Image Authentication Using Stochastic Diffusion 2013 Java Basepaper... · Image Authentication Using Stochastic Diffusion ... embedded in the image using the bit-plane specified

Image Authentication Using Stochastic Diffusion

AbdulRahman I. Al-RawiCollege of Applied Studies

University of BahrainKingdom of [email protected]

Jonathan M. BlackledgeSchool of Electrical Engineering Systems

Dublin Institute of TechnologyDublin, Ireland

[email protected]

Abstract—This paper considers an approach to encryptedinformation hiding based on Stochastic Diffusion for encryptingdigital images coupled with the application of a Least Signifi-cant Bit (LSB) method for information embedding. After pro-viding a brief summary of various information hiding methodsbased on spatial and transform domain techniques, two newmethods are introduced. The first of these considers a binaryimage watermarking algorithm for hiding an image in a singlehost image which is based on binarization of the encrypteddata. The second method extends this approach to solving theproblem of 24-bit image hiding in three host images whichgenerates a near perfect reconstruction after decryption. Bothmethods make use of a ‘hidden code’ technique to randomizethe order of the embedded bits and the location (in the imageplane) of the LSBs which make the embedded informationmore robust to attack. Details of the algorithms developedare provided and examples are given, which have applicationin the field of covert cryptography and the authentication offull colour images for copyright protection and Data RightsManagement.

Keywords-Encrypted Information Hiding; Stochastic Diffu-sion; Hidden Codes.

I. INTRODUCTION

Following rapid developments in computer networks anddigital media transmission (e.g. digital image, audio andvideo data) along with the fast growth of Internet con-nectivity, the demand for securing data exchange over theInternet has become increasingly important. Transmissionof data over networks and Internet-based dissemination ofdigital information has brought about several security issues.Illegal distribution of digital media, copyright protectionof digital data, copying, and unauthorized information in-terception are common problems requiring innovative andnovel solutions. Of these, cryptography remains the mostcommon. There are a large number of commercially avail-able cryptosystems for data encryption that are consideredcomputationally secure and are relatively difficult to break[1]-[9], but using cryptography does not necessarily assuresecurity of a transmission; the meaningless form of data afterencryption leads to suspicion of its importance and potentialattack. In addition, rapid improvements in the computationalperformance and sophistication of attack methods threatenthe security of encryption techniques. Finally, encrypted datamay be incriminating in countries when encryption is illegal.

This paper presents the encrypted information hiding con-cept to reduce the risk of using cryptographic algorithmsalone. Data hiding techniques embed information into an-other medium making it imperceptible to others, exceptfor those that are meant to receive the hidden informationand are aware of it presence. It focuses on methods ofencrypting hidden data in which cryptographic algorithmsare combined with the information hiding techniques toincrease the security of transmitted data. In such schemes,the secret data is first encrypted, then embedded into coverdata to generate ‘stego-data’, which is then sent througha network or via the Internet. The unauthorized recoveryof hidden encrypted data is very difficult because it needsthe interceptor to first detect the existence of the hiddeninformation, determine a way of extracting it from thehost data and then decrypting it to recover the originalinformation.The stochastic diffusion process is used as cryptographymethod. In terms of plaintexts, diffusion ensures that similarplaintexts should result in completely different ciphertextseven when encrypted with the same key [10], [11]. Thisrequires that any element of the input block influences everyelement of the output block in an irregular way. In terms of akey, diffusion ensures that similar keys result in completelydifferent ciphertexts even when used for encrypting the sameblock of plaintext. This requires that any element of the inputshould influence every element of the output in an irregularfashion. This property must also be valid for the decryptionprocess because otherwise an attacker may be able to recoverparts of the input from an observed output by a partiallycorrect guess of the key used for encryption. The diffusionprocess is a function of sensitivity to initial conditions that acryptographic system should have and further, the inherenttopological transitivity that the system should also exhibitcausing the plaintext to be mixed through the action of theencryption process.

