학술논문
Optimum Pixel Expansions for Threshold Visual Secret Sharing Schemes
Document Type
Periodical
Author
Source
IEEE Transactions on Information Forensics and Security IEEE Trans.Inform.Forensic Secur. Information Forensics and Security, IEEE Transactions on. 6(3):960-969 Sep, 2011
Subject
Language
ISSN
1556-6013
1556-6021
1556-6021
Abstract
The optimal pixel expansion of an $(n, n)$ visual cryptographic scheme (VCS) was proven as $2^{n-1}$ in 1995; and that of a $(2, n)$-VCS was proposed in 2002. Yet, most existing best pixel expansions of $(k, n)$ -VCSs for $k \geq 3$ have not been improved since 1996. Whether they are already optimal, and if not how to find the optimums have never been explored. In this paper, we model the minimization of the pixel expansion in a $(k, n)$-VCS into an integer linear program to acquire the optimum solution. Computational results demonstrate that our integer linear program is simple, effective to obtain the optimum solution and flexible for coping with various types of $(k, n)$-VCSs.