Синтез груп двохоперандних операцій криптоперетворення на основі перестановлюваних схем. SYNTHESIS OF GROUPS TWO-OPERAND OPERATIONS OF CRIPTOCONVERSION ON THE BASIS OF PERMUTATION SCHEMES
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Date
2018
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Abstract
Cryptography is one of the most effective means of data protection nowadays. One way of increasing the cryptographic algorithms stability is increasing their variability. Increasing the crypto algorithms variability directly depends on the number of cryptographic transformation operations, used in it. Using permutations in constructing modified operations is one of the effective means of expanding the capabilities of developers in building cryptographic algorithms. However, it was not paid enough attention to synthesis the operations’ mathematical groups on the basis of permutations. The purpose of the work is to construct a complete group of two-operand operations of cryptographic transformation, on the basis of the known, due to the establishment and application of permutational interconnections between the truth tables. The following research results were obtained while achieving the goal. In the course of the research, it was found that the permutation schemes for constructing truth tables of the cryptographic transformation of the two-operation sets of operations of the first mathematical group do not overlap. The complex of sets of truth tables of crypto transformation’s two-operand operations of the first mathematical group creates a complete group of sets of cryptographic transformation’s two-operand operations truth tables. The application of the rearrangement schemes group provides the construction of a cryptographic transformation operations complete group based on any of the operations of this group. The use of a group of permutation schemes allows you to build a complete group of permutation tables, presented both explicitly and in a formalized form. The obtained results allow making a conclusion that the application of rearrangement schemes’ constructed group will provide the construction of a complete group of sets of cryptographic transformation’s two-operand operations of an unknown group, based on one known operation. Rearrangement schemes for synthesis the truth tables of cryptographic transformation’s two-operand operations are constructed. It is established that the constructed schemes are not overlapped and create a complete group of sets for the truth tables synthesis. The application of the rearrangement schemes group provides construction the complete group of a cryptographic transformation’s operations, based on any of the operations, and also provides the construction of a complete group of tables of explicitly represented substitutions as well as formalized substitutions.
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захист інформації, криптографічне кодування, криптоперетворення, перестановки, перестановочні схеми, синтез операцій, information protection, cryptographic encoding, cryptographic transformations, permutations, rearrangement schemes, synthesis of operations