Visual secret sharing for multiple secrets
Introduction
With the rapid growth of computer technologies, plenty of applications have been proposed to make human life more and more convenient. On the contrary, the security of secret data is threatened because anyone may tend to intrude the system or eavesdrop via the communication channel. One approach to have the essential information secure not retrieved by malicious users easily is making the essential information shared among several participants. Secret sharing schemes proposed by Blakley [1] and Shamir [2], respectively, are to distribute secret information to participants. The secret can only be obtained by the cooperation of these participants. The ordinary concept of secret sharing is sharing the secret key, and secret sharing schemes are also wildly used for secret transmission nowadays. But most secret sharing schemes are based on cryptography [3], [4], [5], [6], [7], [8], [9], [10], [11] such that the encryption and decryption processes need high computation costs. Visual cryptography, a kind of secret sharing schemes, differs from traditional secret sharing in terms of the efficient decryption process. Visual secret sharing schemes hide the secret image into several share images and distribute these share images to participants. With no computation, human beings are able to obtain the secret image by stacking share images. This property makes visual cryptography especially suited to the low computation load requirement.
In 1994, Naor and Shamir first proposed a (k, k)-threshold visual secret sharing scheme, namely the (k, k)–VSS scheme, to achieve secret sharing [12]. In the (k, k)–VSS scheme, the latter number “k” means that the secret image is hidden into k share images, and the former “k” means that it needs all the k share images to retrieve the secret image. In visual secret sharing schemes, every secret pixel is hidden into a block of sub-pixels. By the property that black pixels absorb the light but transparent (white) pixels do not, two blocks with the same numbers of black and white sub-pixels can get different stacked results according to the different pixel distribution. Therefore, visual colors of the stacked blocks are distinguished from the relative difference.
Many visual cryptography schemes have been proposed to support different requirements. From the (k, k)–VSS scheme, (k, n)–VSS schemes were also proposed to support variable threshold numbers [12], [13], [14], [15], [16], in which the secret image is hidden into n share images and the secret can be retrieved by the cooperation of at least k of them. Then, Ateniese et al. [17] proposed a visual secret sharing scheme that the decryption rule is more general than the threshold ones. Researchers also extended visual secret sharing schemes to support grayscale images [3], [18] and color images [19], [20], [21], [22], [23], [24], [25], [26], and the contrast is also taken into consideration [18], [19], [20], [27]. Iwamoto and Yamamoto [28] proposed another scheme to support color secret images with general decryption rules, and Nakajima and Yamaguchi [29] indicated how to enhance the share images to be meaningful. In addition, Chen et al. proposed a scheme to make the decryption result significant only at a desired stacking angle [30]. But all of the above schemes aim to deal with only one secret image. Participants have to possess lots of share images for different secret images during transmissions. This property results in inefficiency, so some researchers made effort to hide more secret images into two share images [31], [32]. Unfortunately, the existing visual secret sharing schemes restrict the number of secret images.
To extend the number of secret images, this paper proposes a novel visual secret sharing scheme for hiding multiple secret images into two share images. The proposed scheme analyzes the secret pixels and the corresponding share blocks to construct a stacking relationship graph, in which the vertices denote the share blocks and the edges denote two blocks stacked together at the desired decryption angle. According to this graph and the pre-defined visual pattern set, two share images are generated. Unlimited secret images can be hidden (encrypted) such that each secret image can be obtained (decrypted) by stacking these two share images at the corresponding angle. The security of secret images can be also guaranteed since no secret information will leak out in any share image.
The remainder of this paper is organized as follows. In Section 2, the related works of visual cryptography are briefly reviewed. The proposed scheme is introduced in Section 3. Thereafter, the experimental results and comparisons are shown in Section 4. Finally, the Conclusions and future works are provided in the last section.
Section snippets
Visual cryptography for multiple secret images
The basic concept of visual cryptography is introduced in Section 2.1. Then the existing visual secret sharing schemes for multiple secret images are introduced in 2.2 Chen and Wu's visual secret sharing scheme for two secret images, 2.3 The ring shadow image technology.
