Modeling of a cryptographic protocol for matching a shared secret key-permutation of significant dimension with its isomorphic representations

Abstract

A protocol for agreement by user parties of secret keys-permutations of significant dimension and their new isomorphic matrix representations is proposed. Features and advantages of such representations are considered. The need to create such secret permutation keys to improve the cryptographic stability of matrix affine-permutation ciphers and other cryptosystems of the new matrix type is well-founded. The results of modeling the basic procedures of the proposed key agreement protocol in the form of an isomorphic permutation of a significant dimension, namely the processes of generating permutation matrices and their degrees, are given. Model experiments of the protocol as a whole, including accelerated methods of raising permutations to significant degrees, were performed. Such methods use sets of fixed permutation matrices, which are degrees of the underlying permutation matrix, and all these matrices are given in their isomorphic representations. The values of the fixed exponents correspond to the corresponding weights of the digits of the binary or other code representations of the ed random numbers. The results of simulation modeling demonstrated the adequacy and advantages of isomorphic representations of the processes of functioning of matrix-algebraic models of cryptographic transformations and the proposed secret key-permutation agreement protocol.