IMAGE HALFTONE TECHNIQUE IN VISUAL SECRET SHARING

Transcription

1 IMAGE HALFTONE TECHNIQUE IN VISUAL SECRET SHARING Thesis submitted in the partial fulfillment of the requirements for the degree of Master of Technology in Computer Technology in The Faculty of Engineering & Technology Jadavpur University by ARNAB ACHARYYA UNIVERSITY ROLL NO: 5434 REGISTRATION NUMBER: 6926 of 2-22 EXAMINATION ROLL NUMBER: M6TCT4-29 Under the Guidance of PROF. SHOVONLAL KUNDU Department of Computer Science & Engineering, Jadavpur University Faculty of Engineering and Technology JADAVPUR UNIVERSITY, Kolkata- 732 May, 24

2 FACULTY OF ENGINEERING AND TECHNOLOGY JADAVPUR UNIVERSITY To whom it may concern This is to certify that the thesis entitled Image Halftone Technique in Visual Secret Sharing has been satisfactorily completed by Sri Arnab Acharyya under my guidance and supervision and be accepted in partial fulfillment of the requirements of the degree of Master of Technology in Computer Technology of Jadavpur University in the year Prof. Shovonlal Kundu Department of Computer Science and Technology Jadavpur University,Kolkata-732 Forwarded By Prof.Sivaji Bandyopadhyay HOD, Department of Computer Science and Technology Jadavpur University, Kolkata-732 Dean, Faculty of Engineering and Technology Jadavpur University, Kolkata-732 2

3 FACULTY OF ENGINEERING AND TECHNOLOGY JADAVPUR UNIVERSITY CERTIFICATE OF APPROVAL The foregoing thesis, entitled Image Halftone Technique in Visual Secret Sharing is hereby approved as a creditable study of an engineering subject carried out and presented in a manner satisfactory to warrant its acceptance as prerequisite to the degree for which it has been submitted. It is understood that by this approval the undersigned do not necessarily endorse or accept every statement made, opinion expressed or conclusion drawn therein, but approve this thesis only for the purpose for which it has been submitted. Signature of the Examiner Signature of the Supervisor 3

4 Acknowledgements The satisfaction that accompanies the successful completion of any task would be incomplete without mention of the people who make it possible and whose constant guidance and encouragement crown all the efforts with success. The acknowledgement transcends the reality of formality when I would like to express deep gratitude and respect to all those people behind the screen who guided, inspired and helped me for the completion of my project work. I would like to express my deepest gratitude to my project advisor Honorable Prof. Shovonlal Kundu for his valuable support in providing resources, insight and advice during my research as well as throughout my post graduation career. He has constantly given me support and encouragement. I must mention that without him this thesis would have never seen the light of the day. I am also grateful to the higher authority of Technique Polytechnic Institute, my present working place. They have given me all the support to complete this course. Without their helping hand it will not be possible for me to carry out this task. I gracefully acknowledge many helpful comments, corrections and suggestions from my family, friends, teachers and my beloved students. Last but not the least, a word of thanks goes to my beloved parents for their continual encouragement and blessings. Jadavpur University May,24 Arnab Acharyya 4

5 CONTENTS List of Figures Chapter. Introduction.. Overview of Cryptography.2. Traditional Secret Sharing.3. Different Secret Sharing Scheme.4. Background on Visual Cryptography Chapter 2. Visual Secret Sharing 2.. Overview of Visual Secret Sharing 2.2. Related Works in Visual Cryptography 2.3. Pixel Division 2.4. Superposition of Pixels 2.5. Visual Cryptography Schemes Chapter 3. Image Halftone Technology 3.. Overview 3.2. Related Works in Image Halftone 3.3. Floyd-Steinberg Halftoning Algorithm Chapter 4. Discussion on the Experiment Performed 4.. Concept Adapted 4.2. Proposed Algorithm 4.3. System Block Diagram 4.4. Experimental Results 4.5. Advantage 4.6. Limitations 4.7. Summary Chapter 5. Appendices 5.. Appendix : Hardware and Software Requirements 5.2. Appendix 2: Program Listings Bibliography

6 List of Figures... Cryptography 2... Human Visual System Example of Visual Cryptography Different types of pixels Superposition of two pixels Pixel Pattern for (2,2) VCS (2,2) VCS with Consistent Image Size (3,6) VCS Dithering Method Example of Threshold values in Dither Cell Direct Binary Search Error Diffusion Image Result Floyd-Steinberg Error Diffusion Image Result Proposed system block diagram Original Image for Experiment Generated Halftone Share of Original Image Reconstructed Image

