International Journal of Intelligent Information Technology Application 1:1 (2008) 1-9 Available at http://www.engineering-press.org/IJIITA.htm 1999-2459/ Copyright © 2008 Engineering Technology Press,Hong Kong July,2008 A Probabilistic Visual Secret Sharing Scheme for Grayscale Images with Voting Strategy Chin-Chen Chang Department of Information Engineering and Computer Science, Feng Chia University, Taichung 407, Taiwan, R.O.C. Department of Computer Science and Information Engineering, National Chung Cheng University, Chiayi 621, Taiwan, R.O.C. E-mail: ccc@cs.ccu.edu.tw *Chia-Chen Lin Department of Computer Science and Information Management, Providence University, Taichung 433, Taiwan, R.O.C. E-mail: mhlin3@pu.edu.tw T.Hoang Ngan Le, Hoai Bac Le Department of Computer Science, Natural Science University, 227 Nguyen Van Cu, District 5, HCMC, Vietnam. E-mail: {lhbac, lthngan}@fit.hcmuns.edu.vn Abstract—Wang et al. proposed two visual secret sharing schemes based on Boolean operations in 2007. One is a probabilistic (2, n) secret sharing scheme, which is called (2, n) ProbVSS scheme, for binary images and the other is a deterministic (n, n) secret sharing scheme for grayscale images. Although Wang et al. only apply probabilistic concept to design the revealing phase of their (2, n) ProbVSS scheme, their (2, n) ProbVSS and (n, n) VSS schemes solve the problems of computational complexity and pixel expansion at the same time. In Wang et al.’s (n, n) VSS scheme for grayscale images, n generated shadows must be collected in advance to completely reconstruct a secret grayscale image. If Wang et al.’s (2, n) ProbVSS scheme is repeated eight times to deal with grayscale images, the image quality of the reconstructed image is significantly decreased when only any two of n shadows are used to generate the reconstructed grayscale image. To provide a (2, n) ProbVSS scheme that demonstrates better image quality of the reconstructed grayscale image than Wang et al.’s scheme without significantly increasing computational complexity, we apply the voting strategy and the least significant bits abandoning approach in combination with Wang et al.’s (2, n) ProbVSS for binary images to handle grayscale images. Experimental results confirm that the image quality of the reconstructed grayscale image achieved with the proposed scheme is better than one achieved by the pure Wang et al.’s scheme. Index Terms—Probabilistic visual secret sharing, voting strategy, (2, n) ProbVSS scheme, grayscale images I. INTRODUCTION In 1971, a secret sharing scheme also called a (k, n) threshold scheme was firstly introduced by George Blakley [1] and Adi Shamir [2], respectively. The first objective of secret sharing scheme is to protect secret data by dividing it into n pieces; each piece is called a share or a shadow. Later, the set of shadows is distributed to n participants and each participant holds a single piece of the set of shadows. The secret data can be reconstructed if and only if there is complete knowledge of the k shadows, and k-1 or fewer shadows will reveal no information about the secret data, where n k ≤ . Based on the (k, n) threshold scheme, in 1995 Noar and Shamir firstly introduced a secret image sharing scheme, which is also called visual secret sharing (VSS), that focused on image data [3]. Based on Noar and Shamir’s idea, several schemes for grayscale images [4, 7] and for color images [6, 8, 9] have been proposed. In essence, instead of the original image the VSS scheme uses several random-like images called shadows to be the data transmitted over the Internet. The shadows can thwart malicious attackers and prevent the secret image from being directly accessed. The secret image sharing schemes also inherit the properties of the (k, n) threshold scheme mentioned above. Generally, four criteria are used to evaluate the performance of a (k, n) VSS scheme. The first criterion is security: whether the scheme guarantees that fewer k shadows offer no information about the secret image, where n k ≤ . The second criterion is accuracy: the similarity between the reconstructed image and the original one. Basically, accuracy is respect to the image quality of the reconstructed image. A higher quality in the reconstructed image implies higher accuracy of the VSS scheme. The third criterion is computational complexity: the number of operators required to generate shadows for a secret image and to reconstruct the reconstructed image by using the collected shadows. The last criterion is the size of a shadow called the pixel expansion problem. Larger shadow size implies higher transmission cost and storage cost.