Research On Image Secret Sharing Methods Based On Polynomial And Cellular Automata

From the traditional Internet era to today's mobile Internet era with much larger number of users, the secret image related issues become increasingly serious. For example, frequent loss of smart phones often leads to the loss of privacy photographs, and then these images might be peeped by attackers. Image secret sharing method provides an effective way to solve the above problems, which divides a secret image into multiple shadow images and distributes them to multiple participants, and each participant cannot get any information about the secret image from his/her own shadow image. Then, participants in a qualified subset can recover the secret image together, thus avoiding the issue of single-point failure and guaranteeing the privacy of the secret image effectively. In general, the research of image secret sharing can be divided into three categories:image secret sharing based on computing device decoding, image secret sharing based on pure visual decoding, and the combination of the former two methods. This paper proposes four new schemes specific to the first category, involving the aspects of reversible steganography, visual quality, operational performance, and security. Meanwhile, (?) paper proposes a new scheme about scrambling process, security and lossless recovery on the third category. The detailed research results of this paper are as follows:(1) This paper proposes an image secret sharing scheme based on SMbLSBC (Steganography Method based on Least Significant Bits Construction, hereafter referred to as SMbLSBC), polynomial and EDEM (Enhanced Dynamic Embedding Method, hereafter referred to as EDEM), which utilizes the SMbLSBC method with reversible characteristic to overcome the problems of the steganographic method based on modular arithmetic, including arithmetic overflow problem and unusable problem of partial host image's pixels. This scheme also reduces the modification extent on the host image's pixels during the steganography process. Besides, this scheme utilizes EDEM method to improve the visual quality of stego images, and uses the arithmetic operation in Galois field GF(28) to overcome the issues of pixel truncation and image expansion caused by the arithmetic operation in Galois field GF(251). Lastly, this scheme makes comparisons and analysis on the modification extent of host image pixels and the actual operational performance of the scheme.(2) There are some issues existing in image secret sharing schemes based on polynomial (also known as the Shamir method):(a) the problem of mutually different characteristic of input values:some schemes of this kind take the pixels of host image as the input values for a polynomial expression, then if the case of some pixels having the same value happens, there is a need to modify these values to ensure the mutually different characteristic of input values, which leads to the degradation of visual quality of stego images; (b) when a polynomial expression uses modulo 251, there exists issues of pixel truncation and image expansion; (c) the operational performance is relatively low (the computational complexity is O[nlog2n)). To solve these problems, this paper proposes an image secret sharing scheme based on Sudoku table and cellular automata. One dimensional reversible memory cellular automata does not require that the input values should be mutually different, and does not need modulo 251. This scheme utilizes the above two characteristics of one dimensional reversible memory cellular automata to solve the above (a) and (b) problems. This scheme's computational complexity is O(n) and supports parallel computing, thus improving the above (c) problem. Besides, this scheme also utilizes the steganographic method based on Sudoku table with reversible characteristic to overcome the problems of the steganographic method based on modular arithmetic, including arithmetic overflow problem and unusable problem of partial host image's pixels. Experimental results show that this scheme can generate stego images with satisfying visual quality and achieve the lossless recovery of the secret image and the host image. In addition, this paper also proposes an image secret sharing scheme based on SMbLSBC, cellular automata and EDEM, which does not require extra storage. Experimental results show that this scheme not only has the merits of the above scheme, but also enhances the flexibility of embedding capacity and improves the visual quality of stego images.(3) If the values of the cell sum and neighborhood radius are too small, the confusion and diffusion properties of cellular automata cannot break up the high correlation between pixels of the secret image effectively. Therefore, only using one-dimensional reversible memory cellular automata to generate shadow images will cause the issue of leaking some information about the secret image from some shadow images. To solve this security problem, this paper proposes an image secret sharing scheme without third-party scrambling method, which acheives the scrabling process for the secret image by enlarging the values of the cell sum and neighborhood radius, making the two processes of image scrambling and secret image finished by one-dimensional reversible memory cellular automata. Experimental results show that this scheme can generate shadow images with strong randomness to avoid the issue of leaking information about the secret image.(4) For the third category of research, this paper proposes a CVTiOISSS (CAISSS, short for Cellular Automata Image Secret Sharing Scheme; VCS, short for Visual Cryptography Scheme:TiOISSS, short for Two in One Image Secret Sharing Scheme, including computing device decoding process and pure visual decoding process; CAISSS and VCS-combined TiOISSS, hereafter referred to as CVTiOISSS) scheme based on CAISSS and VCS, which solves the issues of current TiOISSS schemes, such as relying on third-party srambling method and the histogram of the scrambled image being the same as that of the secret image.This scheme improves shadow images' security, and owns the merits of lossless recovery of the secret image, small size of shadow images, and adjustable visual quality of preview images.