有效的椭圆曲线求阶算法

下载PDF

导出

摘要介绍了有限域Fq上椭圆曲线群的求阶算法:l-adic求阶方法、p-adic求阶方法.描述了各算法的理论依据,分析、比较了其优劣性及适用情况,为ECC安全参数的选取的设计者提供参考.

作者张亚娟祝跃飞黄秋生

出处《自然科学进展》北大核心 2003年第10期1084-1088,共5页

基金国家重点基础研究发展规划(批准号:G1999035804) 国家自然科学基金(批准号:90204015 19931010) 河南省杰出青年基金(批准号:0212001400)资助项目

关键词椭圆曲线密码体制密码学求阶算法 ι—adic求阶方法 p-adic求阶方法 SEA算法 Satoh算法 SST算法 AGM算法 MSST算法

参考文献17

1School R. Elliptic curves over finite fields and the computation of square roots rood p. Math Comput, 1985, 44:483.
2Elides N. Elliptic and modular curves over finite fields and related computational issues. Computational Perspectives on Number Theory, 1998: 21.
3Atkin A O L. The number of points on an elliptic curve modulo a prime. Series of e-mails to the NMBRTHRY mailing list, 1988.
4Atkin A O L. The number of points on an elliptic curve modulo a prime(ii). Series of e-mails to the NMBRTHRY mailing list, 1992.
5Couveignes J M. Computing 1-isogenies with the p-torsion. ANTS-II Lecture Notes in Comp So, 1996, 1122:59.
6Lercier R, et al. Counting the number of points on elliptic curves over finite fields: Strategies and performances. Eurocryp to 1995,LNCS 2045 : 79.
7Csirik J A. Counting the number of points on an elliptic curve on a low-memory device. The 2nd Elliptic Curve Cryptography Work-shop (ECC'98), www. csirik. net/papers. html.
8Izu T, et at. Efficient implementation of School's algorithm. Asiacrypt, 1998:66.
9Satoh T. The canonical lift of an ordinary elliptic curve over a finite field and its point counting. J Ramanujan Math Soc, 2000, 15:483.
10Skjernaa B. Satoh's algorithm in characteristic 2. Math Com,2003, 72:477.

自然科学进展

2003年第10期

内容加载中请稍等...