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** Description:** The article is based on an analysis of publications and the theoretical foundations of the matrix affine ciphers, including multistep modification, review of mathematical models cipher permutations with estimates of their stability offered by affinitymatrix permutation algorithms for encryption of images as a way to improve and improve the stability of the matrix affine cipher by supplementing their matrix model permutations. These formulas and algorithmic steps and procedures for concrete results encryption and decryption of large black and white and color images. Illustrated by the particular set of permutations of the matrix multiplication operation it as an algebraic group. The estimation of stability and time of cracking in these algorithms. Demonstrated features and benefits of such modifications of algorithms for image processing model experiments in the software environment Mathcad Professional.

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Keywords:
** cryptographic transformation, matrix affinity-commutative algorithm, matrix permutation, algebra, group encryption, decryption, image stability, the attack

Krasylenko, V.H. and Hrabovliak, S.K. (2012), “Matrychni afinno-perestanovochni alhorytmy dlia shyfruvannia ta deshyfruvannia zobrazhen”,