Застосування ізоморфних матричних представлень для моделювання протоколу узгодження секретних ключів-перестановок значної розмірності

Abstract

A The article considers the peculiarities of the application of isomorphic matrix representations for modeling the protocol of matching secret keys-permutations of significant dimension. The situation is considered when for cryptographic transformations of blocks with a length of 256 256 bytes, presented in the form of a matrix of a black-and-white image, it is necessary to rearrange all bytes in accordance with the matrix keys. To generate a basic matrix key and the appearance of the components KeyA and KeyB in the format of two black and white images, a software module using engineering mathematical software Mathcad is proposed. Simulations are performed, for example, with sets of fixed matrix representations. The essence of the protocol of coordination of the main matrix of permutations by the parties is considered. Also shown are software modules in Mathcad for accelerated methods that display the procedure of iterative permutations in a permutation matrix isomorphic to the elevation of the permutation matrix to the desired degree with a certain side, corresponding to specific bits of bits or other code representations of ed random numbers. It is demonstrated that the parties receive new permutation matrices after the first step of the protocol, those sent to the other party, and the identical new permutation matrices received by the parties after the second step of the protocol, ie the secret permutation matrix. Similar qualitative cryptographic transformations have been confirmed using the proposed representations of the permutation matrix based on the results of modeling matrix affine-permutation ciphers and multi-step matrix affine-permutation ciphers for different cases when the components of affine transformations are first executed in different sequences. , and then permutation using the permutation matrix, or vice versa. The model experiments performed in the study demonstrated the adequacy of the functioning of the models proposed by the protocol and methods of generating a permutation matrix and demonstrated their advantages.