenere Cipher(VC) associated with Discrete Fourier Transform (DFT) and then hiding the data behindthe RGB image (i.e. steganography). Earlier developed techniques provide security of eitherPDF data, doc data, text data or image data, but not for all types of two-dimensional dataand existing techniques used either cryptography or steganography for security. But proposed

‡Corresponding author.

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approach is suitable for all types of data and designed for security of information by cryp-tography and steganography. The experimental results for Word Data, PDF document, Textdocument, Gray-scale images and RGB images support the robustness and appropriateness forsecure transmission of these data. The security analysis shows that the presented techniqueis immune from cryptanalytic. This technique further provides security while decryption as acheck on behind which RGB color the information is hidden.

Keywords : Steganography; Cryptography; Discrete Fourier Transform; Two-Dimensional Data;Security; Vigenere Cipher; Block Cipher; Data Encryption; Data Decryption.

1. INTRODUCTION

Networks and communication technologies providea large number of opportunities for people all overthe world to transmit data from one place toanother. These data may contain a lot of privateand valuable information. Security of data is essen-tial for securing the data from various types of secu-rity attacks. The main objective of this paper isto develop high-security for any type of data with-out attracting any suspicion about hidden secretmessage. Proposed cryptosystem provide securityof data by cryptography and steganography, whichis completely different from existing cryptosystemfor security of data. Cryptography allows us totransmit data in such a way that it is understoodonly at the receiver end. In cryptography, the orig-inal data are called the plaintext data,1,2 whichmust be kept secure. The plaintext (original data)changes into encrypted data by some algorithm,this encrypted data are known as ciphertext andthis process is called encryption process. Now, thesteganography is the art of hiding the fact thatcommunication is taking place, by hiding informa-tion in other information. Many different carrierfile formats can be used, but digital images arethe most popular because of their frequency on theinternet. For hiding secret information in images,there exists a large variety of steganography tech-niques some are more complex than others and allof them have respective strong and weak points.Different applications may require absolute invisi-bility of the large secret message. Mingwei et al.3

developed a high capacity image steganographyusing multi-layer embedding, which can enhancethe performance of information hiding system,Hang et al.4 hiding data through GerchbergSaxtonretrieval algorithm in fractional Fourier domain. Inpaper,4 the color components of the color imageare converted into a scrambled image by using

Arnold transform before the hiding operation simul-taneously and these changed images are regardedas the amplitude of fractional Fourier spectrum.Ching-Nung et al.5 have proposed steganographyand authentication in image sharing without paritybits. This paper intends to give an overview of imagesteganography and provide security of data throughsteganography.

Reference6 proposes novel cryptosystem for RGBimages by Random Matrix Affine Cipher (RMAC)with Discrete Wavelet Transform (DWT). In Ref. 6,each component of the RGB image data are sepa-rated, and then the algorithm is applied to it. Thescheme6,7 provides security of image data by thekeys and the arrangement of RMAC parameters,which is two layer security (first layer security bykeys and second layer security by the arrangementof RMAC parameters), and Ref. 8 is designed tosecure cryptosystem for color image data throughpublic-key cryptosystem or asymmetric key cryp-tosystem. In Ref. 9, the security of RGB imagedata developed by Random Hill Cipher (RHC) overSLn(F) domain associated with two-dimensionalDWT. Various schemes have been developed forsecurity of image data; such as: Refs. 10–12 pro-pose security of image data using Fourier transform;the Refs. 13–16 have given security of images ingyrator transform domain; Refs. 17–19 have devel-oped image encryption using Hartley transform;Refs. 20–22 have presented image coding by wavelettransform; the approach Refs. 23–25 have also pro-posed security of image data. The above-discussedcryptosystem provide security of image data only.So, these techniques are not suitable for all type ofdata.

Some techniques also provide security of datathrough watermark. In general, watermark can beembedded in spatial domain or transform domainor compressed domain of the multimedia. Spatial

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A First Cryptosystem for Two-Dimensional Data

domain techniques directly modulate the pixels.The pixel value of an image is modified to embedwatermark information. van Schyndel et al.26 dis-cuss two methods of watermarking. The first isbased on bit-plane manipulation of the LSB, whichoffers easy and rapid decoding. The second methodutilizes linear addition of the watermark to theimage data and is more difficult to decode, offer-ing inherent security. The LSB technique was laterimproved by Johnson and Katezenbeisser,27 whichincluded an additional security, by using a pseudo-random number generator to determine the pixelsto be used for embedding based on a given “seed”or key. A variable block size-based adaptive water-marking in spatial domain was proposed by Kimpanet al.,28 where the original image w divided into dif-ferent blocks of varied size and the watermark wasembedded into the blocks by analyzing and adjust-ing the brightness of a block.