7 CHAPTER INTRODUCTION.. Overview of Cryptography Cryptography is derived from Greek word 'Krypto' which means hidden and 'Grafo', which means written. It is the study and implementation of techniques to hide information, or simply to protect a message or text from being read. The information that is protected can be written text, electronic signals, messages or data transmissions. The process of making the information unreadable is encryption or enciphering and the result of encryption is a ciphertext or cryptogram. Reversing this process and retrieving the original readable information is called decryption or deciphering. To encrypt or decrypt information, an algorithm or so called cipher is used. 8

8 Figure... Cryptography Ever since mankind has existed, people have had secrets, and other people have wanted to know these secrets. The earliest forms of cryptography were performed by pencil and paper, and were available only to those who had access to proper education. Today our lives are completely digitized and cryptography has become an integral part of nearly everyone's daily life, and it's used to protect confidential information from hackers. Nearly all our private information is stored in one of the many databases room the government, banks and health care services and so on. Cryptography protects the right to privacy and the right to communicate confidentially. Secure communications can protect one's intimate private life, business relations, and social or political activities. 9

9 .2. Traditional Secret Sharing Handling secret has been an issue of prominence from the time human beings started to live together. Important things and messages have been always there to be preserved and protected from possible misuse or loss. Some time secret is thought to be secure in a single hand and at other times it is thought to be secure when shared in many hands. Some of the formulae of vital combinations of medicinal plants or roots or leaves, in Ayurveda were known to a single person in a family. When he becomes old enough, he would rather share the secret formula to a chosen person from the family, or from among his disciples. There were times when the person with the secret dies before he could share the secret. Probably, similar incidents might have made the genius of those era to think of sharing the secrets with more than one person so that in the event of death of the present custodian, there will be at least one other person who knows the secret. Secret sharing in other forms were prevailing in the past, for other reasons also. Secrets were divided into number of pieces and given to the same number of people. To ensure unity among the participating people, the head of the family would share the information with respect to wealth

10 among his children and insist that after his death, they all should join together to inherit the wealth. To test the valor of the youth of a nation, a king, would hide treasure in some place in his kingdom and information about it would be placed in pieces at different places of varying grades of difficulty to reach. Only the brave and the intelligent would reach the treasure. Military and defense secrets have been the subject matter for secret sharing in the past as well as in the modern days. Secret sharing is a very hot area of research in Computer Science in the recent past. Digital media has replaced almost all forms of communication and information preservation and processing. Security[2],[29] in digital media has been a matter of serious concern. This has resulted in the development of encryption and cryptography. Uniform secret sharing schemes form a part of this large study. When important secret information is managed by individuals, secrets may leak. Suppose there is a vault that must be opened every day in a bank. Although the bank employs three senior tellers, management may not trust any individual teller. Therefore, it is necessary too and a possible solution to design a system whereby any two of the three senior tellers can gain access

11 to the vault, but no individual teller can do so. This problem can be easily solved using a secret sharing scheme. In a more general situation one may need to specify exactly which subsets of participants should be able to determine the key and which should not. Secret sharing schemes are useful in many situations that require the concurrence of several chosen people as in launching a missile or entering an area of restricted access (e.g., a bank vault)..3. Different Secret Sharing Scheme A Secret sharing scheme is a method of dividing secret information into two or more pieces, with or without medications, and retrieving the information by combining all or predefined sub collection of pieces. The pieces of information are called shares and the process responsible for the division is called dealer. A predefined sub- collection of shares which contains the whole secret in some form is called an allowed coalition. The process responsible for the recovery of the secret information from an allowed coalition is called a combiner. A share contains, logically, a part of the information, but will be of no use. Thus no single share is of any threat to the confidentiality of the secret 2

12 information. It is also envisaged that after the dealer process is over, the original information can be destroyed forever. This would mean that even the person responsible for the dealer process will not be a threat, thereafter. The secret information is recovered from any allowed coalition using the recovery process called combiner. The combiner would be able to recover the secret information, only if, all shares in the allowed coalition is present and not with any fewer number of shares. Thus, in an allowed coalition, each member share is equally important such that without anyone of them, the secret information cannot be accessed. Allowed coalition is also referred in the literature by other names too, such as, authentic collection, qualified collection or authorized set. We, in our work, preferred to call the sub collection of shares as allowed coalition. The set of all allowed 2 coalitions of participants is called the access structure and is usually denoted by. Secret Sharing[],[5],[7],[8],[5] is an important tool in Security and Cryptography. In many cases there is a single master key that provides the access to important secret information. Therefore, it would be desirable to keep the master key in a safe place to avoid accidental and malicious exposure. This scheme is unreliable: if master key is lost or destroyed, then all information accessed by the master key is no longer available. A possible 3

