Public Key Encryption Algorithm Based on Chebyshev Polynomials over Finite Fields

By expanding the definition of Chebyshev polynomials, the Chebyshev polynomials over finite field F_P are formed. After analyzing the system of Chebyshev polynomials over finite field F_P , this paper presents that the system is a divergent system and all curves of T_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_n(x) is a good one-way function over F_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