Algebraic aspects of key generation systems

Abstract

The principle of organization of private communication using public channels was suggested in 1976 by W. Diffie and M. E. Hellman [1]. After their publication, variants of the realization of such private communication were invited. Comparing known systems, we identify three general mathematical objectives among these variants:

• 1. the collection of sets and maps which are used by each subscriber for various computations;

• 2. a protocol describing information exchange;

• 3. a mathematical problem whose complexity provides for the security of the key generation system.

In this paper we consider the first objective in its simplest form: a protocol that includes only one round of information exchange.