Synthesis of Sets of Non-Symmetric Two-Operand Two-Bit Crypto Operations Within the Permutation Accuracy

The object of research is the processes of building operations for cryptographic protection of information, as the requirements for information security are constantly increasing. Increasing the stability of cryptographic transformations directly depends on the complexity and variability of the crypto algorithm. It is possible to increase variability by increasing the range of crypto operations. Significantly increasing the number of crypto operations is possible through the synthesis of asymmetric operations. This paper is devoted to the creation of methodological support for the synthesis and analysis of sets of two-operand two-bit cryptographic operations with precision permutation. The conducted researches are based on the results of a computational experiment, which consists in the synthesis of two-operand two-bit crypto operations based on single-operand, with the subsequent search for pairs of operations of direct and correct inverse crypto transformation on the basis of complete search. In the course of the computational experiment, pairs of two-operand operations were presented, represented by tuples of four single-operand operations. The formalization of the results provided a mathematical representation of operations, suitable for practical implementation. To simplify the complexity of practical implementation, the synthesized operations are divided into 24 sets of 24 operations. Separation of operations occurred due to the use of templates of tables of truth of sets of operations with precision to permutation of operands. It is established that the entire set of operations can be constructed with the precision of permutation based on the use of the template of any operation. In addition, the analysis of the synthesized sets showed that the sets of symmetric and asymmetric operations do not intersect. 20 sets of asymmetric two-operand two-bit operations, as well as 4 sets of symmetric operations are obtained. Further investigation of each synthesized set of asymmetric crypto operations will allow for the relationship between the operands of the operation and between the operations as a whole. The use of synthesized asymmetric operations will improve the reliability of crypto algorithms for streaming encryption of information by significantly increasing the variability of cryptographic transformations. In turn, the use of synthesized sets of operations will simplify practical implementation in computer cryptography