13 solution would be that of storing copies of the key in different safe places or giving copies to trusted people. In such a case the system becomes more vulnerable to security[2],[29] breaches or betrayal. A better solution would be, breaking the master key into pieces in such a way that only the concurrence of certain predefined trusted people can recover it. This has proven to be an important tool in management of cryptographic keys and multi-party secure protocols. As a solution to this problem, a secret sharing scheme divides (sharing) a secret key K among a finite set of n participants in such a way that only certain specified subsets (qualified subsets) of participants can compute the secret key K by gathering their information. It was discovered independently by G.R. Blakley and Adi Shamir[5]. Shamir's secret sharing scheme is an interpolating scheme based on polynomial interpolation while Blakley's secret sharing scheme is geometric in nature. Both of the schemes are k-out-of n schemes but they represent two different ways of constructing such schemes, based on which more advanced secret sharing schemes can be designed. The biggest motivation for secret sharing is secure key management. In particular situations, there will be only one secret key that provides access to many important les. If such a key is lost, then all the important les become inaccessible. 4

14 The basic model for secret sharing is called a k-out-of-n scheme (or sometimes referred as (k, n) threshold scheme). In this scheme, there is a sender and n participants. The secret information is divided into n parts by the sender, and gives each participant one part so that any k parts can be put together to recover the secret, but any k - parts reveal no information about the secret. The pieces are usually called shares or shadows. Different choices for the values of k and n reflect the tradeoff between security[2],[29] and reliability. A secret sharing scheme is perfect if any group of at most k - participant (insiders) has no advantage in guessing the secret over the outsiders. An important issue in the implementation of secret sharing scheme is the size of the shares distributed to the participants, since the security of a system degrades as the amount of the information that must be kept secret increases. So the size of the shares given to the participants is a key point in the design of secret sharing[23],[24] schemes. Therefore, one of the main parameters in secret sharing[25],[28] is, the average information rate; of the scheme, which is defined as the ratio between the average length (in bits) of the shares given to the participants and the length of the secret. Unfortunately, in all secret sharing[3],[32] schemes the size of the shares cannot be less than the size of the secret, and so the information rate cannot 5

15 be less than one. Moreover, there are accesses structures, for which, any corresponding secret sharing[33] scheme must give to some participant a share of size strictly bigger than the secret size. Secret sharing schemes with information rate equal to one are called ideal. A secret sharing scheme is called efficient if the total length of the n shares is polynomial in n..4. Background on Visual Cryptography Cryptography has a long and fascinating history and it is one of the most important fields within the security profession. Visual cryptography uses the characteristics of human vision to decrypt encrypted images and in it the secret image is split into two or more separate random images called shares. To decrypt the encrypted information, the shares are stacked one on top of the other, and the hidden secret image appears. Due to its simplicity, anyone can physically manipulate the elements of the system, and visually see the decryption process in action without any knowledge of cryptography and without performing any cryptographic computations. 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 6

16 commerce, there is an immediate need to solve the problem of ensuring information safety in today's increasingly open network environment. To protect the security of information, various encrypting technologies of traditional cryptography are usually used. With such technologies, the data can become disordered after being encrypted and later it can 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. The following question was asked by Kafri and Keren.Is it possible to create a secret sharing scheme in which the secret image I that can be reconstructed visually by superimposing random grids? Each grid would consist of a transparency, made up of black and white pixels. Later Naor[34] and Shamir introduced a specific implementation that was named visual secret sharing (VSS). This method can securely share image information (printed text, handwritten notes, pictures etc.), and it is possible to decode shared secrets by the human visual system. Based on the secret message (the original image) the VSS scheme generates n images (known as shares) which can be printed on n transparencies. In a k-out-of-n scheme, there would be n transparencies, and if any k or more than k transparencies are superimposed, the original secret image I should appear, but no information 7

17 about the original image can be gained if fewer than the threshold[9] number of k transparencies are stacked (k - shares). The main difference between a traditional threshold scheme and a visual threshold scheme is how the secret is recovered. 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. In both types of schemes the security conditions is the same. 8

18 CHAPTER 2 VISUAL SECRET SHARING 2.. Overview of Visual Secret Sharing Visual cryptography[2],[22] is a cryptographic technique which allows visual information (Image, text, etc) to be encrypted in such a way that the decryption can be performed by the human visual system without the aid of computers. Image is a multimedia component sensed by human. The smallest element of a digital image is pixel. In a 32 bit digital image each pixel consists of 32 bits, which is divided into four parts, namely Alpha, Red, Green and Blue; each with 8 bits. Alpha part represents degree of transparency. If all bits of Alpha part are '', then the image is fully transparent. Human visual system acts as an OR function. If two transparent objects are stacked together, the final stack of objects will be transparent. But if any of them is non-transparent, then the final stack of objects will be nontransparent. Like OR, 2

19 OR =, considering as transparent and OR =, OR =, OR =, considering as non-transparent. SHARE- SHARE-2 FINAL = = = = Transparent () Non-Transparent () Figure 2... Human Visual System Visual cryptography[26],[27] scheme (VCS) is basically a secret-sharing scheme which means the generation of share images of secret images that are transmitted over the channel. The only beauty of such scheme is that, the decryption of the secret image requires neither the prior knowledge about cryptography nor requires any complex computation. The secret image can be obtained only by stacking certain number of shares on to each other. In the case of black and white images, the original secret image is represented as a pattern of black and white pixels. Each of these pixels is divided into sub-pixels which themselves are encoded as black and white to produce the share images. The 2

