ANALYSIS OF THE FACTORIZATION METHOD BASED ON ELLIPTIC CURVES THEORY

Abstract

The purpose of this paper is the analysis of elliptic curve method, in particularly the probabilistic approach of method research, and also the research of subexponential complexity definition. This paper
describes the possibilities of the elliptic curves theory apparatus use. A comparative analysis of the existing factorization methods is given. The choice of the method based on the elliptic curves theory is substantiated. Special attention is paid to the method’s probabilistic and subexponential character. The method’s main directions of development and optimization are described. Possible approaches for described problems solving are given and analyzed. The possibility of creating a probabilistic model which applies the elliptic curves theory in factorization is considered. On the basis of the carried out analysis, further research is performed for all known subexponential factorization algorithms, taking into account the possibility of developing a probabilistic approach.