Researches on Generation of Elliptic Curves on Legendre Form

doi:10.3969/j.issn.1000-3428.2006.24.054

Computer Engineering ›› 2006, Vol. 32 ›› Issue (24): 152-154.

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Researches on Generation of Elliptic Curves on Legendre Form

DING Bao, BAO Wansu, WANG Xiang

(Institute of Electronic Technology, PLA Information Engineering University, Zhenzhou 450004)

Received:1900-01-01 Revised:1900-01-01 Online:2006-12-20 Published:2006-12-20

Legendre-形式椭圆曲线生成方法研究

丁宝，鲍皖苏，汪翔

（解放军信息工程大学电子技术学院，郑州 450004）

Abstract

Abstract:

This paper combines the SST algorithm with SEA algorithm, and substitutes λ-modular polynomial for modular polynomial in the SST algorithm. It proposes an algorithm to generate Legendre form elliptic curves based on lift. The algorithm not only improves the speed of generation of the elliptic curve, but also enhances the efficiency of the curve selection.

Key words: Legendre form elliptic curves, SEA, λ-modular polynomial, Canonical lift, SST

摘要：

将提升算法(SST)与大海算法(SEA)相结合，并把SST中的模多项式用λ-模多项式代替，给出了基于提升思想的Legendre-形式椭圆曲线的生成算法。与原提升算法相比，提高了曲线生成的速度和选取的效率。

关键词: Legendre-形式椭圆曲线, SEA, &lambda, -模多项式, 正规提升, SST

DING Bao; BAO Wansu; WANG Xiang. Researches on Generation of Elliptic Curves on Legendre Form[J]. Computer Engineering, 2006, 32(24): 152-154.

丁宝;鲍皖苏;汪翔. Legendre-形式椭圆曲线生成方法研究[J]. 计算机工程, 2006, 32(24): 152-154.

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