Research of the relationships between the operations in matrix models of cryptographic transformation

Introduction. Data encryption is based on the sequence of cryptographic transformation operations. To decrypt the encrypted data it is necessary to know the sequence of operations for information decrypting. Therefore, an increase in the number of operations suitable for cryptographic transformation of information would allow to build data protection algorithms with better cryptographic properties. The purpose of scientific work. The objective of this research is to identify the relationships between operations in matrix models of direct and reverse cryptographic transformation. Formulation of the problem. In modern printed editions special attention is given to the use of matrix operations of cryptographic transformation and cryptographic primitives, based on them, for the algorithms of information resources protection. However, in these studies, the analysis of the relationships in matrix operations of cryptographic transformation has not been done to implement the encoding and decoding of information. The main material. The article presents the results of the research on the use of the operations of addition modulo two and permutations to implement matrix operations of cryptographic transformation. According to the results of computational experiment the division of matrix models of cryptographic transformation into three groups according to the presence and type of permutation in them: full symmetric cryptographic transformation, the sequences of encryption and decryption operations in which are the same for the whole group; partially asymmetric cryptographic transformation, where the sequences of encryption and decryption operations are not the same; conditional full asymmetric cryptographic transformation, in some models, apart from changing the operation, changing matrix decryption, is carried out. During the analysis of the results of the experiment it is revealed that the relationships between the operations, which are used for cryptographic transformation based on matrix models, are characterized by cycles. Conclusions. The received cycles of the sequences of operations allow to build direct and reverse cryptographic transformation in a group of two-digit matrix operations using the proposed twooperand operations