II. ENCRYPTED INFORMATION HIDING

Compared with information hiding in general, the numberof publications that have addressed the issue of hidingencrypted information are relatively few. The encryptedinformation hiding (EIH) algorithms can be categorized into

15TH INTERNATIONAL CONFERENCE ON COMPUTERMODELLING AND SIMULATION YEAR 2013

two types: (i) Spatial domain EIH, where the original hostimage is directly adjusted, are generally considered simpleand often require lower computational cost. However, theycan be less robust against attacks such as compression. (ii)Transform domain EIH are achieved by transforming thehost image into a suitable transform domain and modify-ing its coefficients to embed information. Such techniquesrequire higher computational cost and are more complexto implement, although they are considered more robustto various attacks. The following two sections provide anoverview of the published literature about EIH techniquesbased on these methods.

A. Encrypted Information Hiding in the Spatial Domain

In [13] a watermarking scheme is described that combineslossless compression and encryption for medical imaging ap-plications. The authors proposed that a doctor/radiologist isinteractively provided with a defined polygonal Region of In-terest (ROI). The data is encrypted using Advanced Encryp-tion Standard (AES) algorithm, and then the watermark iscompressed using an arithmetic integer compression method.The compressed data is then converted to a binary string andembedded in the image using the bit-plane specified by theuser. In [14] the authors proposed a steganographic methodusing PNG formatted images based on an information shar-ing technique. The secret image M is divided into shareswhich are embedded into the alpha-channel of the PNG hostimage. In [15] the authors introduced the principle of imagescrambling and information hiding and proposed a doublerandom scrambling procedure based on image blocks. In[16] a virtually imperceptible image hiding scheme basedon vector quantization (VQ) is proposed. The authors goalwas to design a high quality and a high capacity imagehiding scheme which is based on the VQ compression and aDigital Encryption Standard (DES) based cryptosystem. In[18] an approach to digital watermarking based on the use ofcryptography in conjunction with watermarking is presented.The watermark is encrypted by diffusing it with a cipher toproduce a scrambled image. The scrambled image is then‘confused’ with a host image to hide the encrypted imageand produce to the stego-image.

B. Encrypted Information Hiding in the Transform Domain

A steganographic-based approach is proposed in [19] toprotect the iris code data by hiding it in a digital image forpersonal data identification purposes. The iris code data isencrypted using the logistic chaotic map, then the embeddingis carried out in DCT domain but changing the mid-to-high frequency band in each DCT block, finally the inverseDCT is applied to generate the stego-image. The extractionprocess is performed by transforming the stego-image intothe DCT domain and selecting the correct coefficients toextract the secret data. The authors in [20] proposed a newhybrid scheme based on a Singular Value Decomposition

(SVD), norm quantization and a Modulo-2 approach usingtwo separate procedures to embed two binary watermarkimages into a grayscale image of size 256 ⇥ 256. The firstbinary watermark image of size 32 ⇥ 32 is encrypted andthen embedded into the host image (after applying SVDmatrix norm quantization method to the host). For the secondlevel, the low frequency sub-band from the first level isdecomposed using the IWT-Modulu-2 method resulting infour sub-bands of size 64⇥64. The second binary watermarkis then embedded into the second level decomposition. Anadaptive digital watermarking algorithm based on chaos andimage fusion is presented in [21]. The watermark imageis first encrypted using the logistic chaos map, then theadaptive watermark embedding algorithm is applied basedon NVF (Noise Visibility Function) and image fusion in thewavelet domain.

III. ENCRYPTED IMAGE HIDING USING STOCHASTICDIFFUSION

In ‘image space’, the plaintext is considered to be an im-age p(x, y) of compact support x 2 [�X,X]; y 2 [�Y, Y ].Stochastic diffusion is that process compounded in thefollowing encryption/decryption algorithms:

Encryption

c(x, y) = m(x, y)⌦x

⌦y

p(x, y)

wherem(x, y) = F�1

2 [M(k

x

, k

y

)]

and 8kx

, k

y

M(k

x

, k

y

) =

(N

⇤(kx

,k

y

)|N(k

x

,k

y

)|2 , | N(k

x

, k

y

) | 6= 0;

N

⇤(k

x

, k

y

), | N(k

x

, k

y

) |= 0.

The symbols ⌦x

and ⌦y

denote convolution in x and y,respectively, k

x

and k

y

are the spatial frequencies, F�12

denotes the two-dimensional inverse Fourier transform andthe function N(k

x

, k

y

) is taken to be the Fourier transformof a cipher n(x, y).

