Cryptographic key distribution algorithms

This article examines public key exchange algorithms applying the Diffie-Helmann-Merkel algorithm for commutative groups and the Stickel-Shpilrain algorithm for non-commutative groups. The protocols Diffie–Hellman–Merkel and Stickel–Spilrain key exchange are mathematical methods for the secure exchange of cryptographic keys over a public channel. The Diffie-Helmann-Merkel algorithm is one of the first public key protocols in cryptography. The authors examine the implementation of the respective algorithms through abelian and non-abelian algebraic structures based on the discrete logarithm problem. The man-in-the-middle attack is also examined. Examples are constructed that illustrate the operation of the mentioned algorithms.