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| SEA算法的有效实现 |
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祝跃飞1,2, 顾纯祥1, 裴定一2
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1.信息工程大学,网络工程系,河南,郑州,450002;2.中国科学院,研究生院,信息安全国家重点实验室,北京,100039
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| 摘要: |
| 选取安全椭圆曲线的核心步骤是对椭圆曲线阶的计算.SEA(Schoof Elkies Atkin)算法是计算椭圆曲线阶的有效算法,同种圈(isogeny cycles)方法是Morain对SEA算法改善的一种重要局部优化技术.在实现了Fp上SEA算法的前提下,对同种圈方法作了进一步改进,就SEA算法中各方法的综合运用提出一种方案,并且对用SEA算法选取素数阶和拟素数阶椭圆曲线速度上的优化作了一些讨论,所获得的一些速度指标和国际公开资料上的指标有可比性. |
| 关键词: 椭圆曲线 Frobenius映射 SEA算法 同种圈 |
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| 基金项目:国家自然科学基金资助项目(19931010);国家重大基础研究发展规划973资助项目(G1999035804);河南省杰出青年基金(0212001400) |
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| Efficient Implementation of SEA Algorithm |
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ZHU Yue-fei,GU Chun-xiang,PEI Ding-yi
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| Abstract: |
| The core of choosing a secure elliptic curve for elliptic curve cryptosystems is the calculation of the order of a randomly selected elliptic curve. It is known that SEA (Schoof Elkies Atkin) algorithm is recently the most efficient method to calculate the orders of elliptic curves over Fp. Isogeny cycles method made by Morain is an important local optimized technique to improve SEA algorithm. In this paper, isogeny cycles method is enhanced, and a scheme of more optimal combination of the various techniques in SEA algorithm is provided.Furthermore,some discussions are made on how to speed up the selection of elliptic curves with prime order,and an efficient implementation of SEA algorithm overFp is described. |
| Key words: elliptic curve Frobenius endomorphism SEA （Schoof Elkies Atkin） algorithm isogeny cycle |
