Cryptographic Key Exchange Method for Data Factorial Coding

Abstract

The paper proposes a new cryptographic key exchange method. The basic idea of the proposed method is to use a permutation of a given set as a transformation object. The mathematical background of the method is the property of permutations to be decomposed into the product of disjoint cycles, the property of unique factorization of the product of disjoint cycles raised to the powers smaller than their order, and the complexity of factorization of the product of permutations whose cycles are noncommutative. The conditions to be met by the transformation parameters are defined. The concepts of cycle and block-noncommutative permutations are introduced. These properties of two permutations known to all participants in information exchange are sufficient for the correct operation of the method. The key space cardinality of the values of cycles’ exponents of two open permutations is investigated. It is shown that this cardinality is maximized if the disjoint cycles in the decomposition of open permutations are 3-cycles. The block diagram of a cryptographic system that implements the proposed method is investigated. Its work is described. The proposed method and system make it possible to generate a cryptographic key for information factorial coding without using a secure communication channel. They can also be used to form a non-permutation key.