Sysoienko S. Methods and models for increasing the speed and stability of matrix cryptographic transformation of information

The thesis is devoted to questions of increasing the speed and stability of matrix cryptographic transformation of information by introducing the hierarchical structure of group transformation and establishing new relationships between direct and reverse operations. The first section substantiates the need of improving computer security systems in global computer networks and Internet. It was determined that one of the ways to ensure confidentiality and integrity of information for solving the problems of increasing the stability, speed and reliability of transformations, it is necessary to use matrix operations based on Boolean functions. The second section is devoted to the development of a method for increasing the resistance of pseudo-random sequences constructed on the basis of the operations of matrix cryptographic transformation, by adding them by module, which increased the probability of degenerate transformation results. As a result of the research, it was determined that the improvement of the quality of pseudo-random sequences is achieved by adding several primary sequences by module as a result of which certain generalized transformations become degenerate. The third section is devoted to the synthesis of a nondegenerate cryptographic transformation based on the group use of two-operand data transformation operations. It was proposed to adapt the method of increasing the resistance of pseudo-random sequences to increase the resistance of the results of encryption based on the replacement of the addition module operation by the operation, which will provide the possibility of decryption. The algorithm of a two-operand hierarchical group transformation was introduced, which ensures the synthesis of non-degenerate group operations. The given algorithm was investigated with the purpose of finding both the inverse operation and the inverse algorithm for information reproduction based on the construction of two inverse intermediate transformations and the inverse resultant transformation. A model of direct and inverse two-operand group cryptographic transformation was proposed, which makes it easier to find the reverse cryptographic transformation. The fourth section is devoted to the development of a method for increasing the speed of implementation of group matrix cryptographic transformation based on the proposed generalized mathematical model of group matrix cryptographic transformation, by reducing the complexity of constructing and implementing the inverse transformation, which reduced the mathematical complexity and increased the speed of cryptographic transformation. Based on the mathematical apparatus of block matrices, the correctness of the mathematical model of constructing an inverse group matrix cryptographic transformation was checked. The following practical results were obtained: improved models and developed encryption methods are brought to the structural and functional schemes of devices, encryption algorithms, which provide increased resistance and speed of crypto-conversion. The results of modeling and practical implementation determined that the reduction in the complexity of the implementation of the mathematical model of the group matrix cryptographic transformation was from 8 to 33 times, depending on the matrix size, and also increased the implementation rate by 6-8 % based on the results of practical implementation. The results of the work were implemented at the enterprises and organizations of the Ministry of Education and Science of Ukraine.