An Image Secret Sharing Technique with Block Based ... - IEEE Xplore

2015 Fifth International Conference on Communication Systems and Network Technologies

An Image Secret Sharing Technique with Block Based Image Coding Sujit Kumar Das

Bibhas Chandra Dhara

Department of Information Technology Jadavpur University Kolkata, India Email: [email protected]

Department of Information Technology Jadavpur University Kolkata, India Email: [email protected] This sharing technique is known as (t, n)-threshold secret sharing scheme. In 1979, secret sharing scheme was first proposed by Shamir [23] and Blakley [1] independently. Both methods were (t, n) threshold secret sharing scheme. In Shamir’s method, a polynomial p(x) of degree t − 1 is considered where the constant term is treated as the secret. Then, for different value of x shares are generated as (1, p(1)), (2, p(2)), · · · , (n, p(n)). To construct the share, any t tuples (or shares) are taken and Lagrange interpolation polynomial (L(x)) is constructed and the desired secret is L(0).

Abstract—A (t, n) threshold secret image sharing scheme generates n share images from a secret image in such a way that any t or more share images can be used to reconstruct the secret image. In this paper we have proposed a (t, n) secret image sharing scheme where the secret image is first encoded by block based lossy compression technique and define t sub-images. The image compression technique gives a good quality image. To enhance the security level, the sub-images are scrambled by Arnold transform and then shares are generated. Finally, image hiding (i.e., steganography) concept is adopted to hide the shares within cover images. The proposed method gives good quality of the stego images. Keywords: Secret Sharing, Secret Image Sharing, Block coding, Arnold Transform, Steganography.

I.

Extending the idea of secret sharing in image domain, Naor and Shamir introduced a novel scheme [21], called (t, n) threshold visual secret sharing (VSS) scheme, in which a binary image is encoded to n number of noisy like binary shadow images and t number of shadows are placed in stack to retrieve the secret by visual perception without computation. The main advantage of VSS is less computation time which leads to a number research work [13] [7] [34] [24] [29]. Although, it is not feasible to use VSS in many application for it’s some drawbacks such as large expansion of secret image, low quality of reconstructed image etc. To resolve these problems Thien and Lin [25] proposed an secret image sharing scheme based on Shamir’s scheme. In this scheme, t pixels of a secret image are embedded as coefficients of (t − 1)-degree polynomial function to generate n number of shares and reduced the size of shadow to size oft secret . In this method the intensity of a pixel is assumed 0 − 250 i.e., pixel value greater than 250 is truncated to 250. To remove this drawback, a modified scheme was also proposed in the same paper where intensity g ≥ 250 is divided into two parts like (250, d) such that g = 250 + d. Another scheme was suggested in [30] to reduce more the size of shadows by considering the polynomial over the field GF(28 ). Vector Quantization (VQ) technique is also used to decrease size of shadows. In [4], the VQ indices of the secret are computed by VQ with help of k codebooks constructed from any k out of n host

I NTRODUCTION

Nowadays, transmission of multimedia data over Internet is convenient and popular. Transmission of data through the communication channel faces some problems like: i) transmission cost, ii) privacy and security of the data. One simplest solution to reduce the transmission cost is the data compression. At the same time privacy protection and security of the data are also important requirement. Two techniques namely Cryptography [19] [31] and Steganography [18] [17] [22] are widely used to transmit data securely over communication channel. In cryptography, information is hidden by mapping the current information to another unreadable format. On the other hand Steganography hide the data by embedding it to a another medium called cover. Cover medium with secret data is called stego data. In both cases the final data is a single data unit which may be lost, damaged or modified and the original data can not be recovered. To overcome from this problem Secret Sharing Scheme (SSS) was proposed. Secret sharing scheme is a method by which n shares or shadows are generated from a secret S and distributed them to the participants. Then t or more shares are collected and combined to get back the secret. 978-1-4799-1797-6/15 $31.00 © 2015 IEEE DOI 10.1109/CSNT.2015.37

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images and the these VQ indices are shared among the n shadows by Thien and Lin [25] scheme. VQ based secret image sharing methods also studied in [6] [3].

Secret image B i,j

Block Encoder

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Quantization levels Cluster indices 1

Since, most of the methods generally generate noisylike shadows i.e, meaningless and distorted shadow images. For safety and secure transmission of shadows the steganography concept is used. In steganography, a shadow is embedded into another cover image and the resulting image (i.e., stego image) is distributed to a participant. In image hiding, normally least significant bit (LSB) method [2] [32], DCT based method [8][22] and wavelet based methods [12][20] are used. LSB scheme is very popular and simpler to embed secret images into host images. In [35], the shadows are firstly compressed and then embedded into cover images by modulus operator. In the recent times, a number of research works [33] [27] [26] have been proposed in the same line of research.

