A cryptographic protocol for creating a joint secret key-permutation of significant dimension and its modeling

Abstract

The significant growth of information volumes, the rapid development of mass communications, telecommunication networks, the latest tools and means of information technology have led to the increasingly widespread use of image and video processing technologies. Since video processing is the most general and promising area of image processing in the latest research and development of such equipment, in this work we will focus our attention on advanced technologies of masking, encryption-decryption of images and frames of video files, which require the creation of appropriate secret keys for their joint use by a certain group of users. The paper considers the issues of creating a so-called cooperative protocol for the negotiation of secret keys-permutations of significant dimension by a group of user parties. Various possible types of representations of such keys are considered and the advantages and features of their new isomorphic matrix representations are shown. The need to create such secret keys-permutations is justified to increase the cryptographic stability of matrix affine-permutation ciphers and other cryptosystems of a new matrix type is justified. The results of modeling the main procedures of the proposed protocol for the negotiation of keys in the form of isomorphic permutations of significant dimension are presented, namely, the processes of generating permutation matrices and their matrix powers. Model experiments of the protocol as a whole are described and demonstrated, including accelerated methods of matrix raising permutations to significant powers. For such methods, sets of fixed permutation matrices were used, which are matrix powers of the main permutation matrix. Matrices, i.e. permutation keys, and all procedures over them were given and visualized in their isomorphic representations. The values of fixed matrix powers correspond to the corresponding weights of the bits of the binary or other code representation of the ed random numbers. The results of the simulation modeling of the protocol demonstrated the adequacy and advantages of using isomorphic representations of such permutation keys and the processes of creating a shared secret permutation key agreed upon by the parties using the proposed protocol.