Reversible Multiple Image Secret Sharing using Discrete Haar Wavelet Transform

Received Feb 2, 2018 Revised Jun 30, 2018 Accepted Jul 11, 2018 Multiple Secret Image Sharing scheme is a protected approach to transmit more than one secret image over a communication channel. Conventionally, only single secret image is shared over a channel at a time. But as technology grew up, there is a need to share more than one secret image. A fast (r, n) multiple secret image sharing scheme based on discrete haar wavelet transform has been proposed to encrypt m secret images into n noisy images that are stored over different servers. To recover m secret images r noise images are required. Haar Discrete Wavelet Transform (DWT) is employed as reduction process of each secret image to its quarter size (i.e., LL subband). The LL subbands for all secrets have been combined in one secret that will be split later into r subblocks randomly using proposed high pseudo random generator. Finally, a developed (r, n) threshold multiple image secret sharing based one linear system has been used to generate unrelated shares. The experimental results showed that the generated shares are more secure and unrelated. The size reductions of generated shares were 1:4r of the size of each of original image. Also, the randomness test shows a good degree of randomness and security. Keyword:


RELATED WORKS
In 1979, Shamir [4] introduced the concepts and theory of secret sharing. Shamir's secret sharing scheme was based on a n-degree polynomial, and shares were the points on that polynomial. In 2002, Thien and Lin [5] proposed an extension of Shamir's scheme where the secret image is shared by n shares, and any r (r <n) shares can be used to reconstruct the secret. This scheme is started with a permutation technique to shuffle the image's pixels and de-correlate it, then shares were made by processing the image pixels or patterns in the spatial domain, each participant receiveing his own share as a shadow image looks like a random noise image holding partial information of the secret. Share size is just 1/r of the secret image. In 2007, Chin and Ching [6], introduced a way of share images based on the reversible integer-to-integer (ITI) wavelet transform.
This method processes the transform coefficients in each subband, and each of the resulting combination coefficients were divided into n shares. It was allowing the recovery of the complete secret image using any r or more shares (r ≤ n). This method has larger shadow images without coding than those belong to the methods that applying coding as a preprocessing for the inputting to the sharing phase. Also, in this method, the data is encoded either by Huffman coding or by arithmetic coding before the data is sent to the sharing phase. Also, in this method the Huffman coding or arithmetic coding have been used to encode data before it is sent to the sharing phase. In 2007, Jun et al [7], proposed a scalable secure approach to share and hide secret image. The secret image given first is divided into numerous nonoverlapping blocks, and each block is then transformed into one-level discrete wavelet transform. Then, the wavelet coefficients have been quantized into 256 gray levels. After that the gray value information of the quantized image was rearranged by using a bit-plane scanning method. Finally, the image data is rearranged into n shadows by using multiple thresholds. Finally, each shadow image of R, G, and B channels is hidden in the cover image.
The results of the test indicated that the increasing of the number of shadows can lead to recovery of the secret image with better quality. In 2011, Yang et al [8], suggested a fast secret image sharing method based on Haar wavelet transform and Shamir's method. Firstly, they used discrete Haar wavelet transform to reduce the secret image to its quarter size (i.e., 1-level LL subband). Then, the modified Shamir's algorithm has been applied to only this LL subband for generating the shadow images. In 2011, T. Hoang and et al [9], proposed a (2, n) gray image secret sharing scheme. The proposed scheme is basis on three existing approaches: block truncation coding (BTC), vector quantization (VQ) and discrete wavelet transform (DWT). In this scheme, the set of generated shares have been much smaller than the original image. Any gray image can be reconstructed by combining at least two shadows.
The quality of the reconstructed image ranged from 29.5 bears to 36.5 dB. In 2012, Sagar et al. [10] proposed a new method to perform color visual cryptography based on wavelet transform. Wavelet transform has been utilized to obtain a gray image from a color image where the intensity image (Y) formed from the YCbCr color transform. Then, Error-Diffusion Filter has been applied on the obtained grey image. After that the visual cryptography system (VCS) model was applied on the generated halftone image. In 2014, Ashwaq and Loay [2] introduce a security secret color image sharing based on transform coding, using wavelet or cosine transformation to produce secure secret shares by first compress the image using one of the transform coding techniques mentioned earlier. The compressed stream is then subject to a data diffuser followed by a random generator to shuffle the image into shares; a secret shares generator system is then applied on these shares to produce the secret shares.

