Modeling relationships in non-commutative two-operand two-bit cet-operations of a double cycle when permuting the operands

The object of the research is relationships in non-commutative two-operand two-bit CET-operations of a double cycle when operands are permuted. The article is devoted to studying the results of the computational experiment, which is in building a model of relationships in non-commutative two-operand two-bit CET-operations of a double cycle with the operands permutation in order to ensure the possibility of building cryptographic systems with XOR sequence encryption. The theoretical and practical results of the work are obtained on the basis of the computational experiment data. The results of researching the CET-operations data make it possible to build cryptographic systems with XOR sequence ciphering and to improve the quality of low-resource stream encryption systems. The mathematical description of the computational experiment results made it possible to establish relationships between pairs of non-commutative two-operand two-bit CET-operations of a double cycle when operands are permuted. The possibility of constructing a group of commutative two-operand two-bit CET-operations of a double cycle based on the modification of a known two-operand operation by one-operand operations to within the permutation of the crypto-transformation results has been studied. The correctness of constructing a group of CET-operations, both without operand permutation and such that allow operand permutation, has been verified. The model for building a group of asymmetric two-operand two-bit CET-operations of a double cycle, which allow the operands permutation is proposed. Applying the substitution model made it possible to obtain pairs of interrelated operations in this group. The obtained pairs of interconnected operations provide a description of modification for direct and inverse non-commutative CET operations when permuting the operands. The obtained results provide the possibility of building cryptographic systems that encrypt both the input open information under the control of the XOR sequence and the XOR sequence under the control of the input open information. Further research will be aimed at establishing relationships in non-commutative two-operand two-bit CET operations of the triple cycle when operands are permuted.