Secret Sharing In Visual Cryptography

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Cryptography is a complex and difficult subject for students to learn: a simple message is scrambled using a key and an algorithm that tends to be highly abstract. Therefore new technologies have been explored to make it more concrete and easier to understand. One of these is visual cryptography. Visual Cryptography was originally proposed for the problem of secret sharing.

Secret sharing is one of the early problems to be considered in Cryptography. In visual cryptography, the "key" is simply a sheet of clear plastic with apparently-random dots printed on it. The "encrypted message" is another such sheet, which also appears to be random. But when the two sheets are set on top of each other, a hidden message appears.

There is an enormous literature on visual cryptography (see the References section). It was originally invented and developed for cryptographic reasons, but the pedagogical uses are clear. It allows the student to physically manipulate the elements of the system, and visually see the decryption process in action.With the near universal use of the Internet in every field, the need to share important documents from one office to other, via this medium becomes increasingly more necessary. With the coming era of the electronic commerce, there is an urgent need to solve the problem of ensuring information safety in today's increasingly open network environment.

The encrypting technologies of traditional cryptography are usually used to protect information security. With such technologies, the data become disordered after being encrypted and can then be recovered by a correct key. Without the correct key, the encrypted source content can hardly be detected even though unauthorized persons steal the data.

Naor and Shamir [1] proposed a new cryptography area, visual cryptography, in 1994. Visual cryptography is a technique, to provide privacy protection when transmitting sensitive data between offices. It is a secret sharing scheme that can securely share image information (printed text, handwritten notes, pictures, etc.), and it is possible to decode shared secrets by the human visual system.

This modern technique also makes it difficult for the recipient to modify the source, maintaining the authenticity of the document.

Problem Background

When important secret information is managed by individuals, secrets may leak out by not enough management or personal grudge, and there is a possibility of exploitation. Assume a bank vault must be opened every day. Although the bank employs three senior tellers, management does not want to entrust any individual with the combination.

Therefore bank management would like a vault access system that requires any two of the three senior tellers. This problem can be easily solved using a two-out-of-three threshold scheme.Here is an interesting "real-world" example of this situation: According to Time Magazine, control of nuclear weapons in Russia in the early 1990s depended upon a similar "two-out-of-three" access mechanism. The three parties involved were the President, the Defense Minister and the Defense Ministry.The (k, n) threshold scheme for secret sharing was proposed by G.R.

Blakley and Adi Shamir [2, 12] and since then many researchers have further investigated. Generally a secret sharing scheme is a method of distributing a secret among a set of associates in such a way that qualified subsets of associates can reconstruct the value of the secret by combining their shares, whereas any non-qualified subset of associates cannot determine anything about the value of the secret by any way. In this basic secret sharing scheme, however, cryptographic computations using computer are necessary to share a secret and decode the secret from shared data.

In all the secret sharing schemes, a great deal of complexity is necessary to encrypt and decode a secret, and therefore computers are essential.

The Model

In a (k, n)-threshold problem, a secret is divided into n pieces. With any k of the n pieces, the secret can be perfectly reconstructed, while even complete knowledge of k-1 pieces reveals absolutely no information about the secret. Visual cryptography illustrated a new paradigm to solve the (k, n) problem. It was originally proposed by Moni Naor and Adi Shamir [1].

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 be recovered if any k or more than k transparencies are stacked together, but no information about the original image can be gained if fewer than the 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 visual system. Therefore, a system employing visual cryptography can be used by anyone without any knowledge of cryptography. Another interesting thing about visual cryptography is that it is a perfectly secure chipper.

There is a simple analogy of the one time-pad cipher to visual cryptography.Besides introducing the new paradigm, Naor and Shamir also provided their constructions of visual cryptographic solutions for the general k out of n secret sharing problem. One can assume that every secret message can be represented as an image, and furthermore that the image is just a collection of black and white pixels i.e. it is assumed to be a binary image. Each original pixel appears in n modified versions (called shares) of the image, one for each transparency. Each share consists of m black and white sub-pixels. Each share of sub-pixels is printed on the transparency in close proximity (to best aid the human perception, they are typically arranged together to form a square with m selected as a square number).

The resulting structure can be described by a Boolean matrix M = (mij)n Ã- m where mij = 1 if and only if the j-th sub-pixel of the i-th share (transparency) is black. Usually, we will use R0 to refer to the constructed M when the pixel in the original image is white, and similarly R1 when the pixel in the original image is black. The important parameters of the scheme are:m, the number of pixels in a share. This parameter represents the loss in resolution from the original image to the recovered one.α, the relative difference in the weight between the combined shares that come from a white pixel and a black pixel in the original image.

