Cryptanalysis of RSA Based on Parallel Factorization Method

The paper aims to break the RSA cryptosystem in the shortest possible time. The basic idea is based on factorizing N in a parallel way. Firstly, the solution search space of N was determined. Secondly, limited points K for this space were computed using a specific mathematical formula. Thirdly, these were used as start points for new small solution search spaces. The search for factors of N will be achieved in parallel in all minor solution search spaces using K computers. Whenever factors appeared on one of K's computers, execution on all computers was stopped. This method has been compared to methods V-factor, TDM, MFF, MFF2, MFF3 and MFF4. Results showed that it is superior to the mentioned methods in terms of elapsed time, iterations, and speed up. It solved the problem of the V-Factor. Results showed that the proposed method effectively factored numbers with convergent or divergent factors. The success in analyzing numbers in the shortest possible time threatens the security of cryptosystems based on factorization of N, such as RSA.