It is important to save our valuable informationfrom the attacker, therefore we have applied multi-ple protection layers on our data by first encryptingit and then hiding it. In our method proposed ini-tially, we have taken binary file as an input, thisprovides us with versatility of different formats ofdata as actually any kind of data is stored in binaryin a computer. So, we can take any two-dimensionaldata like text, doc, image or PDF as input in uint8format, then we apply Vigenere Cipher (VC): blockor stream to convert it into cipher text, then weapply discrete Fourier transform (fft to make theconversions fast) which provide us with floatingpoint values. Then we hide these values using fixedpoint numeric object in Matlab behind an image.To conceal the very presence of our data we hidethe data in Least Significant Bit (LSB) of coverimage. Thus, making it undetectable to naked eyeas now change in the pixel value is minimum andthus making histogram of the image insignificantlyaffected. Further it can be hidden in middle bitsso as to be revealed as some watermark. So, wepass our important information unnoticed from theattacker, even if he/she attains some kind of attrac-tion from cover image, it is hard to decipher it asit is double encrypted by VC and further Fouriertransform.

The proposed technique can further be used asan Invisible Digital watermark that is more secure,highly imperceptible and robust technique for pro-tection and verification of copyright in data ineither in the form of text, doc, images or PDFwhen data are embedded at middle bits, it can be

retrieved or extracted by authenticated persons anddecrypted to check whether the copyright symbolor text obtained is valid or not. In this way, byhiding the data at middle bits instead of LSB weget the advantage that data are not easily lost ordegraded by many operations like compression ornoise in the image. Thus, by means of watermark-ing, the work is always accessible but permanentlymarked. Digital watermarking is having a variety ofuseful applications such as digital cameras, medicalimaging, image databases, video on demand sys-tems and many others. The mark could be usedto serialize a piece of data as it is sold or usedas a method to mark a valuable image. For exam-ple, this marking allows an owner to safely post animage for viewing but legally provides an embed-ded copyright to prohibit others from posting thesame image.

The rest of this paper is organized as follows. InSec. 2, we have presented VC for two-dimensionaldata. The mathematical formulation of DFT formultidimensional data is given in Sec. 3. The Infor-mation of encryption and decryption by VC andDFT is mentioned in Sec. 4. In Sec. 5, we havediscussed about computer simulation and experi-mental results for appropriateness of the cryptosys-tems. We have given the error analysis in Sec. 6.Comparison between presented cryptosystem andother existing approaches is given in Sec. 7. Finally,the proposed approach has been concluded inSec. 8.

2. VIGENERE CIPHER FORTWO-DIMENSIONAL DATA

Block Ciphers are a form of symmetric key cryp-tosystem. A block cipher is a function which mapsn-bit plaintext blocks to n-bit ciphertext blocks.The plaintext is divided into blocks of fixed lengthand every block is encrypted one at a time. It maybe viewed as a simple substitution cipher with largedata size. The function is parameterized by a k-bitkey K. Use of plaintext and ciphertext blocks ofequal size avoids data expansion. To allow uniquedecryption, the encryption function must be one-to-one (i.e. invertible). For n-bit plaintext and cipher-text blocks and a fixed key, the encryption functionis a bijection, defining a permutation on n-bitvectors.

Let a and n ≥ 1 be integers. The set of all integerswhich have the same remainder as a when dividedby n is called the congruence class of a modulo n,

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and is denoted by [a]n, where

[a]n = {x ∈ Z |x ≡ a (mod n)}. (1)

The collection of all congruence classes modulo n iscalled the set of integers modulo n, denoted by Zn

i.e.

Zn = {[0]n, [1]n, [2]n, . . . , [n − 1]n}. (2)

Encryption formula for two-dimensional data byBlock Cipher:

Let the key: K = (K1,K2, . . . ,Kk) ∈Z256 ⊕ Z256⊕, . . . ,⊕Z256︸︷︷︸, then the cipher data C =

(C1, C2, . . . , Ck) such that

C = EK(M) = (M + K) (mod 256), (3)

(C1, C2, . . . , Ck)

= EK(M1,M2, . . . ,Mk)

= (M1 + K1,M2 + K2,

. . . ,Mk + Kk) (mod 256), (4)

where, M = (M1,M2, . . . ,Mk) is block of the orig-inal data and C = (C1, C2, . . . , Ck) is block ofthe encrypted data. The length of the key K =(K1,K2, . . . ,Kk) depends on the length of block ofthe original data, which is defined by the choice ofuser.

Now, the decryption formula for two-dimensionaldata by inverse Block Cipher:

M = E−1K (C) = (C + (256 − K)) (mod 256), (5)

(M1,M2, . . . ,Mk)

= DK(C1, C2, . . . , Ck)

= (M1 + (256 − K1),M2 + (256 − K2),

. . . ,Mk + (256 − Kk)) (mod 256). (6)

The inverse of K1,K2, . . . ,Kk with respect to mod-ulo 256 is equal to 256 − K1, 256 − K2, . . . , 256 −Kk,29 respectively.