This parameter represents the loss in contrast.γ, the size of the collection of C0 and C1. C0 refers to the sub-pixel patterns in the shares for a white pixel and black refers to the sub-pixel patterns in the shares for the C1 pixel.The difference between a visual threshold scheme and a traditional threshold scheme is in how the secret is reconstructed. A traditional-threshold scheme typically involves computations in a finite field; in a visual-threshold scheme, the computation is performed by the human visual system. The security condition is the same in the two types of schemes.In general, there are four criteria's, used to evaluate the performance of a (k, n) Visual secret sharing scheme.

The first criterion is security: fewer k shadows offer no information about the secret image, where k ≤ n. The second criterion is accuracy: it is similarity between the reconstructed image and the original one. The next criterion is computational complexity: the number of operators is required to produce shadows and to generate the reconstructed image. The last criterion is the size of a shadow, which is also called the pixel expansion problem.So here, we propose a new recursive hiding of secrets, with applications to both images and text, to increase the efficiency of visual cryptography and to make it possible to incorporate additional secret information that serves as a steganographic channel [5]. Here, we extend the idea of recursive hiding of secrets to 3 out of 5 threshold scheme and apply it to both images and text.

However we deal with only binary images and regard each pixel as one bit of information, denoting black or white pixel. We also propose to extend this to gray scale images and observe how secret sharing takes place. Experimental results confirm that the grayscale image quality in this proposed scheme is better than anything and this allow high quality images including that of perfect (original) quality to be reconstructed.The whole document is organized as follows: Chapter II of this document outlines the previous work that has been done in this field.

Chapter III explains the proposed approach in detail, i.e., how the secret information break down into smaller secrets in shares of larger secrets by doubling the secret size at every step. Chapter IV explains secret sharing scheme for gray scale images. Summary and conclusion are presented in Chapter V.CHAPTER IIREVIEW OF LITERATURE

Visual Cryptography Approach

Visual cryptography is a special encryption technique to hide information in images in such a way that it can be decrypted by the human vision if the correct key image is used. The technique was proposed by Naor and Shamir in 1994. Visual Cryptography uses two or more transient images (called shares). One image contains random pixels and the other image contains the secret information.

It is impossible to retrieve the secret information from one of the images. Either transparent images or layers are required to reveal the information. The easiest way to implement visual cryptography is to print the two layers onto a transparent sheet.

When the random image contains truly random pixels it can be seen as a one-time pad system and will offer unbreakable encryption. In the overlay animation you can observe the two layers sliding over each other until they are correctly aligned and the hidden information appears.In visual secret sharing, the message bit consists of a collection of black and white pixels and each pixel is handled separately.Each pixel in the original image appears in n modified versions, one for each transparency and they are called shares.Each share is a collection of m black and white sub-pixels.Here is a simple example that explains the idea of how visual cryptography works.Visual_crypto_animation_demoWikipediaFigure-1, Example to show how VC worksFrom Figure-1 we can observe that the original image is broken up into two parts and they are called shares. Separately these shares look like random noise but when combining reveals an image.

Every single pixel is split into sub-pixels and the human vision still perceives them as one pixel.

Two-out-of-Two Scheme (2 sub-pixels)

Naor and Shamir [1], proposed encoding scheme to share a binary image into two shares Share1 and Share2. Each pixel is divided into a black and a white sub-pixel placed next to each other. For the case of white pixel, one of the two combinations of sub-pixels will be chosen with a probability of 0.5 to represent the pixel in each of the shares. When these shares are placed one on top of the other, the pixel are visually ORed and hence a white pixel looks gray (half black and half white) to the human eye. The pixels are chosen in a similar manner for the case of a black pixel.

But when the sub-pixels are visually ORed, the two black sub-pixels placed next to each other appear as a single black pixel. The above described idea can be applied to images to develop a basic Two-out-of-Two scheme by using 2 sub-pixels.Figure-2, Partitions for black and white pixels for 2-out-of-2 scheme (2 sub-pixels)

Two-out-of-Two Scheme (4 sub-pixels)

The original problem of visual cryptography is the special case of a Two-out-of-Two visual secret sharing problem. It can be solved with 2 sub-pixels per pixel, but in practice this can distort the aspect ratio of the original image. It is thus recommended to use 4 sub-pixels arranged in a 2 Ã- 2 array where each share has one of the visual forms in Figure-3. A white pixel is shared into two identical arrays from this list, and a black pixel is shared into two complementary arrays from this list.

Any single share is a random choice of two black and two white sub-pixels, which looks medium grey. When two shares are stacked together, the result is either medium grey (which represents white) or completely black (which represents black).Horizontal Shares

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