Information Security Coding Based on Information Theory: Secure Coding with Non-Perfect Secrecy

Abstract

This paper deals with the Shannon cipher system, secret sharing communication systems, secret sharing systems, secure network coding, and wiretap channel coding, which are tools for the secure coding of information based on information theory. In coding problems, it is usually studied how to achieve the perfect secrecy of information. However, in this paper, we show that we can achieve secure coding even in the case of no-perfect secrecy. We divide secret information into several pieces, and we achieve perfect secrecy for every piece individually to insure the security of information. On the other hand, by allowing the nonperfect secrecy of the whole information, we can decrease the bit length of random number and/or codewords. Hence, the coding techniques shown in this paper attain secure and efficient coding in the above coding systems.