20 recovered secret image is also a pattern of black and white sub-pixels which should visually reveal the original secret image if a qualified set of share images is stacked. It can encrypt a black-and-white secret image into n shares, which are transmitted over the channel. Depending on the type of threshold scheme certain numbers of shares out of n number are stacked together to get back the secret image. For example, in a k-out-of-n VSS scheme, the secret is visible only when at least k or more shares are stacked together. In order to provide perfect secrecy and the maximum clarity of the recovered secret images, most researchers use the concept of pixel expansion, which was SHARE- ORIGINAL IMAGE RECOVERED IMAGE SHARE-2 Figure Example of Visual Cryptography first introduced by Naor[34] and Shamir to design their visual cryptography[3],[35],[36] schemes. That is, each pixel of the binary secret image is encoded into m sub22

21 pixels on each share, where m is called the parameter of pixel expansion of the scheme. By analyzing any block of m sub-pixels of the forbidden set of shares, one cannot distinguish which color was used in the secret pixel. But when the shares of the qualified set are stacked up, the block of any m sub-pixels corresponding to a black secret pixel will provide more black sub-pixels than a block of sub-pixel corresponding to a white secret pixel. Thus, the blocks corresponding to black secret pixels will have more blackness and those blocks corresponding to white secret pixels will have less blackness. This property makes it possible for someone to distinguish black and white blocks, and hence the secret image can reveal the stacked image by losing some contrast of the original secret image Related Works in Visual Cryptography In 995, Naor and Shamir introduced a very interesting and simple cryptographic method called visual cryptography[2],[36] to protect secrets. Basically, visual cryptography has two important features. The first feature is its perfect secrecy and the second is its decryption method which requires neither complex decryption algorithms nor the aid of computers. It uses only human visual system to identify the secret from the stacked image of some authorized set of shares. Therefore, visual cryptography is a very convenient way to protect secrets 23

22 when computers or other decryption devices are not available. The simple decryption method is the reason that attracts many researchers to make further detailed enquiries in this research area. Nowadays, many related methods concerning the theory and the applications of visual cryptography are proposed. An extended visual cryptography scheme (EVCS) was proposed by Ateniese et al.. Extended[9],[] visual cryptography[],[2] schemes permits the construction of visual secret sharing schemes within which the shares are meaningful as opposed to having random noise on the shares. After the sets of shares are superimposed, this meaningful information disappears and the secret is recovered. This is the basis for the extended form of visual cryptography. The image size invariant visual cryptography[3],[4] was proposed by Ito et al. The traditional visual cryptography schemes employ pixel expansion. In pixel expansion, each share is m times the size of the secret image. Thus, it can lead to the difficulty in carrying these shares and consumption of more storage space. Ito's scheme removes the need for this pixel expansion. That is, the reconstructed image is identical to the original image. There are also some other studies which focus on the methods without pixel expansion. In 996, Naor and Shamir proposed an alternative VCS model for improving the contrast. In 999, Blundo et al. analyzed the contrast of the reconstructed image in k-out-of-n VCS schemes. Blundo[5] et al. gave a complete 24

23 characterization of 2-out-of-n VCS schemes having optimal contrast and minimum pixel expansion in terms of certain balanced incomplete block designs. Blundo et al.'s research results are valuable for the researchers who are interested in the area of visual cryptography[6],[7]. Viet and Kurosawa proposed a VCS with reversing, in which the participants are also allowed to reverse their transparencies. But in this scheme there is a loss of resolution, since the number of pixels in the reconstructed image is greater than that in the original secret image. The concept of recursive hiding[29] of secrets in visual cryptography was proposed by Gnanaguruparan and Kak. This provides a method of hiding secrets recursively in the shares of threshold schemes, which permits an efficient utilization of data. In recursive hiding[29] of secrets, several additional messages can be hidden in one of the shares of the original secret image. By using recursive threshold visual cryptography in network application, network load can be reduced. Recently, visual cryptography schemes were also proposed to deal with gray-level images. The use of halftoning[2] techniques make it possible that the readymade schemes designed for binary secret images can be directly applied to gray-level images. The different gray-level visual cryptography schemes are studied by researchers. 25