Decryption

p(x, y) = n(x, y)�x

�y

c(x, y)

where �x

and �y

denote correlation in x and y, respectively.For digital image hiding, we consider a discrete imagearray p

ij

, i = 1, 2, ..., I; j = 1, 2, ..., J of size I ⇥ J anddiscrete versions of the operators involved, i.e. applicationof a discrete Fourier transform and discrete convolution andcorrelation sums.

For applications in image watermarking, stochastic diffu-sion has two principal advantages:

• a stochastic field provides uniform diffusion;• stochastic fields can be computed using random number

generators that depend on a single initial value or

seed which can be used as a private key for theencryption/decryption process.

Detailed information about stochastic diffusion and itsmathematical background can be found in [12]

A. Binary Image WatermarkingWe consider the plaintext image p(x, y) to be of binary

form, such that the output of stochastic diffusion can bebinarized to give a binary ciphertext. The rationale forimposing this condition is based on considering a systemin which a user is interested in covertly communicatingdocuments such as confidential letters and certificates.

If we consider a plaintext image p(x, y) which is a binaryarray, then stochastic diffusion using a pre-conditioned ci-pher 0 m(x, y) 1 consisting of an array of floatingpoint numbers will generate a floating point output. TheShannon Information Entropy of of any array A(x

i

, y

i

) withProbability Mass Function (PMF) p(z

i

) is given by

I = �X

i=1

p(z

i

) log2 p(zi)

The information entropy of a binary plaintext image (withPMF consisting of two components whose sum is 1) istherefore significantly less than the information entropy ofthe ciphertext image. In other words, for a binary plaintextand a non-binary cipher, the ciphertext is data redundant.This provides us with the opportunity of binarizing theciphertext by applying a threshold, i.e. if c

b

(x, y) is thebinary ciphertext, then

c

b

(x, y) =

(1, c(x, y) > T

0, c(x, y) T

where 0 c(x, y) 18x, y. A digital binary ciphertextimage c

b

(x

i

, y

j

) where

c

b

(x

i

, y

i

) =

(1, or

0, for any x

i

, y

j

can then be used to watermark an 8-bit host imageh(x, y), h 2 [0, 255] by replacing the lowest 1-bit layerwith c

b

(x

i

, x

j

). To recover this information, the 1-bit layeris extracted from the image and the result correlated withthe digital cipher n(x

i

, y

j

). Note that the original floatingpoint cipher n is required to recover the plaintext image andthat the binary watermark can not therefore be attacked onan exhaustive XOR basis using trial binary ciphers. Thus,binarization of a stochastically diffused data field is entirelyirreversible.

B. Principal AlgorithmsThe principal algorithms associated with the application

of stochastic diffusion for watermarking with ciphers are asfollows:Algorithm I: Encryption and Watermarking Algorithm

Step 1: Read the binary plaintext image and compute thesize I ⇥ J of the image.Step 2: Compute a cipher of size I ⇥ J using a private keyand pre-condition the result.Step 3: Convolve the binary plaintext image with the pre-conditioned cipher and normalise the output.Step 4: Binarize the output obtained in Step 3 using athreshold based on computing the mode of the Gaussiandistributed ciphertext.Step 5: Embed the binary output obtained in Step 4 intothe host image Least Significant Bit (LSB) to generate thestego-image.The following points should be noted:(i) The host image is an 8-bit or higher grey level imagewhich must ideally be the same size as the plaintext imageor else resized accordingly using the same proportions.(ii) Pre-conditioning the cipher and the convolution pro-cesses are undertaken using a Discrete Fourier Transform(DFT).(iii) The output given in Step 3 will include negative floatingpoint numbers upon taking the real component of a complexarray. The array must be rectified by adding the largestnegative value in the output array to the same array beforenormalisation.(iv) For colour host images, the binary ciphertext can beinserted into one or all of the RGB components.(v) The binary plaintext image should have homogeneousmargins to minimise the effects of ringing due to ‘edge-effects’ when processing the data using Fourier transform.

Algorithm II: Decryption and Extraction Algorithm

Step 1: Read the stego-image and extract its lowest 1-bitlayer.Step 2: Regenerate the (non-preconditioned) cipher usingthe same key used in Algorithm I.Step 3: Correlate the cipher with the input obtained in Step1 and normalise the result.Step 4: Quantize and format the output from Step 3 toconstruct the original image.The following points should be noted:(i) The correlation operation should be undertaken using aDFT.(ii) For colour images, the data is decomposed into eachRGB component and each 1-bit layer is extracted andcorrelated with the appropriate cipher.(iii) The output obtained in Step 3 has a low dynamicrange and therefore requires to be quantized into an 8-bitimage based on floating point numbers within the rangemax(array)-min(array).

