Optimal Method of Integer Factorization

The object of the research is performance of integer factorization algorithms and possibility of mathematical methods using in these algorithms. The subject of the research is cryptographic properties GNFS method. Methods of research are methods of the theory of elliptic curves, finite fields, abstract algebra and advanced the theory of factorization algorithms. As a result of this work, the dependence of the properties of a minimal time of factorization and choice of algebraic factor bases over the ring Zn, where n=pq was established. Moreover, we have implemented the general number field sieve (GNFS), which is the most efficient classical algorithm known for factoring integers.