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