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Steganography

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(a) Share generation process

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Secret extraction

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Inverse Arnold transform t

Quantization levels Cluster indices

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In this work we have proposed a secret image sharing scheme. In the proposed scheme, first the secret image is encoded by a block based lossy compression technique which gives better quality than two well known spatial domain methods BTC [15] [11] [10] and VQ [14] [16]. From the encoded information shares are generated by extending the Shamir’s scheme in GF(28 ). The proposed method is a (t, n)-threshold sharing scheme. To increase the security level the encoded information is also scrambled by using Arnold transform (AT) [5] [28]. The size of shares, given by proposed method, is much less than Thien and Lin method [25]. In this paper, our main concern is to generate the shares and for steganography purpose we have relied on LSB method.

’ B i,j Reconstructed secret image

(b) Secret reconstruction process Fig. 1. Block diagram of the proposed secret image sharing scheme

1) Image Coding: In image coding step, we have used a spatial coding technique, which is very simple (both in terms of algorithm and implementation), fast method and results high quality image. The method is as follows.

The organization of the rest of the paper is as follows. The proposed secret image sharing is discussed in section II. The result of the proposed method is analyzed in section III. At the end, the paper is concluded in section IV. II.

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Share construction

2

Let the secret image is of size N × N and the image is partitioned into blocks of size p × p. The reason why we consider the square image is explained later. The image block B p×p (i, j) is partitioned into c clusters by some clustering technique (say, k-means). For each pixel of the block, we note the cluster index and the pixels of a cluster is encoded by the cluster mean. To encode a block we have to store c graylevels and p × p indices. Say, total bit requirement is r-bits and let t =  8r . For each block we have t-bytes information and considering each byte is a part of a sub-image. Thus, t sub-images of size Np × Np can be defined.

P ROPOSED M ETHOD

In this article, we have proposed secret image sharing scheme for grayscale images. The proposed method is divided into two phases: i) share generation and ii) secret image reconstruction. A. Share Generation Phase

2) Arnold Transform: First of all restrict the discussion over 2D, since the image plane is 2D. Arnold transform (AT) is a geometric transform which maps a point (x, y) to another position (x , y ). This transformation works on a square grid (i.e., image must be square) and for simplicity we consider both N and p are of the form 2u and 2v such that u > v. AT is periodic as well as invertible. If AT applied w-times on an image, then the original image can be retrieved by applying inverse AT (ATinv ) w-times. Here, the value w may be considered

In the share generation phase, first the secret is encoded by a block based lossy image compression technique. Then, the encoded information is used to generate the shares. In this process, before doing the actual share generation, the collection of encoded information is scrambled by Arnold transformation. Finally, steganography is applied to hide the shares. The block diagram of the proposed share generation method is given in the Fig. 1(a). 649

same irreducible polynomial h(x). This gives the i-th pixel of each of the t sub-images. Repeat this process for all pixels of the shares. Now, t sub-images with quantization levels and cluster indices of the blocks are available. But, these sub-images are scrambled by AT. Apply ATinv w times to get back unscrambled version of the sub-images. The collection of q-th value of the sub-images give the tuple (v(q,1) , v(q,2) , · · · , v(q,t) ) and obtain the quantization levels and cluster indices of the q-th block of the secret image. Finally, we get the secret image. The block diagram of the secret reconstruction method is presented in Fig. 1(b) and corresponding secret reconstruction algorithm is given below.

as a ‘key’ value. 3) Share construction: Applying AT we obtain tscrambled sub-images of size Np × Np . From t subimages, we consider i-th pixel which gives a tuple vi = (v(i,1) , v(i,2) , · · · , v(i,t) ). Using this tuple, a polynomial of degree (t − 1) over GF(28 ) respect to an irreducible polynomial h(x) is defined as fi (x) = v(i,1) xt−1 + v(i,2) xt−2 + · · · + v(i,t) mod h(x) (1) Here, the degree of h(x) is eight and in this experiment we consider h(x) = x8 + x4 + x3 + x2 + 1. The share of j-th participant is Pj for Pj = { fi ( j), ∀i}. 4) Steganography: A number of image steganography methods are available in the literature. Since image hiding is not our main concern, so for the hiding purpose we have used the simplest method which is known as LSB method.

