Parallelized Self-Initializing Quadratic Sieve using OpenMP

Factorization, SIQS, Parallelization, OpenMP, RSA Cryptanalysis, Profilation

The paper deals with integer factorization. Factorization is popular and used method for RSA cryptanalysis. SIQS (Self-Initialization Quadratic Sieve) is chosen as a factorization method which is used in this paper. This method is chosen because of its balance between difficulty to learn and implement and its factorization capabilities. QS (Quadratic Sieve) is considered as the second fastest factorization method and the fastest method to factorize numbers with less than 100 decimal digits (332 bits). SIQS is the most optimized version of QS. The method was implemented and well documented in this work. Whereby, this paper tries to fill the gap between theoretic description of the method and already existing implementations. Although, SIQS is the fastest method up to 100 decimal digits, it can't be effectively used to work in polynomial time. Therefore, it is desirable to look up for options how to speedup the method as much as possible. Two of the possible ways of achieving a speedup are parallelization and optimization which were used in this paper. OpenMP was chosen to parallelize critical code segments. Also, the goal of this paper is to show how easily is possible to use parallelization and thanks to detailed source code analysis with optimization it is possible to reach large speedup. Method of iterative optimization showed itself as a very effective tool. Using this method the implementation of SIQS achieved almost 100x speedup and at some parts of the code even more.