Misko V. Computational methods based on a quadratic sieve for cryptanalysis of RSA algorithm using hardware and software solution.

The purpose of this work is to reduce the computational complexity of the methods of factorization of multi-digit numbers based on the ideas of the quadratic sieve method. For the first time, the method of multiple quadratic k-sieve (MQkS), the method of diagonalization of the matrix "on the fly", the method of determining a sufficient number of B - smooth numbers, the method of conditionally B-smooth numbers are developed. Methods for implementing the MQkS method on hardware and software are proposed. The results of the work allow us to add another stage of RSA cryptanalysis by hardware and software, as a consequence, to increase the efficiency of cryptanalysis of commercial and state expertise in the field of new cryptocurrencies.