3. DISCRETE FOURIERTRANSFORM FORMULTI-DIMENSIONAL DATA

DFT30 is generally considered as an approxima-tion to continuous Fourier transform as values aretaken at discrete intervals of time and space. In our

proposed approach, for each pixel value of image wehave converted discrete spatial or time domain val-ues, i.e. samples taken at regular intervals of timeor space, into discrete frequency domain values, i.e.sum of amplitude of sine and cosine waves. thus,producing n complex number values, where n variesas number of pixel in the image depending uponthe size of image. This process is said to be forwardDFT.

Fu =M−1∑x=0

fx exp(−j2πux/M), (7)

where u = 0, 1, 2, . . . ,M − 1. Here, u is the fre-quency variable and x is the image coordinate vari-able. For two dimensions u, v are used as frequencyvariables, and x and y are used as image coordi-nates. At the time of decryption, frequency domainvalues obtained at each pixel position are convertedback to their spatial domain values and this processis known as inverse DFT or Synthesis.

fx =1M

M−1∑u=0

Fu exp(j2πux/M), (8)

where x = 0, 1, 2, . . . ,M − 1. Both these equa-tions are termed as 1D DFT pair, as these areinter-convertible, i.e. one can convert these two-dimensional values into frequency component val-ues and vice-versa. The Fast Fourier Transformrefers to algorithms that compute the DFT ina numerically efficient manner (Reduces compu-tations for two-dimensional data from the order(MN)2 summations and additions to MN log2 MNmultiplications and additions), thus giving its prac-tical approach. Algorithms like:-decimation in timeand decimation in frequency. Thus, these daysmostly FFT is used, as it runs fast on mod-ern computers and produce the same result infraction of computation time when compared tonormal DFT.

Further, one-dimensional DFT can be extendedinto multidimensional DFT for multidimensionaldata:

Fu1,u2,...,ud=

M1−1∑x1=0

exp(−j2πu1x1/M1)

×M2−1∑x2=0

exp(−j2πu2x2/M2) . . .

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×Md−1∑xd=0

exp(−j2πudxd/Md)

∗ fx1,x2,...,xd

,

(9)

where, d is the output indices run from ul = 0, 1,2, . . . ,Ml − 1. This is more compactly expressed invector notation, where we define x= (x1, x2, . . . , xd)and u = (u1, u2, . . . , ud) as d-dimensional vectors ofindices from 0 to M−1, which we define as M−1 =(M1 − 1,M2 − 1, . . . ,Md − 1), such that

Fu =M−1∑x=0

(fx exp(−j2πu(x/M))), (10)

where the division x/M is defined as x/M =(x1/M1,x2/M2, . . . , xd/Md) to be performed element-wise,and the sum denotes the set of nested summations.The inverse of the multidimensional DFT for mul-tidimensional data:

fx1,x2,...,xd=

1∏dl=1 Ml

M1−1∑u1=0

exp(j2πu1x1/M1)

×M2−1∑u2=0

exp(j2πu2x2/M2) . . .

×Md−1∑ud=0

exp(j2πudxd/Md)

∗ Fu1,u2,...,ud

, (11)

where,∏d

l=1 Ml = M1∗M2, . . . , ∗Md. Equation (11)can also be written as:

fx =1∏d

l=1 Ml

M−1∑u=0

(exp(j2πn(u/M))Fu). (12)

As the one-dimensional DFT expresses the inputfx as a superposition of sinusoids, the multidimen-sional DFT expresses the input as a superposi-tion of plane waves, or multidimensional sinusoids.The direction of oscillation in space is u/M =(u1/M1, u2/M2, . . . , ud/Md) and the amplitude isFu = Fu1,u2,...,ud

. The DFT has been widely usedacross a large number of fields such as spec-tral analysis, image processing, data compression,etc.

4. INFORMATION OFENCRYPTION ANDDECRYPTION BY VC ANDDFT

Encryption is the process to convert the simple butimportant information which we do not want toreveal to any unauthorized person, into cipher text(not understood by the third party). So, in thispaper we propose a novel cryptosystem for secu-rity of data to hide the actual data by merging twotechniques: Cryptography and Steganography. Oneimportant aspect of the approach is that it workswell for important or secret information either in theform of text, document, colored/gray-scale image orPDF. As information can be in any form depend-ing upon its purpose and use which is explainedand shown in figures by different examples taken.The procedure of creation of Crypto-Stego-Imageis given in Fig. 1 and procedure for reconstructionof data from Crypto-Stego-Image is discussed inFig. 2. In this method, we firstly convert uniformlyany kind of data into binary and then apply oneof the classical ciphers called VC using variable keylength. Most of the examples shown use block cipheralthough the proposed technique also works well forstream cipher. Encrypted data obtained from VCare further converted into their frequency domainvalues by DFT which makes data hard to decryptand finally we hide these values behind RGB com-ponents of a color image, to avoid any kind of suspi-cion from our data. In forward direction, firstly weapply cryptography then apply steganography forrobustness of the cryptosystem.

