《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (1): 96-102.

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### GF(3m)上Hessian曲线的三进制Montgomery算法

1. 西安邮电大学通信与信息工程学院, 陕西 西安 710121
• 发布日期:2019-01-23
• 作者简介:刘双根(1979— ),男, 博士, 副教授, 硕士生导师, 主要研究方向为密码学与信息安全. E-mail:liusgxupt@163.com*通信作者简介:王蓉蓉(1994— ), 女, 硕士研究生, 主要研究方向为密码学. E-mail:wangrr28170@163.com
• 基金资助:
国家自然科学基金资助项目(61272525);陕西省自然科学基金资助项目(2017JQ6010)

### Ternary Montgomery algorithm on Hessian curve over GF(3m)

1. School of Communication and Information Engineering, Xian University of Posts and Telecommunications, Xian 710121, Shaanxi, China
• Published:2019-01-23

Abstract: To raise the efficiency of scalar multiplication on Hessian elliptic curves, a scalar multiplication algorithm on Hessian curve over GF(3m)is proposed by expressing the scalar k in ternary form and combining with the original Montgomery algorithm, and the formulas for fast point addition, point doubling and point tripling are used on the bottom layer. The analysis results show that compared with the original Montgomery ladder algorithm in different coordinate systems, the new algorithm is improved by 20.5% on average. Compared with the scalar multiplication algorithm based on Co-Z operation, the improvement is 34.8%. Compared with signed width-4 sliding windows on the same curve, the improved efficiencies in JacIntersect coordinates and standard projective coordinates are 2.03% and 13.8%, respectively. In different projective coordinates, the new algorithm on the Hessian curve is 33.3% ~ 48% faster than on the Weierstrass curve.

• TP309
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