THE TINY ENCRYPTION ALGORITHM
The Tiny Encryption Algorithm (TEA) is a block cipher known as a simple of description and easy to implement. This cipher was firstly introduced by (Wheeler and Needham 1994). TEA works on 64-bit plaintext at a time and using 128-bit key. It is a Feistel network of 64 rounds, typically applied on pairs termed rounds. The key schedule was extremely simple by mixing all of the key material in exactly the same way for each round. Various multiples of a magic constant have been utilized to prevent simple attacks on basis of the symmetry of the rounds. The magic constant, 2654435769 or 9E3779B916 has been chosen to be 232/ϕ, where ϕ was the golden ratio [12]. Figure 1 shows the structure of TEA algorithm. TEA is a Feistel cipher that uses different (orthogonal) algebraic groups -XOR, ADD and SHIFT in this instance. This is a truly ingenious way of saving Shannon's twin properties of diffusion and confusion which are important for a secure block cipher, without needing the explicitly of P-boxes and S-boxes respectively. It seems highly resistant to differential cryptanalysis, and achieves complete diffusion (where a one bit difference in the plaintext will cause about 32 bit differences in the cipher text) after only six cycles [13].

THE PROPOSED SYSTEM
An approach of multiple image secret sharing for secret gray images for set of participants has been proposed. In this approach, each participant can share a gray secret image with the other of participants in a way that of all them can reconstruct your secret gray image if only k out of n shares have been collected. The proposed approach is basis on: (i) Applying Haar DWT to reduce each input image to its quarter size, (ii) Using proposed pseudo random generator to distribute the combined compressed streams into r subblocks randomly and (iii) Performing the developed multiple image secret sharing based on linear system to generate unrelated shares. Algorithm (1) shows the steps of proposed system. Step3: Separate the total image T into r sub blocks randomly using proposed pseudo random generator system Step 4: Generate n shares Sh1, Sh2, …, Shn using Linear System

Proposed Pseudo Random Generator
Digital cryptography relies greatly on randomness in providing the security requirements imposed by various information systems. Just as different requirements call for specific cryptographic techniques, randomness takes upon a variety of roles in order to ensure the proper strength of these cryptographic primitives. Block ciphers are the most popular cryptographic primitives; due to the standardization of DES followed by AES, but also due to the fact that block ciphers constitute some of the fundamental building blocks for pseudorandom number generators, stream ciphers, hash functions and message authentication codes.
A pseudo random generator has been proposed.thw length of random sequence that has been generated by proposed system is 192 bits. This step is to decorrelate the output result from compression stage; it has been distributed into rsubblocks. By using a proposed pseudo random generator based on a secret key, it will be generated a random sequence of numbers each has a length equal to the length of combined secret data for all images after compression and the values of generated sequence are ranged to be 1..r, then the secret information will be permuted randomly into nsubblocks according to generated sequence. Algorithm (2) illustrates the detail steps of the proposed pseudo random generator. Figure 1 depicts the general structure of the pseudo random generator where the keystream generator (KSG) is a pseudo random number generator based on block cipher and the keys (i.e., K1, K'1) is the seed of the pseudo random generator. The KSG is a consecutive of two proposed block ciphers. Each of them is a cascaded design of TEA block cipher, denoted by Cascaded TEA1 and Cascaded TEA2. The Cipher Block Chaining encryption mode has been used in proposed block cipher where the input to the first Cascaded TEA is a public IV, and the inputs to each of them is one of two master keys, denoted kiand k'i respectively, these keys is considered as a seed for the pseudorandom generator. Figure 2 shows the block diagram of KSG.
Step3: The KSG output yi is computed as: Step4: The new input for the next Cascaded TEA is: Step5: In the KSG design, the internal state at each step has been used to update running keys such as following ki+1 = ki⊕ mi (7) and The k and k' represented the master keys and the ki and k'i the running keys. Step6: Repeat step2 to step5 until generate yiwhere i=1..n Step7: For each yi components (i.e.,C1, C2, and C3) where i=1..n, Do the following: Step7