The similar process is applied for reconstructionof data from Crypto-Stego-Image. Figure 2 showsthe decryption procedure of the presented cryp-tosystem. At time of decryption, message lengthand variable length word key (for block cipher) orrandom key generated (in case of stream cipher) arepassed together as parameter as KEY for decryp-tion. Here, relevant information from an imageis obtained and then inverse DFT is applied ondata recovered from Crypto-Stego-Image. Finally,inverse of VC are applied to obtain informationin binary form which is converted into its origi-nal form. We have shown the experimental resultsthrough examples of “Word Data”, “PDF Data”,“Text Document”, “Gray-Scale Image Data” and“Colored Image Data” in Sec. 5, which show thatthe proposed cryptosystem is suitable for any typeof data.

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Fig. 1 Procedure for construction of CRYPTO-STEGO-IMAGE.

5. COMPUTER SIMULATIONAND EXPERIMENTALRESULTS

In this section, we have discussed computer simula-tion and experimental results in detail. The experi-mental results for Word data, PDF document data,Text document, Gray-scale image and Color imagedata are presented in the Sec. 5.1–5.5, respectively.These analyses show that the presented technique issuitable for secure transmission of all type of data.The computer simulation and experimental resultsare given below:

5.1. Results for Word Data

The experimental results, correlation at horizontal,vertical, and diagonal pixels, and histogram analysisof cover image and Crypto-Stego-Image for worddocument are given in the Figs. 3–5, respectively.Figure 3a is the original word document data, andRGB cover image is given in Fig. 3b. The Crypto-Stego-Image in Fig. 3c is obtained after hiding ofsecured word data. The secured word data are gen-erated by VC and DFT, while Fig. 3d is the recov-ered word document from Crypto-Stego-Image. TheCrypto-Stego-Image [Fig. 3c] is same as the cover

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Fig. 2 Procedure for reconstruction of data from CRYPTO-STEGO-IMAGE.

image [Fig. 3b], which shows that no one can sayabout any data hidden inside the image. The cor-relation at horizontal, vertical, and diagonal pix-els of the cover image and Crypto-Stego-Image arediscussed in Fig. 4. Figures 4a–4c are correlationsat horizontal, vertical and diagonal pixels of coverimage and Figs. 4d–4f are correlations at horizon-tal, vertical and diagonal pixels of Crypto-Stego-Image. Figure 4d is similar to Figs. 4a, Fig. 4eis similar to Fig. 4b and Fig. 4f is similar toFig. 4c. The similar correlation at horizontal, ver-tical, and diagonal pixels of the cover image and

Crypto-Stego-Image shows that the data of Crypto-Stego-Image are similar to the data of original coverimage.

The histograms of cover image [Fig. 3b] andCrypto-Stego-Image [Fig. 3c] are given in Figs. 5aand 5b, respectively. The histogram of Crypto-Stego-Image is similar to the histogram of coverimage. So, the attacker cannot say about anyinformation hidden inside the Crypto-Stego-Image.The experimental results, correlation analysis andhistogram analysis for the “word data” supportthe robustness and appropriateness of proposed

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(a) (b)

(c) (d)

Fig. 3 Results for word data: (a) original word document data; (b) RGB cover image; (c) Crypto-Stego-Image; (d) recoveredword document from Crypto-Stego-Image.

cryptosystems. So, the cryptosystem is applicablefor “word data”.

5.2. Results for PDF DocumentData

The experimental results for PDF document areshown in Fig. 6, and the pixel intensity distributionsof cover image and Crypto-Stego-Image are givenin Fig. 7. Figure 6a shows a question paper in PDFform for exam as a sample PDF, which is encryptedby VC and DFT and then we hide the outputobtained at LSB of RGB cover image [Fig. 6b].

Figure 6b is the RGB cover image used for hidingof PDF data and Fig. 6c is Crypto-Stego-Imageobtained after applying steganography for PDFdocuments. Figure 6d is sample of PDF obtainedby Crypto-Stego-Image after applying inverse pro-cedure of proposed cryptosystem. The PDF docu-ment [Fig. 6d] recovered from Crypto-Stego-Imageis exactly similar to the original PDF document[Fig. 6a], which shows that the PDF data are com-pletely recovered from Crypto-Stego-Image withoutloss of any information.

The pixel intensity distributions at horizontal,vertical and diagonal pixels of the color cover image

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(a) (b)

(c) (d)

(e) (f)

Fig. 4 Pixel intensity distributions: (a) pixel intensity distributions at horizontal direction of Fig. 3b; (b) pixel intensity dis-tributions at vertical direction of Fig. 3b; (c) pixel intensity distributions at diagonal direction of Fig. 3b; (d) pixel intensitydistributions at horizontal direction of Fig. 3c; (e) pixel intensity distributions at vertical direction of Fig. 3c; (f) pixel intensitydistributions at diagonal direction of Fig. 3c.

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(a) (b)

Fig. 5 Histogram analysis of Fig. 3: (a) histogram of Fig. 3b; (b) histogram of Fig. 3c.

(a) (b)

Fig. 6 Results for PDF data: (a) original PDF document data; (b) RGB cover image; (c) Crypto-Stego-Image; (d) recoveredPDF document from Crypto-Stego-Image.

