Parameter Selection in Public Key Cryptosystem based on Chebyshev Polynomials over Finite Field

A recently proposed public key cryptosystem based on Chebyshev polynomials suggests a new approach to data encryption. But the security of the cryptosystem has not been investigated in depth, for lack of an appropriate analysis method. In this paper, a new representation of Chebyshev polynomial is introduced to study security issues of the cryptosystem. The properties of Chebyshev polynomial sequence are presented, and their impact on the cryptosystem are discussed. Finally some principles for parameter selection for the cryptosystem are proposed. The methodology used in this paper is supposed to offer a useful means for future researches on this topic.