24 Applying visual cryptography techniques to colour images is a very important area of research because it allows the use of natural colour images. Color images are also highly popular and have a wider range of uses when compared to other image types. In 997, Verheul and Van Tilborg proposed a colored visual cryptography scheme. In 2, Yang and Laih proposed a different construction mechanism for the colored visual cryptography scheme. They argued that their method can be easily implemented and can get much better block length than Verheul and Van Tilborg's scheme. A major common disadvantage of the above reviewed colored VCS schemes is that the number of colors and the number of sub-pixels determine the resolution of the revealed secret image. If many colors are used, the sub-pixels require a large matrix to represent it. Also, the contrast of the revealed secret image will go down drastically. Consequently, how to correctly stack these shared transparencies and recognize the revealed secret image are the major issues. Almost all color visual cryptography schemes proposed required few computations. Recently, more and more applications of visual cryptography, such as authentication, human identification, copyright protection, watermarking, mobile ticket validation, visual signature checking etc. are introduced. 26

25 The print and scan application of VCS can be found in. In this application, scan the shares into a computer system and then digitally superimpose their corresponding shares. This would make possible secure verification of e-tickets or other documents Pixel Division In this section, we shall review the basic visual cryptography scheme proposed by Naor[34] and Shamir. Here a secret black and white image is divided into two grey images. In order to share a secret black and white image, the concept of their scheme is to transform one pixel into two sub-pixels and divide each subpixel two color regions. The sub-pixels are half white and half black. (a) (b) (c) (d) (a) Black () (b) White () (c) Left Black () (d) Right Black () Figure Different types of pixels 27

26 For example, this figure represents four different types of pixels. The first is a white pixel, the next is a black pixel, and the last two are grey pixels. Note that in the grey pixels, the black and white portions are different. Let us call these pixels as RB and LB pixels respectively. We represent a white pixel by, black by, LB-pixel by and RB-pixel by. They can be thought of as modified version of pixels to be used in shares Superposition of Pixels If we stack two LB pixels (or two RB pixels) we get nothing new, whereas, if we stack an LB pixel and an RB pixel, we get a black pixel. This can be shown as in the following figure. We can see that by the representation used for pixels, the superposition of two pixels can be thought of as if a binary "OR" operation. = V= = V= = V= = V= Figure Superposition of two pixels 28

27 2.5. Visual Cryptography Schemes The visual cryptography schemes (VCS) describe the way in which an image is encrypted and decrypted. There are different types of visual cryptography schemes. For example, there is the k-out-of-n scheme that says n shares will be produced to encrypt an image, and k shares must be stacked to decrypt the image. If the number of shares stacked is less than k, the original image is not revealed. The other schemes are 2-out-of-n and n-out-of-n VCS. The most of the constructions of visual cryptography schemes are realized using two n X m matrices, S and S, called basis matrices The Construction of 2-out-of-2 VCS. ORIGINAL IMAGE SHARE- FINAL IMAGE SHARE-2 = = = = Figure Pixel Pattern for (2,2) VCS 29

28 Let us consider a binary secret image S containing exactly m pixels. The dealer creates two shares (binary images), S and S2, consisting of exactly two pixels for each pixel in the secret image as shown in the following figure. If the pixel in S is white, the dealer randomly chooses one row from the first two rows of the table. Similarly, if the pixel in S is black, the dealer randomly chooses one row from the last two rows of the table. To analyze the security[2],[29] of the 2-out-of-2 VCS, the dealer randomly chooses one of the two pixel patterns (black or white) from the table for the shares S and S2. The pixel selection is random so that the shares S and S2 consist of equal number of black and white pixels. Therefore, by inspecting a single share, one cannot identify the secret pixel as black or white. This method provides perfect security. The two participants can recover the secret pixel by superimposing the two shared sub-pixels. If the superimposition results in two black sub-pixels, the original pixel was black; if the superimposition creates one black and one white sub-pixel, it indicates that the original pixel was white. In visual cryptography, the white pixel is representing by and the black pixel by. For the 2-out-of-2 VCS, the basis matrices, S and S are designed as follows: S S 3

29 There are two collections of matrices, C for encoding white pixels and C for encoding black pixels. Let C and C be the following two collections of matrices: = { ( )} = { ( )} Where π(s) and π(s) represents the collection of all matrices obtained by permuting the columns of matrices S and S respectively. That is, C { C {, } and, } To share a white pixel, the dealer randomly selects one of the matrices in C, and to share a black pixel, the dealer randomly selects one of the matrices in C. The first row of the chosen matrix is used for share and the second row for share2. 3

30 ORIGINAL IMAGE ADDING NOISE TO IMAGE SHARE- SHARE-2 RECOVERED IMAGE Figure (2,2) VCS with Consistent Image Size The problem that arises with this scheme is that for every pixel encoded from the original image into two sub-pixels and placed on each share in a horizontal or vertical fashion (here horizontal), the shares have a size of s x 2s if the secret image is of size s x s. Hence there is distortion. 32

