Visual Cryptography Vs Bit Level Secret Sharing For Image Encryption

Secret sharing is a scheme used to distribute secret among a group of users.Rather than making duplicated copies of secrets among users, the secret is dividedinto a number of pieces, called shares. The secret can be revealed if a certainnumber of user shares are combined. The method proposed here (i)utilizes bit-leveldecomposition and stacking operations to both encrypt and decrypt B-bit image,(ii) preserves all the features of traditional (k, n) sharing schemes, (iii) allows forperfect reconstruction of the input B-bit image, (iv) encrypts binary, gray-scale andcolor images, and (v) can be effectively implemented either in software orhardware.

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section_content: Secret sharing is one type of key establishment protocols. The Trusted Authority (TA) divides the secret into pieces and distributes the pieces to different users. These pieces are called shares. Shares contain partial information about the secret. 

However, shares are constructed in such a way that although the secret can be reconstructed by combining a number of shares, simply examining individual user's share will not reveal the secret information at all [1] Naor and Shamir [3]. The original scheme generates n images (known as shares) based on the secret message (the original image) which can be printed on n transparencies. The original message can then be recovered if any k or more than k of the transparencies are stacked together, but no information about the original image can be gained if fewer than threshold number of k transparencies are stacked. Visual cryptography is a unique technique in the sense that the encrypted messages can be decrypted directly by the human. [3, 4] To encrypt a (k1 × k2) binary image using visual cryptography, each binary pixel r(i,j) ( i. e. r(i,j)=1 for white and r(i,j)= 0 for black) is handled separately via an encryption function FEnc(•) to produce a (m1 × m2) block of black and white pixels in each of the n shares. Thus, a (k1×k2) input binary image is encrypted into (n) binary shares S1, S2,. ., Sn each one with resolution of (m1k1×m2k2) pixels. Since the arrangement of the pixels varies from block to block, it is impossible to recover the useful information without accessing a predefined number of shares. [4, 5] Let FEnc(•) be the encryption function which maps a reference binary pixel r(i,j ) located at position (i,j) in the original image into (m1×m2) sized blocks in the various shares. Assuming for simplicity a basic (2, 2) scheme with (2 × 2) blocks, the encryption process is given by: For each pixel r(i,j) in the binary image F Enc (r(i,j )) {if r(i,j) = 1 (white) then Select random block from C (Fig. 1 ) and insert the block at locations: Else {b(i,j) = 0} Select random block from C and insert the block at locations: Share1 [(2i-1,2j-1), (2i-1,2j), (2i,2j -1), (2i,2j)] insert the complement of C at locations: Share2 [(2i-1,2j-1), (2i-1,2j), (2i,2j -1), (2i,2j)] } as shown in Fig. (1) The size of the basis matrices depends on the expansion factor m1m2 and the number of participants, which is given by n. Since m1m2 represents the factor by which each share is larger than the original image, it is desirable to make m1m2 as small as possible [6, 7]. For a (2, 2) scheme considered here, each pixel in Share1 is equivalent to each pixel in Share2 if r(i, j) = 1, and each pixel in Share1 should complement each pixel in Share2 if r(i,j )=0. The decryption function FDec ( Share1(u,v), Share2(u,v)) is defined as follows:

) and b is the decrypted image as shown in figure (1).
section_name: 1-Introduction

section_content: The coding algorithm of our proposed system: Step1: Read a digital image (k1 x k2) with B-bit/pixel. (in this paper B=8)

Step2: Decompose the input image to eight binary images, ranging from (0) for the least significant bit (LSB) to (7) for the most significant bit (MSB) (b0 … b7) as shown in figure (2). [8] Step3: implement the following procedure: for plane = 0 to 7 for i = 1 to height of image for j = 1 to width of image if b(i, j, plane) = 0 (black) then select random block from C and insert the block at locations:

Where u = 2*image height & v= 2 * image width As shown in figure (3)
section_name: 3-Bit level based secret sharing (Coding algorithm)

section_name: Visual Cryptography Vs Bit-Level Secret

section_content: Decoding algorithm: To faithfully decrypt the original B-bit image from its shares, the decryption function must satisfy the perfect reconstruction property meaning that the output should be identical to the original input. This can be obtained only if the encryption and decryption operations are reciprocal. 