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(c) (d)

Fig. 6 (Continued)

(a) (b)


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(c) (d)

(e) (f)

Fig. 7 (Continued)

[Fig. 6b], are given in Figs. 7a–7c, respectively andFigs. 7d–7f are pixel intensity distributions at hori-zontal, vertical and diagonal pixels of Crypto-Stego-Image [Fig. 6c]. The pixel intensity distribution ofcover image and Crypto-Stego-Image support therobustness and stalwartness of the proposed tech-nique. Figures 8a and 8b show the histogram ofcover image before embedding the data in it andafter embedding the data, respectively. which showsthat both differ minutely.

5.3. Results for Text Document

Figure 9 shows the results for text data obtainedby the proposed technique. Figure 9a is an exampleof text containing some important news. Figure 9bshows the RGB cover image in which we will hidedata. Figure 9c is the Crypto-Stego-Image obtained

after hiding the cipher data obtained from textdocument after applying VC and DFT into Coverimage. Now, the original text document is recoveredfrom Crypto-Stego-Image at the receiver’s side afterapplying inverse DFT and inverse VC as shownin Fig. 9d. Now, Figs. 10a–10c are pixel intensitydistributions obtained for horizontal, vertical anddiagonal values of Fig. 9b, respectively, i.e. coverimage, and Figs. 10d–10f are pixel intensity dis-tributions for horizontal, vertical and diagonal val-ues of Fig. 9c, respectively, i.e. Crypto-Stego-Imageproduced by merging encrypted text in it. Thepixel intensity distribution at horizontal direction inFig. 10a looks same as pixel intensity distribution athorizontal direction in Fig. 10d, pixel intensity dis-tribution at vertical direction in Fig. 10b is similaras pixel intensity distribution at vertical direction inFig. 10e and pixel intensity distribution at diagonal

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(a) (b)


(a) (b)

Fig. 9 Results for tex data: (a) original tex data; (b) cover image; (c) Crypto-Stego-Image; (d) recovered text data fromCrypto-Stego-Image.

direction in Fig. 10c looks same as pixel intensitydistribution at diagonal direction in Fig. 10f, Theseanalyses show that the data of Crypto-Stego-Imageare similar to the data of the cover image. Fur-ther, Figs. 11a and 11b are the histograms of the

cover image and Crypto-Stego-Image, respectively.The similar visual effect of both histograms supportthat Crypto-Stego-Image obtained after hiding datashow hardly any changes when compared to coverimage.

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(c) (d)

Fig. 9 (Continued)

5.4. Results for Two-DimensionalGray-Scale Image

This subsection shows similar results as for thecolored image, here for gray-scale image. In thisexample, we have taken 256 × 256 size Barbaragray-scale image as shown in Figs. 12a and 12bas the RGB cover image for hiding data. Now,we embed an encrypted image of Barbara insideanother cover image itself. Figure 12c is the Crypto-Stego-Image produced after embedding the data.Figure 12c seems to be same as the actual coverimage in Fig. 12b, thus depicting minimum chances

of a suspicion on cover image while communication.Finally, at reception of image, the actual Barbaraimage is recovered as shown in Fig. 12d.

Figures 13a–13c are pixel intensity distribu-tions obtained for horizontal, vertical and diag-onal values of Fig. 12b, respectively, i.e. coverimage and Figs. 13d–13f are pixel intensity distri-bution obtained for horizontal, vertical and diag-onal values of Fig. 12c, respectively. The his-tograms of Figs. 12a–12d are given in Figs. 14a–14d,respectively. These histograms suggest the sameresult as Figs. 14b and 14c, i.e. Cover image andCrypto-Stego-Image obtained looked the same. Also

(a) (b)


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(c) (d)

(e) (f)

Fig. 10 (Continued)

(a) (b)


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(a) (b)

(c) (d)

Fig. 12 Results for gray-scale image: (a) original Barbara gray-scale image of size 256 × 256 × 3; (b) RGB cover image; (c)Crypto-Stego-Image; (d) recovered color lena image from Crypto-Stego-Image.

the histogram of the image obtained after decryp-tion is exactly similar to the histogram of the origi-nal image. A similar histogram shows that the orig-inal data are completely recovered without loss ofany sensitive information.

5.5. Results for Two-DimensionalColor Image Data

In this section, we have discussed the security forcolor image data. The proposed cryptosystem isapplied on RGB lena image of size 256×256×3. Fig-ure 15a is the lena color image, Fig. 15b is the coverimage. The Crypto-Stego-Image is given in the

Fig. 15c and the recovered RGB lena image is givenin Fig. 15d. The Crypto-Stego-Image in Fig. 15cis exactly similar to the cover image in Fig. 15b,which represent shows that no one can say aboutany image inserted inside the cover image. Recov-ered color lena image from Crypto-Stego-ImageFig. 15d has the same visual effect as the originalone. Now, Figs. 16a–16c are pixel intensity distribu-tions obtained for horizontal, vertical and diagonalvalues of Fig. 15b, respectively, i.e. cover image, andFigs. 16d–16f are pixel intensity distributions forhorizontal, vertical and diagonal values of Fig. 15c,respectively, i.e. Crypto-Stego-Image produced by

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(a) (b)

(c) (d)

(e) (f)

Fig. 13 Pixel intensity distributions: (a) pixel intensity distributions at horizontal direction of Fig. 12b; (b) pixel intensitydistributions at vertical direction of Fig. 12b; (c) pixel intensity distributions at diagonal direction of Fig. 12b; (d) pixelintensity distributions at horizontal direction of Fig. 12c; (e) pixel intensity distributions at vertical direction of Fig. 12c; (f)pixel intensity distributions at diagonal direction of Fig. 12c.