31 The Construction of k-out-of-n VCS The general k out of n visual cryptography[7],[8] schemes were introduced by Naor[34] and Shamir. However, their constructions were quite inefficient, since a large number of sub-pixels were needed to encode a given pixel. A much more efficient construction mechanism was introduced by Ateniese et al. This construction significantly reduces the number of subpixels needed for encoding. Consider a starting n x l matrix SM (n, l, k) whose entries are elements of a ground set {,,., }, with the SM(n, l, k), then there exists a k-out-of- n VCS with pixel expansion m = l X 2k-. The n x m basis matrices S and S are constructed by respectively replacing the symbols {,,., } with the st,2nd,, kth rows of the corresponding basis matrices of the k-out-of-k VCS The Basis Matrices for k-out-of-n VCS. The k-out-of-n visual cryptography can be illustrated by a 3-out-of- 6VCS case. The starting matrix SM designed as: a a a SM 2 a2 a3 a3 33 a2 a3 a a3 a a2 a3 a2 a3 a a2 a

32 Substituting the rows of the basis matrix S of 3-out-of-3 VCS for a, a2, a3 in SM to obtain the basis matrix S in 3-out-of-6 VCS. That is: S Similarly the basis matrix S is obtained by replacing a, a2, a3 of SM by the rows of the basis matrix S of 3-out-of-3 VCS: S The basis matrices S and S are met the three conditions. The matrices C and C can be designed as: C { ( S )} { (,,,,,,,,,,, )} 34

33 C { ( S )} { (,,,,,,,,,,, )} The following figures depict 3-out-of-6 VCS using the above matrices C and C. ORIGINAL IMAGE SHARE-4 SHARE- SHARE-2 SHARE-5 SHARE-6 Figure (3,6) VCS 35 SHARE-3 RECOVERED IMAGE

34 CHAPTER 3 IMAGE HALFTONE TECHNOLOGY 3.. Overview The perceived quality of a printed image depends on the halftone algorithm and the printing process. The focus of this study was theoretical and experimental research on topics in the fields of half toning, image processing and compression, and image quality. Several commonly used dither algorithms, including clustereddot dither and dispersed-dot dither, are evaluated. Next, images halftoned with the dither algorithms and the Floyd-Steinberg[],[4] error diffusion algorithm are compared in the frequency domain. Finally, a perception-based halftone image distortion measure is proposed. The halftone[2] algorithms are ranked according to the proposed distortion measure. The effects of using human visual models with different peak sensitivity frequencies are examined. A new class of dithering algorithms for black and white (B/W) images is presented. The basic idea behind the technique is to divide the image into small 37

35 blocks and minimize the distortion between the original continuous-tone image and its low-pass-filtered halftone. This corresponds to a quadratic programming problem with linear constraints, which is solved via standard optimization techniques. Examples of B/W halftone[2] images obtained by this technique are compared to halftones obtained via existing dithering algorithm and error diffusion algorithm. This paper proposes a deterministic importance sampling[3] algorithm for complex integrands. The idea is based on the recognition that halftoning algorithms are equivalent to importance sampling if the gray-scale image and a resulting white pixel are considered as the target importance function and the sampling position, respectively. We adopt the Floyd-Steinberg[],[4] halftoning algorithm, extend it to higher dimensions, and rephrase it as a sampling method. As the Floyd-Steinberg[],[4] halftoning places a sample also considering where other samples are located, our sampling[3] algorithm distributes samples in a stratified way. Halftone[2] image data hiding can be divided into two classes. One class embeds digital data into halftone image such that the data is invisible but can be read by applying some extraction process on the halftone image. 38

36 3.2. Related Works in Image Halftone A plenty number of work has been done on image dithering algorithm. An image dithering algorithm first published in 976 by Robert W. Floyd and Louis Steinberg[],[4], which is known as Floyd Steinberg[],[4] dithering Idea About Halftone Halftone[2] is the reprographic technique that simulates continuous tone[6] imagery through the use of dots, varying either in size, in shape or in spacing. Halftone" can also be used to refer specifically to the image that is produced by this process. Halftoning[2] is a technique to render gray-scale images on a black and white display. The idea is to put more white points at brighter areas and less points at darker parts. The spatial density of white points in a region around a pixel is expected to be proportional to the gray level of that particular pixel. If we consider the gray level of the original image to be a scalar importance function and the white pixels of the resulting image to be sample locations, then we can realize that halftoning is equivalent to a deterministic importance sampling[3] algorithm. This holds for an arbitrary halftoning 39

37 algorithm, including the random and ordered halftoning methods that add random noise or a periodic pattern to the original image before quantization, or, for example, the Floyd-Steinberg[],[4] algorithm Halftoning Methods The following halfoning methods are very popular Dithering Dither is an intentionally applied form of noise used to randomize quantization error, preventing large-scale patterns such as color banding in images. Figure Dithering Method 4

38 n Cell Dither n gray values n equally spaced threshold values Figure Threshold values in Dither Cell Figure Example of Threshold values in Dither Cell 4