Multiple Secret Image Sharing Based on Linear System
The input I1, I2, …, Im images have been reduced (i.e., to its quarter size) and shuffled randomly into rsubblocks. In the multiple secret images sharing, the input content is composed by a set of equal sized blocks (i.e., SBk1, SBk2,…, SBkr). Each of the blocks can be any type of content. For a block of data {Qj| j=1..r} (i.e., each Qjis a byte from j th block), the i th share is calculated by using the linear equations adapted from [2] and shown in (9) Where, Shi is the i th share which is generated for the subblockQ(), cij is the j th coefficient belong to the linear equation denoted the i th share.

EXPERIMENTAL RESULTS AND DISCUSSION
Different tests were implemented to evaluate the proposed system algorithm performance. Six grays of size 512×512 images ("Lena", "Jet-plane", "Splash", "Peppers" and "Sailboat" and "House") have been used. The test images have different visual properties, like a natural scene, having lot of edges and having high correlated sections. These six test images are shown in Figure 5.  Table 1 lists the PSNR after applying haar DWT; the only distortion of the proposed multiple secret image sharing was due to the use of this step, no further loss was caused by the rest operations or functions of the proposed system. The results that have been listed in Table 1 showed that the size of each has been reduced, 1/4 of the size of the original secret image and the qualities of all images were at acceptable level (i.e., greater than30 dB). So that the total size for all input images have been reduced to 1/4r after applying a (r, n) threshold multiple secret image sharing.
The proposed Pseudo-random number generator depends on two master keys and an initial vector to generate and many random numbers as needed. Many statistical tests have been applied to test the randomness of a sequence, in general many sequences that considered random may be easy to predict. So it's important to test the generators to prove its efficiency. Table 2 shows first three samples generated using the specified initial vector and keys. Table 3 shows the differences between each two consecutive generated sequences. Table 4 shows the results of randomness test of 18 random sequences that are generated in table 2.  Third random  sequence   6  0  0   11111111111  11111111111  11111111111  11111111111  11111111111  11111111111  11111111111  11111111111  11111111111  11111111111  11111111111  111111   0001111001111000  1100100010001101  0010011010011001  1010111011010000  1001111000110111  0111100110111001  1101101111100100  1101001100110001  1001011011000100  0000000101001100  0101100111001011  1011100101010010   0010010111100101  0000110110110110  1111000101010001  1001011010011000  0011010111010010  0100001001010010  0000111111100001  0111101011010111  0110111100111011  0111111001011100  0100010011101110  0010101010100110   1001010101110101  0111100101111001  0100000110101111  0010110100110100  0001111101000011  1011011010110010  1011111011011111  0101010111100111  1101101010110110  1110101000000100 1101000110100010 0000100100101001  The result listed in Table 3 shows that most differences are greater than 50% of the length of generated random sequences while Table 4 shows that all the P-values are greater than α (α = 0.01 )value. So the proposed pseudo random generator output have passed NIST statistical test suite. Figures 6 and 7 show an example of coding and decoding of proposed multiple image secret sharing phases. Table 5 illustrates the time required to recover the secret images of size 512×512 when applying (2,5) threshold multiple secret image using linear system and the sharing coefficient values for share1 are: a11=131, a12=132 and for share2 the coefficient values are: a21=133, a22=135.

CONCLUSION
In this paper, a (r, n)-threshold multiple image secret sharing based on linear system with the haar wavelet transform has been proposed. The benefit of a small computation time of reduced data has been exploited after applying haar wavelet. All secret images have been preserved of their quality (i.e., greater than 30 Db) after the reduced their sizes to quarter size. The proposed system employed pseudo random number generator to permute the transformed images data in pre-generated shares randomaly. The proposed pseudo random generator based on block cipher technique which is depended on a re-keying approach to overcome key schedule weakness in TEA algorithm and used the rounds of the TEA which is a highly random block cipher algorithm. The developed multiple secret image sharing has been applied to generate uncorrelated shares to store in different servers. If any r out of n shares have been collected, can be recovered the m secret images.