摘要
Abstract
Properties of aggregatable pairs are analyzed,a Fermat number decomposition algorithm based on aggregatable number pairs is proposed.Prime factors of Fermat numbers F5 to F25 are searched,Fermat number F8 are decomposed by algorithm.The algorithm is compared with elliptic curve decomposition algorithm,continued fraction algorithm,quadratic sieve,number field sieve,Pollard's rho decomposition algorithm,Brent algorithm,Williams p+1algorithm and p-1algorithm.The experimental results show that for the decomposition algorithms of Fermat numbers F8,in order of efficiency,they are elliptic curve decomposition algorithm,Brent algorithm,Fermat number decomposition algorithm based on aggregatable number pairs,quadratic screening method,and number domain screening algorithm;continuous fraction algorithm,Pollard's rho decomposition algorithm,p-1algorithm,Williams p+1algorithm are invalid.关键词
费马数/椭圆曲线分解算法/数域筛法/可聚结数对Key words
Fermat numbers/elliptic curve decomposition algorithm/number field sieve/aggregable pairs分类
信息技术与安全科学