39 Direct Binary Search Direct binary search is an iterative method to refine a halftone to improve visual quality. Direct binary search toggles pixels and swaps pixels among neighboring pixels to minimize a distortion measure, such as a weighted mean square error, between the halftone and the original image. The weighting is generally based on a linear spatially-invariant model of the human visual system. Given an error metric: d(i(x,y),b(x,y)) example: d(i,b) = Σ((I(x,y)-b(x,y))2) Initialize binary image b(x,y) Randomly chose a pixel (x,y) in b(x,y) ~ ~ if d(i, b ) < d(i,b) then assign b = b ~ ~ where b is b except for b (x,y) =-b(x,y) Repeat last step until d(i,b) - d(i,b) is small. Error metric can be smart for example based on Human Visual System. 42

40 Figure Direct Binary Search Error Diffusion Error diffusion was introduced in 976 by Floyd and Steinberg[],[4]. Error diffusion produces halftones of much higher quality than classical screening, with the trade-off of requiring more computation and memory. Screening amounts to pixel-based thresholding, whereas error diffusion requires a neighborhood operation and thresholding. The neighbourhood operation distributes the quantization error due to thresholding to the unhalftoned neighbours of the current pixel. The term "error diffusion" refers to the process of diffusing the quantization error along the path of the image scan. In the case of a raster scan, the quantization error diffuses across and down the image. "Qualitatively speaking, error diffusion 43

41 accurately reproduces the gray level in a local region by driving the average error to zero through the use of feedback" The generalized Error Diffusion Algorithm. Choose an enumeration of the pixels. 2. At each pixel location, add to the input I(i) a weighted average of the previous errors in some neighborhood to obtain the modified input M(i). 3. Choose O(i) an element of V closest to M(i). 4. Define the error e(i) as M(i)-O(i). Algorithm is not necessarily deterministic. ORIGINAL IMAGE HALFTONED IMAGE Figure Error Diffusion Image Result 44

42 3.3. Floyd-Steinberg Halftoning Algorithm The Floyd-Steinberg[],[4] halftoning provides better results than random or ordered halftoning, because it makes not only local decisions, but the gathered information is also distributed in neighbouring pixels. It means that it takes other samples into account as well, so the sample positions are stratified, making the resulting image smoother and reducing the noise compared to random or dithered approaches. The Floyd-Steinberg[],[4] Error Diffusion Pseudo code is as follows: for each y from top to bottom for each x from left to right oldpixel := pixel[x][y] newpixel := find_closest_palette_color(oldpixel) pixel[x][y] := newpixel quant_error := oldpixel - newpixel pixel[x+][y] := pixel[x+][y] + 7/6 * quant_error pixel[x-][y+] := pixel[x-][y+] + 3/6 * quant_error pixel[x][y+] := pixel[x][y+] + 5/6 * quant_error pixel[x+][y+] := pixel[x+][y+] + /6 * quant_error Due to its good properties and automatic stratification, we developed our sampler based on the Floyd-Steinberg [],[4] method. Random dithering, which is similar to importance resampling, was implemented for 45

43 comparison. We expected the same improvement in importance sampling[3] as provided by the Floyd-Steinberg[],[4] halftoning over random dithering. As stated in the introduction, there are several image halftoning techniques or approaches. Among these methods Error Diffusion and Dot Diffusion display pretty good performance. In Error Diffusion halftoning, the quantization error at each pixel is filtered and fed back to the input in order to diffuse the error among neighbouring grayscale pixels. Here I used Floyd-Steinberg Error diffusion technique to diffuse the error to neighbouring pixels. The Floyd-Steinberg error diffusion filter is shown in figure, where X denotes the current pixel. The error diffusion algorithm transforms a gray scale image, I, with pixel values in the interval [.,.], to a black-and-white image. ORIGINAL IMAGE HALFTONED IMAGE Figure Floyd-Steinberg Error Diffusion Image Result 46

44 CHAPTER 4 DISCUSSION ON THE EXPERIMENT PERFORMED 4.. Concept Adapted 4... Extension of k,n Visual Cryptography Scheme In visual secret sharing, the message bit consists of a collection of black and white pixels i.e. it is assumed to be a binary image and each pixel is handled separately. 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 the 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 number). The resulting structure can be described by a [n x m] (n = number of shares, m = pixel expansion) Boolean matrix S = (Sij)nXm where Sij = if and only if the jth sub-pixel in the ith share (transparency) is black and Sij = 48