Figure 1. Certificate with binary watermark (left) and decrypt (right).

IV. BINARY IMAGE WATERMARKING USING HIDDENCODES

In order to avoid the LSB extraction, increase the securityof the hidden data and improve the robustness of the binarywatermarking algorithms discussed earlier, we consider amethod of randomizing the cipher bits over multiple hostimage LSBs as well as randomizing the embedding bitsorder using different noise distribution (models) as hiddencodes. We consider the Gaussian, Log-normal, and Uniformdistributions as hidden codes.

A. Gaussian DistributionGaussian coding is performed by generating a Gaussian

distributed noise pattern, and then randomizing the bit-levelof host image embedding according to this distribution.Theoretically, any host image bits can be used for embeddingthe binary cipher. However, using all 8-bits of the host imagereduces image quality, especially over flat or homogeneousregions. Since most of the information is hidden in the firstLSB of the host image, extracting the LSB and correlating itwith the original cipher (if exposed) may reveal the originaldata, especially when the number of host image bits used forhiding decreases. We concur that at least 5-bits for hidingthe binary cipher should be used thus reducing the amountof information hidden in the LSB. An alternative solutionis to use different noise distributions as discussed in thefollowing sections.

B. Log-normal DistributionIn order to reduce the amount of data stored in the first

LSB of the host image, a log-normal distribution can beused for bit-level coding. This reduces the potential forunauthorized document access.

C. Uniform DistributionThe uniform distribution provide an alternative to the

previous described techniques, with the major advantagebeing that the binary cipher is scattered uniformly over thehost image bits. This makes the host image more secureagainst LSB extraction attack.

V. ENCRYPTED GREY SCALE IMAGE HIDING

The binary image watermarking method discussed earlieris suitable for document authentication, but the lossy natureof the reconstruction generated through binarization of thecipher (illustrated in Figure 1) is not suitable for 8-bitimages. In this section we introduce an algorithm for hidinggrey scale image in full colour images. Figure 2 shows ablock diagram illustrating the proposed approach for hidingan encrypted 8-bit grey scale image into a 24-bit colourhost image. Referring to Figure 2, the stochastic diffusionapproach is used to encrypt the 8-bit image and embed it intoa 24-bit colour host image with a near perfect decryption.In this scheme, the cipher is converted into binary form,then 1st and 2nd Least Significant Bits (LSBs) are ignoredand the 3rd and 4th bits are embedded into the two LSBsof the host image’s red channel. Similarly, the 5th and 6thbits are embedded into the two LSBs of the host image’sgreen channel, and finally the 7th and 8th bits are embeddedinto the two LSBs of the host image’s blue channel. Theinverse process is based on extracting the relevant bits fromthe associated channels. The extracted bits are then usedto re-generate the original cipher and the reconstructionobtained by correlation with the original noise field. A two-steps Hidden Codes approach is applied(uniform randomdistribution is used to generate the two codes). In the firststep, code1 is used to shuffle the embedding bits order, sothe first secret dataset is not embedded in the first pixel ofthe host image, but rather in any other pixel based on randomlocations. In the second step, code2 is applied to scatter thetwo secret bits over multiple LSBs instead of only two (i.e.1st to 6th LSBs instead of 1st and 2nd). The hidden codeslead to the following advantages:(i) The randomized embedding bits order will make it verydifficult for intruders to extract the secret bits in correct orderwithout knowing the correct code key.(ii) The randomized LSBs will make the hidden data morerobust and secure to LSB attacks, as losing the 1st and2nd will only decrease the quality of the reconstructedcipher whilst keeping the ability to recognize the hiddeninformation. Figure 4 shows the result of embedding 8-bitimage into a 24-bit host image which is based on the blockdiagram given in Figure 2.