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(a) (b)

(c) (d)

Fig. 14 Histogram analysis of Fig. 12: (a) histogram of Fig. 12a; (b) histogram of Fig. 12b; (c) histogram of Fig. 12c; (d)histogram of Fig. 12d.

merging encrypted text in it. The pixel inten-sity distribution at horizontal direction in Fig. 16alooks the same as the pixel intensity distributionat horizontal direction in Fig. 16d, pixel inten-sity distribution at vertical direction in Fig. 16b is

similar to the pixel intensity distribution at verticaldirection in Fig. 16e and pixel intensity distributionat diagonal direction in Fig. 16c looks the same asthe pixel intensity distribution at diagonal directionin Fig. 16f, These analyses show that the data of

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(a) (b)

(c) (d)

Fig. 15 Results for color image: (a) original color lena image of size 256 × 256× 3; (b) RGB cover image; (c) Crypto-Stego-Image; (d) recovered color lena image from Crypto-Stego-Image.

(a) (b)

Fig. 16 Pixel intensity distributions: (a) pixel intensity distributions at horizontal direction of Fig. 15b; (b) pixel intensitydistributions at vertical direction of Fig. 15b; (c) pixel intensity distributions at diagonal direction of Fig. 15b; (d) pixelintensity distributions at horizontal direction of Fig. 15c; (e) pixel intensity distributions at vertical direction of Fig. 15c; (f)pixel intensity distributions at diagonal direction of Fig. 15c.

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D. C. Mishra et al.

(c) (d)

(e) (f)

Fig. 16 (Continued)

(a) (b)

Fig. 17 Histogram analysis of Fig. 15: (a) histogram of Fig. 15a; (b) histogram of Fig. 15b; (c) histogram of Fig. 15c; (d)histogram of Fig. 15d.

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(c) (d)

Fig. 17 (Continued)

Crypto-Stego-Image are similar to the data of thecover image. Moreover, the histograms of Figs. 15a–15d are given in Figs. 17a–17d, respectively. Thehistogram of original image, in Fig. 15a is the sameas the histogram of recovered image, Fig. 15d, whichshows that the original image is completely recov-ered from Crypto-Stego-Image Fig. 15c without lossof any information. The histogram of Crypto-Stego-Image in Fig. 15c is almost similar to the his-togram of the cover image, Fig. 15b, the similarhistogram of Crypto-Stego-Image and cover imageshows that the Crypto-Stego-Image is similar tothe cover image, so the intended secret messagedoes not attract attention to itself as an object ofscrutiny.

6. ERROR ANALYSIS

In this section, we have discussed Mean SquareError (MSE), Peak Signal-to-Noise Ratio (PSNR)and Correlation Coefficient (Cr) of input and out-put data.

6.1. Mean Square Error

The MSE between the original and reconstructedRGB color image for red (R), green (G) and blue

(B) components are computed from

MSE(O,Re) =1

N × M

N∑n=1

M∑m=1

[|f(n∆x,m∆y)

− f0(n∆x,m∆y)|2], (13)

where O and Re denote the original frame andreconstructed frame, respectively, N and M are thepixels of the frame, and ∆x and ∆y are the pixelsizes.

6.2. Peak Signal-to-Noise Ratio

The PSNR between the original and reconstructedcolor image is computed by

PSNR(O, Re)

= 10 · log10

0B@

MAX2I

1N×M

PNn=1

PMm=1[|f(n∆x, m∆y)

− f0(n∆x,m∆y)|2]

1CA,

= 20 · log10

0BBBBB@

MAXIvuuuuut

1N×M

PNn=1

PMm=1

[|f(n∆x, m∆y)

−f0(n∆x, m∆y)|2]

1CCCCCA

, (14)

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D. C. Mishra et al.

where O and Re denote the original and recon-structed frames and MAXI is the maximum pos-sible pixel value of the image. More generally,when samples are represented using Linear Pulse-code Modulation (LPCM) with B1 bits per sample,MAXI is 2B1 − 1.

