Increasing security to public key cryptography for point-to-point communication

In the beginning of 2020, the new idea of public key cryptography was proposed. This method is from the combining between RSA and Chebyshev maps. It is very difficult to break this system because it is based on both of Integer Factorization Problem (IFP) and Chaotic maps Discrete Logarithm Problem (CMDL). However, Chebyshev polynomials taking many computation costs (many modular multiplications and modular subtraction operations) are the equation to find the result of Chebyshev maps. In this paper, the new improvement of public-key cryptography is proposed for point-to-point communication. The main key is to reduce time and increase the security level. In fact, time is reduced by replacing some Chebyshev maps with modular exponentiation equations using only modular multiplication processes. In addition, the security level can be increased, because it is based on three problems, IFP, CMDL and Discrete Logarithm Problem (DLP). Although, DLP is included in the proposed method, it does not affect the computation time in both of encryption and decryption sides, because DLP is selected to exchange the RSA's public key. The experimental results show that time can be reduced in both sides especially in decryption side. The reason is that the private key of the compared method must be assigned too large, it is larger than the traditional RSA's private key. On the other hand, the private key for the proposed method is similar to RSA's private key.