VI. ENCRYPTED FULL COLOUR IMAGE HIDING

The method of grey scale image hiding can be generalizedto embed a 24-bit colour image. The above method ismodified to use three full colour images as a host imagesas shown in Figure 3. The same algorithm is then appliedby treating each colour channel of the secret image as agrey scale image and embed it into one of the host images,and hidden codes are applied as discussed earlier with theability to add another hidden code for shuffling the orderof colour channels in the secret image (i.e instead of RGB,

it could be GBR, BRG, etc). In this case the red channelis not necessarily embedded in the first host image, and soon. In order to increase algorithm security, a different keycan be used to encrypt each channel. Therefore, the attackerneeds to have three correct keys to break the cipher. Theinverse process is identical to that discussed in the previoussection. The three reconstructed channels are then combinedto generate the original 24-bit image. Figure 5 shows anexample of the method based on the block diagram givenin Figure 3 that embed 24-bit image into three colour hostimages.

8-bitInput Image

Cipher xKey

Host Image

Encrypt input image

Embed encrypted

image based on the first and second

hidden codes

Generate random embedding locations Key

Generating Hidden Code 1

Generate random LSBs indices Key

Generating Hidden Code 2

8-bitStego Image

CipherKey

Host Image

Decrypt extracted

image

Extract encrypted

image based on the first and second

hidden codes

Generate random embedding locations Key

Generating Hidden Code 1

Generate random LSBs indices Key

Generating Hidden Code 2

8-bitstego Image

8-bitreconstracted Image

Embedding Process Extracting Process

Figure 2. Block Diagram for hiding an encrypted 8-bit image into 24-bitcolour host image.

VII. CONCLUSION

In this paper, the concept of encrypted information hidinghas been presented. The use of cryptographic algorithms to-gether with steganography and watermarking methods makeit almost impossible for interceptor to recover the encryptedhidden data as this requires the interceptor to detect theexistence of the information before attempting to decryptit. To recover the original data, the attacker needs to firstfind a way to extract the hidden encrypted information fromthe stego-data, which requires knowledge of the data hidingcodes and the appropriate algorithm/key(s). The exposureof the encryption key(s), the encryption algorithm and theembedding technique along with the hidden codes to thoseother than the intended receiver is practically impossible.We have considered the application of stochastic diffusionfor encrypting image data prior to embedding it into ahost image. Embedding a binary watermark into a hostimage obtained by binarizing a floating point ciphertext,as discussed in Section III, provides a cryptographicallysecure solution. This is because binarization is an entirelyone-way process. Thus, although the watermark may beremoved from the stego-image, it can not be decryptedwithout the recipient having access to the correct encryptionkey. However, This paper focuses on two key issues: (i)

24-bit ColorInput Image

Separate Input ImageChannels

Green Channel Blue ChannelRed Channel

Cipher-1 xKey-1 Cipher-2 xKey-2 Cipher-3 xKey-3

Host Image-1 Host Image-2 Host Image-3

24-bit Colorreconstracted Image

Combine extracted Image Channels

Green Channel Blue ChannelRed Channel

Cipher-1Key-1 Cipher-2Key-2 Cipher-3Key-3

Encrypt input image

Decrypt extracted

image

Embed encrypted

image based on the first and second

hidden codes

Extract hidden

image based on the first and second

hidden codes

Generate random embedding locations Key

Generating Hidden Code 1

Generate random LSBs indicesKey

Generating Hidden Code 2

Generate random embedding locations Key

Generating Hidden Code 1

Generate random LSBs indicesKey

Generating Hidden Code 2

Figure 3. Block Diagram for hiding an encrypted 24-bit colour image intothree 24-bit colour host images.

Figure 4. The original image (left), the reconstructed image (middle) andthe stego-image (right).

extending the application of stochastic diffusion to hide 8-bit and 24-bit images into a full colour and a set of threefull colour images respectively to provide a high fidelitydecrypt. Coupled with appropriate key-exchange protocolsto initiate cryptographically strong ciphers, the approachprovides a generic method of encrypting and hiding highfidelity digital image information. (ii) the use of the HiddenCodes in the embedding process in two phases; the firstphase is to shuffle the embedding bits order making, whilethe second one randomizes the encrypted cipher bits overmultiple LSBs making it more secure and robust to certainattacks. However, modifying or destroying the host image

Figure 5. From left to right: the original image, the reconstructed image and the stego-images

LSB (due to compression methods, for example) will notcause full loss of the cipher bits because they are scatteredalong multiple bits which enables the intended receiver torecover the hidden data.

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