New Research on Elliptic Curve Cryptosystem Algorithm Based on System of Chebyshev Polynomial

It is the first time to combine Chebyshev Polynomial with Elliptic Curve. In this paper it construct a Elliptic Curve Cryptosystem Algorithm based on Chebyshev Polynomial. This paper use the semi-groop Character of the Chebyshev and the character of the Elliptic Curve to make a Cryptosystem Algorithm in the Elliptic Curve. This Algorithm has solved the problem that it can´t get inversion in the process of decrypting the message. This Algorithm has the advantages of the Chaotic and Elliptic Curve Cryptographic Algorithm. Through the analysis of the Algorithm, it is thought that the Algorithm is simple and has high safety and the scheme is feasible.