The Application of Chebyshev Polynomial on the Three-Pass Protocol

Chebyshev polynomial has wide applications in applied Mathematics. The Three Pass Protocol is a cryptographic protocol that is used for the encryption and decryption of data without the need to exchange the keys. We propose in this paper a new cryptosystem based on applying the Chebyshev polynomial to the Three Pass Protocol. The proposed cryptosystem is structured as asymmetric encryption that provides a high level of security to transmit the data. This cryptosystem depends on the fact that the Chebyshev polynomial forms a semigroup based on the composition property. The features of the proposed cryptosystem that are provided by the Chebyshev polynomial are similar to the features that are provided by the Discrete Logarithm. That is, it is secure from attacks, and it is faster to do mathematical calculations. Therefore, the proposed cryptosystem is reliable, secure and faster compared to the other cryptosystems.