Algorithm: Secret Reconstruction t stego images, c number of classes, w number of times ATinv will iterated Output: The reconstructed secret image S . Input:

The algorithm to generate shares is as follows:

1)

Algorithm: Share generation Secret Image S, key w, c number of clusters and n cover images CI1 ,CI2 , · · · ,CIn . Output: n stego images S1 , S2 , · · · , sn Input:

1) 2)

3) 4) 5)

6)

Partition S into B p×p (i, j) blocks. For each block B do 3.1 Partition B into c classes 3.2 Compute class means 3.3 Note the cluster index of each pixel of B 3.4 t-bytes are needed to encode the information taken from 3.2 and 3.3 3.5 Each byte is a part of a ‘sub-image’ Apply Arnold transform, w times, on each of the t sub-images Si = φ for i = 1 to n Repeat for all pixels of the sub-images 5.1 i-th pixel of each sub-image form a polynomial as given in Equn.(1) 5.2 Evaluate value of fi ( j) and S j =S j # fi ( j) for j = 1 to n Apply LSB-steganography to hide S j into CI j which gives stego image Sj , for j = 1 to n

2) 3)

For each q-th pixel of the shares do 1.1 Apply Lagrange interpolation on (v(q,1) , v(q,2) , · · · , v(q,t) ) over the field GF(28 ) with respect to the irreducible function h(x). 1.2 Obtain q-th pixel of the t sub-images Apply ATinv w times to each sub-image and get unscrambled sub-images For each pixel of the sub-images do 3.1 q-th pixel of the sub-images give (v(q,1) , v(q,2) , · · · , v(q,t) ) 3.2 Find c quantization levels and p2 indice -s and reconstruct the q-th block of the secret III.

E XPERIMENTAL RESULTS

In this section, some experimental results are shown to prove the feasibility of the proposed method. In this work, we have worked with four grayscale images ‘Lena’, ‘Baboon’, ‘Lake’ and ‘Peppers’ of size 512 × 512. For our simplicity, we consider the value of each parameter {N, p, c} as of the form 2u . The image is partitioned into blocks of size either p = 4 or p = 8. Each block is clustered into 2 or 4 classes. Depending on the parameter p and c, quality of the secret, size of the shares, quality of the stego and value of the threshold t for (t, n) are determined. The quality is measured in terms of PSNR. Number of bits required to encode a block is r = p2 × log2 c + c × 8 and value of the threshold t is  8r , size of the shares is Np × Np and in this experiment we consider 256×256 grayscale images as the cover image to hide the shares. The performance of the proposed coding method is shown in Table I.

B. Secret Image Reconstruction The secret image reconstruction phase is opposite of the first phase. First, from n stego images select any t and from these obtain t shares. To describe the secret reconstruction, for simplicity, first t stego images are considered. Then, t shares are extracted from stego images. Select i-th value and use Lagrange’s interpolation technique over GF(28 ) with respect to the 650

TABLE I.

T HE PERFORMANCE OF THE PROPOSED BLOCK

TABLE III.

AVERAGE QUALITY OF THE STEGO IMAGES FOR DIFFERENT SECRET IMAGES WITH DIFFERENT PARAMETERS

CODING METHOD

p, c 4,2 8,2 8,4

r 32 80 160

t 4 10 20

Lena 38.02 35.51 39.84

PSNR Baboon Lake 32.39 35.28 31.24 33.40 34.86 37.17

p, c, n 4, 2, 5 8, 2, 12 8, 4, 25

Peppers 38.35 35.67 39.93

T HE PERFORMANCE OF THE BLOCK CODING METHOD WITH AND WITHOUT A RNOLD T RANSFORM

Lena Baboon Lake Peppers

without AT 38.02 32.39 35.28 38.35

1 37.02 31.84 34.14 36.79

PSNR with AT, number of 2 3 34.54 32.26 31.05 30.28 32.62 31.33 34.07 31.55

iterations 4 30.39 29.46 30.01 29.63

Baboon 47.12 57.13 57.13

Lake 47.10 57.14 57.10

Peppers 47.10 57.13 57.15

(see Fig. 2(a)). Applying AT on the sub-images we obtain the scrambled sub-images (see Fig. 2(b)). From the sub-images (see Fig. 2(b)) shares are generated (see Fig. 2(c)) and these are distributed to the participants after the steganography. The stego images for ‘Lena’ are shown in Fig. 2(d)–(f) and average quality of the stego images with different parameters for the test images are given in Table III. The results are satisfactory from the viewpoint of secret hiding effectiveness and stego-image quality.

TABLE II.

Image

Lena 47.09 57.15 57.16

5 29.16 28.86 29.13 28.57

Two well known spatial techniques encode the image are BTC and VQ method. In BTC method, 4 × 4 block are partitioned into 2 classes and quantization levels are computed so that first order and second order moments are preserved. In VQ, image block is matched with some pre-defined patterns. The pattern which fits best is used to reconstruct the block. The index of the best fit pattern is stored for reconstruction. Since, in BTC method p = 4 and c = 2 for the comparison purpose we consider a binary patternbook (taken from [9]) for VQ method and class mean is used as the quantization level. In the proposed block coding method, the block clustering is determined without any restriction and quantization levels are the class mean values. Hence, the quality of the secret, given by proposed coding method, is much better compare to BTC and VQ method. For example, in case of ‘Lena’ image the PSNR of the BTC method is 32.89dB, and VQ gives 31.59 dB whereas quality of the proposed method is 38.02dB.

quantization levels index of pixels (a) Sub-images after block coding

(b) Scrambled sub-images

(c) Generated shares

In this experiment, we have employed AT after the compression of secret image. AT maps the pixels from one position to another position, which reduces the spatial correlation of the pixel intensity values and this degrades the quality of the encoded secret image. For example, in Table II the quality of ‘Lena’ with and without AT are given. It may be noted that AT is periodic and hence quality will be degraded to a certain number of iterations and then for more iterations quality will be increased.