The proposed scheme
In order to share multiple secret images in two share images, a novel scheme is proposed to hide m secrets and to reveal the secrets by stacking the share images at m aliquot angles, respectively. The proposed scheme is a 2-out-of-2 m-way extended visual secret sharing scheme for m secret images, denoted as a (2, 2)-m-VSSM scheme. Before constructing the two share images, the stacking rules and the relationship between these two share images must be indicated. Then the proposed scheme can be
Comparisons and experimental results
For visual secret sharing schemes, there are two evaluation terms: expanding size and contrast. Expanding size is the ratio of the share image size over the original secret image size, and the smaller number means a better performance. In Naor and Shamir's (2, 2)–VSS scheme, the expanding size is 4 since each secret pixel becomes a share block with 4 sub-pixels. Contrast is the difference between the revealed black and white secret pixels. The larger contrast indicates that it is easier to
Conclusions and future works
This paper proposes an extended visual secret sharing scheme to share multiple secret images into two share images. The relationship between blocks of share images is modeled first. Then the share images are constructed by using the pre-defined visual patterns. An arbitrary number of different secret images can be hidden in two share images, and they can be decrypted at aliquot stacking angles. From the properties described in Section 4, the visual patterns are directly related to the quality
About the Author—JEN-BANG FENG was born in Taichung, Taiwan, on January 10, 1978. He received his B.S. and M.S. degrees in the Department of Applied Mathematics in 2001 and 2003, and his Ph.D. degree in Department of Computer Science and Engineering in 2008 from the Chung Hsing University. He is an Assistant Professor of Department of Information Engineering and Informatics of Tzu Chi College of Technique. His current research interests include visual cryptography, secret sharing, data hiding,
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About the Author—JEN-BANG FENG was born in Taichung, Taiwan, on January 10, 1978. He received his B.S. and M.S. degrees in the Department of Applied Mathematics in 2001 and 2003, and his Ph.D. degree in Department of Computer Science and Engineering in 2008 from the Chung Hsing University. He is an Assistant Professor of Department of Information Engineering and Informatics of Tzu Chi College of Technique. His current research interests include visual cryptography, secret sharing, data hiding, image processing, and multimedia system.
About the Author—HSIEN-CHU WU was born in Tainan, Taiwan, Republic of China, on October 26, 1962. She received the B.S. and M.S. degrees in Applied Mathematics in 1985 and 1987, respectively, from the National Chung Hsing University, Taichung, Taiwan. She received her Ph.D. in Computer Science and Information Engineering in 2002 from National Chung Cheng University, Chiayi, Taiwan. From 1987 to 2002, she was a lecturer of the Department of Information Management at National Taichung Institute Technology, Taichung, Taiwan. From August 2002 to July 2005, she was an associate professor of the Department of Information Management at National Taichung Institute Technology, Taichung, Taiwan. Since August 2005, she has worked as an professor of the Department of Information Management at National Taichung Institute Technology, Taichung, Taiwan. Her research interests include image authentication, digital watermarking, data hiding, image processing and information security.
About the Author—CHWEI-SHYONG TSAI was born in Changhua, Taiwan, Republic of China, on September 3, 1962. He received his B.S. degree in Applied Mathematics in 1984 from the National Chung Hsing University, Taichung, Taiwan. He received his M.S. degree in Computer Science and Electronic Engineering in 1986 from the National Central University, Chungli, Taiwan. He received his Ph.D. degree in Computer Science and Information Engineering in 2002 from the National Chung Cheng University, Chiayi, Taiwan. In August 2002, he received his tenure as associate professor of the Department of Information Management at National Taichung Institute of Technology, Taichung, Taiwan. Since August 2004, he is an associate professor of the Department of Management Information Systems at National Chung Hsing University, Taichung, Taiwan. His research interests include image watermarking, image authentication, information hiding, bio-information and E-learning.
About the Author—YA-FEN CHANG received her B.S. degree in Computer Science and Information Engineering from National Chiao Tung University, Hsinchu, Taiwan in 2000. She received her Ph.D. degree in Computer Science and Information Engineering in 2005 from National Chung Cheng University, Chiayi, Taiwan. Since 2006, she has been an Assistant Professor of National Taichung Institute of Technology. Her current research interests include electronic commerce, information security, cryptography, and mobile communications.
About the Author—YEN-PING CHU is a Professor of the Computer Science and Information Engineering and Head of the Library of Tung Hai University, Taichung, Taiwan. His research interests include high-speed networks, operating system, neural network, and computer assistant learning.