6.3. Correlation Coefficient (Cr)

Correlation coefficient (Cr) of red (R), green (G)and blue (B) channels of original image (O) andreconstructed image (Re) are computed by

Cr(O,Re) =∑

m

∑n(Amn − A)(Bmn − B)√[∑m

∑n(Amn − A)

]2[∑m

∑n(Bmn − B)

]2

, (15)

where A and B are, respectively, mean of input(original image) and output (reconstructed image)images. The correlation coefficient between two

images vary from −1 to +1, i.e. −1 ≤ Cr ≤ +1. Twoimages A and B have a strong positive linear corre-lation if the correlation coefficient Cr is close to +1.The −1 value of the correlation coefficient Cr indi-cates a negative relationship between two imagesand the correlation coefficient zero represents norelationship between two images. The MSE, PSNRand Cr of red (R), green (G) and blue (B) chan-nels of output and input RGB images are given inTables 1–7.

The MSE, PSNR and correlation coefficient (Cr)of Crypto-Stego-Image with respect to the coverimage of Word Data, PDF document, Text docu-ment, Gray-scale images and RGB images are givenin the Tables 1–4 and 6, respectively. The valuesof MSE, PSNR and correlation coefficient representthat the Crypto-Stego-Image is similar to the coverimage for all data, which support to the robust-ness of the proposed cryptosytem. The values of

Table 1 Statistical Analysis for Word Data: Analysis BetweenCover Image and Crypto-Stego-Image.

S.No. Components of RGB Image MSE PSNR Correlation

1. Red component of RGB image 0.4709 51.4012 1.002. Green component of RGB image 0.00 ∞ 1.003. Blue component of RGB image 0.00 ∞ 1.00

Table 2 Statistical Analysis for PDF Document: Analysis BetweenCover Image and Crypto-Stego-Image.



Table 3 Statistical Analysis for Text Document: Analysis BetweenCover Image and Crypto-Stego-Image.



Table 4 Statistical Analysis for Gray-Scale Image: AnalysisBetween Cover Image and Crypto-Stego-Image.



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Table 5 Statistical Analysis for Gray-Scale Image: Analy-sis Between Barbara Original Image Fig. 12a and BarbaraDecrypted Image Fig. 12d.

S.No. Gray-Scale Image MSE PSNR Correlation

1. Barbara Gray-scale image 0.00 ∞ 1.00

Table 6 Statistical Analysis for Color Image: Analysis BetweenCover Image and Crypto-Stego-Image.



Table 7 Statistical Analysis for Color Image: Analysis BetweenLena Original Image Fig. 15a and Lena Decrypted Image Fig. 15d.


1. Red component of RGB image 0.00 ∞ 1.002. Green component of RGB image 0.00 ∞ 1.003. Blue component of RGB image 0.00 ∞ 1.00

MSE, PSNR and correlation of Tables 5 and 7shows that the decrypted gray-scale image and colorimage are completely recovered without loss of anyinformation.

7. KEY SPACE ANALYSIS

In cryptography, an algorithm’s key space refersto the set of all possible keys that can be usedto generate a key, and is one of the most impor-tant attributes that determines the strength of acryptosystem. The key space has been individu-ally investigated to show the robustness of cryp-tosystem on brute-force attack. VC uses key toencrypt the data, key space is the maximum possi-ble size of a key, i.e. therefore dependent on lengthof key. In our paper we have taken binary key asan example shown in figure to encrypt the datait is [118 105 110 101 103 101 114], this valueis in uint-8, therefore key space is (255)m, wherem is the size of key. As in our example (255)7,i.e. 7.0110209207109375 × 1016 is our key space.So, for brute force attack the key space is quitelarge. Further, our approach works well for streamcipher, thus making the key space (255)n, where nis the length of the message. As in stream cipher,the key is randomly selected till the length ofthe message, thus preventinf frequency analysis ofcipher text.

8. COMPARISON OF THEPROPOSED CRYPTOSYSTEMWITH EXISTING METHODS

The presented cryptosystem is compared with exist-ing techniqus for security of data such as: Ming-wei et al.,3 Hang et al.,4 Ching-Nung et al.,5

Abuturab,14 Chen et al.,22 Abuturab14 developeda secure cryptosystem for color images with thehelp of Arnold transform and Chen et al.22 havediscussed color image encoding in dual fractionalFourier-wavelet domain with random phases. Theauthors Abuturab14 and Chen et al.22 both havedesigned algorithms for only image encryption anddecryption by cryptography. These techniques pro-vides security of image data only, which is not suit-able for Word data, PDF data, Text document. Fur-ther, Refs. 14 and 22, the attacker always know thedata are secured by some algorithm. So, attack-ers try to decrypt the secret message by usingsome cryptanalysis. The experimental results andcomputer simulation of MR Abuturab14 and Chenet al.22 are given in Figs. 18 and 19, respectively.The encryption and decryption results of Fig. 18represent that the data are scrambled by some algo-rithms, and the security of image data designedby MR Abuturab14 depends on keys only. If theattacker is knows about the exact keys, then theattacker can decrypt the original information easily.

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(a) (b)

(c) (d)

Fig. 18 Results of the proposed color image encryption and decryption: (a) original image with 512× 512 pixels and 24 bitsused in numerical simulation; (b) encrypted image, (c) decrypted image with all the correct keys; (d) decrypted image withtransformation angles for component images changed by 0.004 but correct iterative numbers and random phase functions.