Step1: Decompose each input share1 and share2 to eight binary images (2k1 x 2k2), ranging from (0) for the least significant bit (LSB) to (7) for the most significant bit (MSB). 

Step2: implement the following procedure:

for plane = 0 to 7 for i = 1 to k1 for j = 1 to k2 if Share1(2i-1,2j-1,plane)= Share2(2i-1, 2j-1, plane) then b(i, j, plane) =1 else b(i, j, plane) =0 next j : next i: next plane Step3: the eight binary images b (k1 x k2) are constituted by bit-level stacking using (equation 4) to obtain the original image.
section_name: Sharing For Image Encryption 1343

section_content: Visual cryptography of the binary image indicates that: (i) the decrypted image is darker, and (ii) the input image is of quarter size compared to the decrypted output. Visual cryptography (iii) cannot provide perfect reconstruction, either in terms of pixel intensity or spatial resolution, and (iv) is not appropriate for real-time applications as shown in fig (5). Thus, an alternative solution is needed [9, 10]. 

The method proposed here (i) utilizes bit-level decomposition and stacking operations to both encrypt and decrypt B-bit image, (ii) preserves all the features of traditional {k, n} sharing schemes, (iii) allows for perfect reconstruction of the input Bbit image, (iv) encrypts binary, grayscale and color images, and (v) can be effectively implemented either in software or hardware as shown in fig. (6, 7).
section_name: 4-Visual cryptography vs bit level secret sharing

section_content: We use MATLAB language to implement visual cryptography and B-bit-level algorithm, the following figures (5, 6, 7) offers a visual comparison between two methods.
section_name: 5-Implementation

section_content: A B-bit secret sharing framework that affords perfect reconstruction of the encrypted image input was introduced. The method proposed here (i) utilizes bit-level decomposition and stacking operations to both encrypt and decrypt B-bit image, (ii) preserves all the features of traditional {k, n} sharing schemes, (iii) allows for perfect reconstruction of the input Bbit image, (iv) encrypts binary, grayscale and color images, and (v) can be effectively implemented either in software or hardware.
section_name: Conclusions

section_content: There has been a steadily growing interest in visual cryptography. Despite its appearance of being a simple technique, visual cryptography is a secure and effective cryptographic scheme. Since the origin of this new paradigm, various extensions to the basic scheme have been developed to improve the contrast and the areas of application have also been greatly expanded.
section_name: visual cryptography researches

section_content: In [1' ], the construction of (n,n)-VCS was extended for (k,n)-VCS. In 1996, the same authors introduced the idea of cover based semi-group to further improve the contrast [2' ]. Ateniese et al. [3'] provided the first construction of (2, n)-VCS having the best possible contrast for any n<=2. Blundo et al. [4' ] provided a contrast optimal (3,n)-VCS and gave a proof on the upper bound on the contrast of any (3,n)-VCS. [1' ] first considered the problem of concealing the existence of the secret image. [5' ] provided a general solution for that problem. The random nature of secret shares makes shares unsuitable for transmission over an open channel. [5' ] used a modified scheme to embed some meaningful images into the shares. [6' ] used different moiré patterns to visualize the secret instead of different gray levels. As far as extending to color images goes, [7' ] provided a primitive scheme for images of 24 colors. Hou [8' ] then proposed a novel approach to share color images based on halftoning. Other interesting topics include visual authentication [9' ] and watermarking based on visual cryptography [10' ]. Recently, there has been an attempt to build a physical visual cryptographic system based on optical interferometry [11']. However, all of these works result in a decrypted image of reduced quality.
section_name: Sharing For Image Encryption 1344