基于可聚结数对的费马数分解算法OA
Fermat number decomposition algorithm based on aggregatable number pairs
分析可聚结数对的有关性质,提出基于可聚结数对的费马数分解算法.利用算法搜索费马数F5 至F25 的素因子,并利用算法分解费马数F8.将算法与椭圆曲线分解算法、连分数算法、二次筛法、数域筛算法、Pollard's rho 分解算法、Brent算法、Williams p+1算法、p-1算法进行比较.实验结果表明,对于费马数F8 的分解,按效率高低依次为椭圆曲线分解算法、Brent 算法、基于可聚结数对的费马数分解算法、二次筛法、数域筛算法;连分数算法、Pollard's rho 分解算法、p-1算法、Williams p+1算法失效.
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.
周利荣
衢州职业技术学院 信息工程学院,浙江 衢州 324000
信息技术与安全科学
费马数椭圆曲线分解算法数域筛法可聚结数对
Fermat numberselliptic curve decomposition algorithmnumber field sieveaggregable pairs
《高师理科学刊》 2026 (3)
10-16,7
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