Applying Extended Chebyshev Polynomials to Construct a Trap-Door One-Way Function in Real Field

In this paper, the characteristics of Chebyshev Polynomials are analysed and the key point is the feature of semi-group, which might be applied in the cryptography. Next, we extend Chebyshev polynomials from real field to finite field, and propose a trap-door one-way function. According to the proposed function, a secure and practical encryption scheme is given and the feasibility and security of the scheme is discussed. In the end, we conclude that the cryptography algorithm is rational and practical.