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  5. Modeling of coordination protocols of secret matrix key for cryptographic transformation and matrix type systems

Modeling of coordination protocols of secret matrix key for cryptographic transformation and matrix type systems

V. Krasilenko, D. Nikitovich
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The article is devoted to the simulation of secret matrix key negotiation protocols for cryptographic transformations in matrix type systems and models. The basis of such protocols is the generalization of the known Diffie-Hellman and others protocols to the matrix case and the corresponding mathematical procedures-algorithms based on matrix models for the formation of twodimensional keys. The necessity and advantages of creation, matching and application of matrix keys for improved matrix-type cryptographic systems and image encryption-decryption procedures are substantiated. New modifications of matrix matching protocols are proposed with the aim of improving their resistance to attacks. To confirm the reliability of the proposed protocols and their modifications and compare their characteristics, the complexity of the computational procedures, a number of model experiments were performed in the software environment of Mathcad Professional. The advantages of fast computational calculations for element-by-element matrix modular exponentiation are shown on the basis of matrix AC transformations and using fixed weight matrix degrees modulo and binary bit matrices for controlled selection of weighted components. Computational procedures and matrix models take into account the specificity of images and easily adapt to parallel implementations and the latest hardware matrix processors. The results of modeling the creation of secret matrix keys in the form of high-dimensional images are presented on the basis of the proposed protocol modifications.
Keywords: Cryptographic image transformations, Diffie-Hellman matrix algorithm, generalized matrix models, secret matrix key, decryption, secret shared key negotiation protocol, modular exponentiation