Integer Factorization of Semi-Primes Based on Analysis of a Sequence of Modular Elliptic Equations

• 作者: Boris S. Verkhovsky
• 来源期刊: 通讯、网络与系统学国际期刊(英文)
• 学科: 数学
• 关键词: Integer FACTORIZATION FACTORIZATION of Semi-Primes Non-Deterministic Algorithm ELLIPTIC CURVES Counting Points on ELLIPTIC CURVES Crypto-Immunity Dual ELLIPTIC CURVES
• 年，卷（期）: 2011,（10）
• 页码范围: 609-615
• 页数: 7页
• 分类号: O1

摘要

In this paper is demonstrated a method for reduction of integer factorization problem to an analysis of a sequence of modular elliptic equations. As a result, the paper provides a non-deterministic algorithm that computes a factor of a semi-prime integer n=pq, where prime factors p and q are unknown. The proposed algorithm is based on counting points on a sequence of at least four elliptic curves y2=x(x2+b2)(modn) , where b is a control parameter. Although in the worst case, for some n the number of required values of parameter b that must be considered (the number of basic steps of the algorithm) substantially exceeds four, hundreds of computer experiments indicate that the average number of the basic steps does not exceed six. These experiments also confirm all important facts discussed in this paper.