(d) Stego images: p = 4, c = 2, average PSNR 47.09 dB

Applying block coding we obtain t sub-images. Some of which are generated by quantization levels (like sub-sampled version) and rest are by merging the class index of the pixels, e.g., for p = 4 and c = 2 we have 4 sub-images first two sub-images are constructed using quantization two levels and last two using pixels index

(f) Stego images: p = 8, c = 4, average PSNR 57.16 dB

(e) Stego images: p = 8, c = 2, average PSNR 57.15 dB

Fig. 2. Experimental result on secret image ‘Lena’: (a)-(c) share generation (with p = 4 and c = 2): (a) sub-images by block coding, (b) scrambled sub-images, (c) generated shares; (d)-(f) quality of stego images.

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IV.

C ONCLUSIONS

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In this paper, we have proposed a block based image secret sharing with the help of Shamir’s secret sharing. As a whole the proposed method is lossy. At the same time the current method gives better image quality than BTC and VQ and in the proposed method for lossless secret sharing Shamir’s method is executed over GF(28 ). For steganography purpose, we have adopted LSB method and quality of the stego images is also quite satisfactory. To increase the security level of the proposed method AT based image scrambling technique has been used. R EFERENCES [1] George Robert Blakley. Safeguarding cryptographic keys. In Managing Requirements Knowledge, International Workshop on, pages 313–313. IEEE Computer Society, 1979. [2] Chi-Kwong Chan and Lee-Ming Cheng. Hiding data in images by simple lsb substitution. Pattern recognition, 37(3):469–474, 2004. [3] Chin-Chen Chang and Ren-Junn Hwang. Sharing secret images using shadow codebooks. Information Sciences, 111(1):335– 345, 1998. [4] Lee Shu-Teng Chen, Wei-Kai Su, and Ja-Chen Lin. Secret image sharing based on vector quantization. Int. J. Circ. Syst. Signal Process, 3(3):137–144, 2009. [5] Linfei Chen, Daomu Zhao, and Fan Ge. Image encryption based on singular value decomposition and arnold transform in fractional domain. Optics Communications, 291:98–103, 2013. [6] Tung-Shou Chen and Chin-Chen Chang. New method of secret image sharing based upon vector quantization. Journal of Electronic Imaging, 10(4):988–997, 2001. [7] Tzung-Her Chen, Yao-Sheng Lee, Wei-Lun Huang, Justie SuTzu Juan, Ying-Yu Chen, and Ming-Jheng Li. Quality-adaptive visual secret sharing by random grids. Journal of Systems and Software, 86(5):1267–1274, 2013. [8] Rufeng Chu, Xinggang You, Xiangwei Kong, and Xiaohui Ba. A dct-based image steganographic method resisting statistical attacks. In Acoustics, Speech, and Signal Processing, International Conference on, volume 5, pages V–953. IEEE, 2004. [9] Bibhas Chandra Dhara and Bhabatosh Chanda. Block truncation coding using pattern fitting. Pattern Recognition, 37(11):2131–2139, 2004. [10] Bibhas Chandra Dhara and Bhabatosh Chanda. Color image compression based on block truncation coding using pattern fitting principle. Pattern Recognition, 40(9):2408–2417, 2007. [11] Bibhas Chandra Dhara and Bhabatosh Chanda. A fast progressive image transmission scheme using block truncation coding by pattern fitting. Journal of Visual Communication and Image Representation, 23(2):313–322, 2012. [12] RO El Safy, HH Zayed, and A El Dessouki. An adaptive steganographic technique based on integer wavelet transform. In Networking and Media Convergence, 2009. ICNM 2009. International Conference on, pages 111–117. IEEE, 2009. [13] Young-Chang Hou, Zen-Yu Quan, Chih-Fong Tsai, and AYu Tseng. Block-based progressive visual secret sharing. Information Sciences, 233:290–304, 2013. [14] Yu-Chen Hu, Wu-Lin Chen, Chun-Chi Lo, Chang-Ming Wu, and Chia-Hsien Wen. Efficient vq-based image coding scheme using inverse function and lossless index coding. Signal Processing, 93(9):2432–2439, 2013.

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