Public Key Encryption Algorithm Based on Chebyshev Polynomials over Finite Fields

摘要

By expanding the definition of Chebyshev polynomials, the Chebyshev polynomials over finite field F{sub}p are formed. After analyzing the system of Chebyshev polynomials over finite field F{sub}p, this paper presents that the system is a divergent system and all curves of T{sub}n(x) at n>1 are pseudo-random sequences when P is enough large. For the pseudo-random property and expand of definition of Chebyshev polynomials, T{sub}n(x) is a good one-way function over F{sub}p. Using one-way and semi-group properties, a novel public key encryption algorithm is presented. The running of the algorithm doesn't need large prime numbers and primitive elements, but integer number.