ПОБУДОВА МАТЕМАТИЧНОЇ ГРУПИ СИМЕТРИЧНИХ ОПЕРАЦІЙ НА ОСНОВІ ДОДАВАННЯ ЗА МОДУЛЕМ ДВА. THE SYMMETRIC OPERATIONS’ MATHEMATICAL GROUP CONSTRUCTING BASED ON MODULO-2 ADDITION
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Date
2019
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Abstract
The article is devoted to improving the quality of the stream ciphering systems for confidential information encryption through increasing the variability of cryptographic transformations by using a new group of two-operand two-bit operations synthesized basing on modulo-2 addition. For achieving the aim, a comparative analysis of two-operand operations with one-operand operations was performed, which showed that the first four operations can be obtained basing on the first four one-operand operations of the first operand processing, by adding the modulo-2 addition operation of their base operation of transforming the second operand, and by modulo-2 adding the basic operation of processing the second operand it can be obtained the other two-operand operations from inversion operations’ subgroups. The results of classifying a group of two- operand two-bit symmetric operations of information’s cryptographic transformation were visualized, which made it possible to establish relationships between groups of one-and two-operand operations. Basing on the obtained results, a method for synthesizing the operations’ group of modulo-2 addition is developed for stream ciphering based on the modulo-2 addition operation. The method’s crux is in the base group’s two-bit two-operand operations synthesis, based on combining the same basic operations of converting the first and second operands by modulo-2 addition. Constructing a complete mathematical group of these operations is carried out by the additional use of permutation operations and operands’ inversion of the base group operations. The application of the method allows synthesizing all the twenty-four modifications of two-bit symmetric modulo-2 addition operations based on applying the three basic one-operand two-bit operations of information cryptographic conversion.
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Keywords
криптографічна операція, модифікації операції, математична група операцій, додавання за модулем, моделі операції, потокове шифрування, cryptographic operation, modifications of operations, mathematical group of operations, module addition, operation models, streaming encryption