Now, Fig. 19 also shows that Chen et al.22 changeoriginal image data by using some of the techniques.The procedure of encryption and decryption arealso depends on keys only. So, the scheme22 providesonly one layer of security of image data. Hence,the security of schemes14,22 depends on keys andthese cryptosystems are suitable for image only.Further, Mingwei et al.,3 Hang et al.4 and Ching-Nung et al.5 designed secure cryptosystems fortwo-dimensional data through steganography only.Mingwei Tanga et al.3 has developed a high capacityimage steganography using multi-layer embedding,which can enhance the performance of informationhiding system. Hang et al.4 has proposed Opti-cal color image hiding scheme by using Gerchberg–Saxton algorithm in fractional Fourier domain, and

Ching-Nung et al.5 has given steganography andauthentication in image sharing without parity bits.The papers3–5 are also appropriate for image datasecurity. The experimental results of paper3 aregiven in Figs. 20 and 21. Now, computer simulationof the technique5 is shown in Fig. 22. Figures 20–22show that the papers3 and5 developed secure cryp-tosystem through steganography. So, Refs. 3–5 pro-vide only one layer of security for image data. Butthe proposed cryptosystem “A first cryptosystemfor security of two dimensional data” is designedby cryptography and steganography which are suit-able for secure transmission of all types of datasuch as Word Data, PDF document, Text docu-ment, Gray-scale images and RGB images. In theproposed cryptosystem, if the attackers know all

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(a) (b) (c)

(d) (e) (f)

Fig. 19 Computer simulation results of color image encoding and decoding: (a) an original RGB picture with 512 × 512pixels; (b) its color encryption result; (c)–(e) the incorrect decryption results; (f) the correctly reconstructed image.

(a) (b)

Fig. 20 The experiment data: (a) the host image and (b) the secret image.

the exact keys of cryptography but not aware ofthe procedure of embedding the data, then he/shecannot recover the original information and if theattacker has information about the procedure ofembedding the data but no information about thekeys and key length of the VC and DFT, thenhe/she can not decrypt the original data. Moreover,

if the attacker knows all exact keys but no infor-mation about which RGB color data exists, orderof encryption and position of DFT, then the origi-nal image cannot be recovered from Crypto-Stego-Image. So, the presented cryptosystem is morerobust and appropriate in comparison to Refs. 3–5,14, 22.

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(a) (b)

Fig. 21 The experiment results: (a) the encrypted image and (b) the extracted secret image.

(a) Jet (b-1) Lena: 52.91 dB (b-2) Pepper: 52.91 dB

(b-3) Baboon: 52.91 dB (b-4) Elaine: 52.90 dB (b-5) Boat: 52.91 dB

Fig. 22 The reconstructed images and five stego-images for the proposed (3,5)SAIS scheme: (a) a 256 × 256-pixeled secretimage; (b) five 512 × 512-pixeled stego-images.

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Summing up, the facts shown above, includ-ing all-experimental results, statistical analysis ofthe proposed cryptosystem, and comparison to theexisting techniques for security of data, support tothe robustness and appropriateness of the presentedcryptosystem of secure transmission of all type ofdata.

9. CONCLUSION

This paper proposed a novel cryptosystem for secu-rity of Word Data, PDF document, Text docu-ment, Gray-scale images and RGB images. In thepresented cryptosystem, we have considered VC aseither block encoding or stream encoding followedby DFT for cryptography and then we hide thedata in LSB of cover image such that it is notvisible to human eye. So, the presented cryptosys-tem provides security of data through cryptogra-phy and steganography. The main advantage of theproposed technique is that the intended secret mes-sage does not attract attention to itself as an objectof scrutiny. Moreover, the technique further pro-vides security while decryption as a check on behindwhich RGB color the information is hidden. Fur-ther, the decryption of information is done in thesame manner in reverse order. In this technique,even if somebody gets to know that something ishidden behind the image, it is still hard to retrievethe original information as it is triple protected:as one first needs to know behind which color theinformation is hidden or the correct order in whichone should put the information, secondly informa-tion is in its frequency representation, so one cannotmake out the original information which is furtherprotected by VC encryption. The recovered dataare exactly similar to the original data, which sig-nify that the presented cryptosystem provides secu-rity of data without loss of any information. Theexisting techniques for security of data designed byeither cryptography or steganography only, and fur-ther, these developed techniques are suitable onlyfor Image data or Text documents, but the proposedapproach proved security of data by both cryptogra-phy and steganography and this technique is appro-priate for all types of data. The security analy-sis and statistical analysis support the robustnessand appropriateness of secure transmission of datathrough any network. So, this technique can be usedfor transmission of information represented in anyof these formats like Word Data, PDF document,Text document, Images (Colored and Gray-scale)

efficiently and securely through insecure channelwithout loss of any information.

ACKNOWLEDGMENTS

This work has been supported by University ofDelhi, under grant number RC/2015/9677, NewDelhi-110007, India.

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