45 if and only if the jth sub-pixel in the ith share (transparency) is white. When transparencies i, i2,, ir are stacked together in a way which properly aligns the sub-pixels, we see a combined share whose black sub-pixels are represented by the Boolean OR of rows i, i2,, ir in S. The grey level of this combined share is proportional to the Hamming weight H (V) of the OR ed m-vector V. This grey level is interpreted by the visual system of the users as white if H(V ) < d-α.m and as black if H(V ) > d for some fixed threshold d m and relative difference α >. Now, (k,n) Extended Visual Cryptography[7] scheme allows the construction of visual secret sharing scheme within which the shares are meaningful as opposed to having random noise on the shares. After the sets of shares are superimposed, this meaningful information disappears and the secret is recovered. 49

46 4.2. Proposed Algorithm In this experiment two techniques halftone and k, n VCS have been merged to obtain a better result. The steps of the proposed algorithm are as follows: Step: K, Input the threshold value for the no. of share required to reconstruct the image. Step2: N, Input the maximum no. of share. Step3: Input the index of share to reconstruct original image. Step4: Input Image Step5: Read the Image data Step6: Making halftone of the original image Step7: Creating the maximum N no of share of the halftone image. Step8: Calculating the required image for reconstruction of original image. Step9: Recovering the original image. 5

47 4.3. System Block Diagram ORIGINAL IMAGE SHARED IMAGE Applying image halftone technique Applying (k,n) VCS reconstruction algorithm SHARED IMAGE 2 HALFTONE IMAGE SHARED IMAGE 3 Applying (k,n) VCS Sharing Algorithm SHARED IMAGE 4 SHARED IMAGE N Figure Proposed system block diagram 5 RECOVERED IMAGE

48 4.4. Experimental Results K=4, N=8 Figure Original Image for Experiment SHARE- SHARE-2 SHARE-3 SHARE-4 SHARE-5 SHARE-6 SHARE-7 SHARE-8 Figure Generated Halftone Share of Original Image Figure Reconstructed Image 52

49 4.5. Advantages. Simple to implement 2. No Decryption algorithm required as Human Visual System used. 3. Lower computational cost. 4. As each share is a halftone share, fewer details will be transmitted per share Limitations. The image quality is not maintained. 2. Perfect alignment of the encrypted shares are troublesome. 3. This proposed system is restricted only to grayscale images. For colored images, additional computations have to be done. 4. This scheme is applicable for only grayscale (with.bin extensions) images. 53

50 4.7. Summary Visual cryptography provides a secure way to transfer images. The advantage of visual cryptography is that it exploits human eyes to decrypt secret images with no computation required.. Visual Cryptography allows easy decoding of the secret image by a simple stacking of the printed share transparencies. However, there are some practical issues that need careful consideration. The transparencies should be precisely aligned in order to obtain a clear reconstruction of the secret image. There is also some unavoidable noise introduced during the printing process. Furthermore, the stacking method can only simulate the OR operation which always leads to a loss in contrast. The loss of contrast can be rectified by further processing. As visual cryptography schemes operate at the pixel levels, each pixel on one share must be matched correctly with the corresponding pixel on the other share. Superimposing the shares with even a slight change in the alignment may results in a drastic degradation in the quality of the reconstructed image. The thesis described Embedded Extended (k,n) VCS for black and white images. In this scheme the original image is converted to halftone image and then it is divided into equal dimension of shares. This scheme can reconstruct the secret image precisely and has low computational complexity. The probability of reconstruction of the image from individual shares is very less so this method ensures satisfactory results in the field of security. The drawback of this scheme is that it works with only grayscale images. So this scheme can be extended to work with other image formats. Also emerging technique like, color visual secret sharing scheme can be used along with this algorithm. The concept of general access structure can also be used with this scheme. Also we can use key based approach for secret share. 54

51 CHAPTER 5 APPENDICES 5.. Appendix : Hardware and Software Requirements Processor Dual Core, 2.4GHz Hard Disk 5 GB RAM 4GB Keyboard & Mouse Logitech Table : Hardware Used Operating System Windows XP SP2 IDE Matlab 22 Table 2: Software Used 5.. Appendix 2: Program List %% Main Function function ImageSharing clear; close all; Height = 256; Width =256; t = 4; w = 8; Users = [5,6,7,8]; base = 257; Sub_width = Width/t^(.5); Sub_height = Height/t^(.5); 56

52 if(length(users)<t) error('invalid length of Users'); end; if(mod(sub_height,) ~= ) error('invalid length of Sub height'); end; Im_Name = 'lena.bin'; [Im_linear, Im_Square] = ReadImage(Im_Name,Height,Width); P_Im = GetPreparedIm(Im_linear,t); Shadow_Image = GetShadow_Image(P_Im,w,base); a = find(shadow_image>256); ShowShadowImage(Shadow_Image,Sub_width,Sub_height); RequiredShadowImage = GetRequiredShadowImage(Shadow_Image,Users); RecoveredImage = RecoverImage(RequiredShadowImage,Users,Height,Width,base); figure; rec_im=uint8(recoveredimage); imshow(rec_im); imwrite(rec_im,'recovered_im.bmp','bmp'); title('recovered Image'); 57

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