Maksymenko Y. The Computational methods based on the algorithm of Fermat's factorization method during cryptanalysis of RSA algorithm by hardware and software methods

Object of research: The process of factorization of multi-digit numbers during cryptanalysis of the RSA algorithm. Research subject: Computational methods of factorization of multi-digit numbers, based on the Fermat algorithm and using effective methods of thinning and reducing the computational complexity of operations with multi-digit numbers. The aim of research: Reducing the computational complexity of factorization methods for multi-digit numbers to improve the performance of hardware and software in solving RSA algorithm cryptanalysis tasks. Research methods: methods of number theory, optimization theory, algorithmic theory of multi-digit numbers, theory of complexity computation, numerical methods, methods of computer modeling. Dissertation is devoted to the improvement of computing factorization methods based on the Fermat's algorithm, which are used in the research of cryptographic algorithms and protocols which are used in the means and complexes of cryptographic protection of information (CPI) based on the creation of more effective methods of screening and reducing the computational operations of complex multi-digit numbers. The results of the work allow to increase the speed of hardware and software which are used for conducting thematic researches of means for cryptographic information protection and protocols based on RSA-algorithm.