Faster Pairing Computation on Jacobi Quartic Curves with High-Degree Twists

被引：1
|
作者：
Zhang, Fan [1 ]
Li, Liangze [1 ,2 ]
Wu, Hongfeng [3 ]
机构：
[1] Peking Univ, Sch Math Sci, LMAM, Beijing 100871, Peoples R China
[2] Beijing Int Ctr Math Res, Beijing 100871, Peoples R China
[3] North China Univ Technol, Coll Sci, Beijing 100144, Peoples R China
来源：
TRUSTED SYSTEMS, INTRUST 2014 | 2015年 / 9473卷
关键词：
Elliptic curve; Jacobi quartic curve; Tate pairing; Miller function; Group law; ELLIPTIC-CURVES; FACTORIZATION; FORM;
D O I：
10.1007/978-3-319-27998-5_20
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we first propose a geometric approach to explain the group law on Jacobi quartic curves which are seen as the intersection of two quadratic surfaces in space. Using the geometry interpretation we construct Miller function. Then we present explicit formulae for the addition and doubling steps in Miller's algorithm to compute the Tate pairing on Jacobi quartic curves. Our formulae on Jacobi quartic curves are better than previously proposed ones for the general case of even embedding degree. Finally, we present efficient formulas for Jacobi quartic curves with twists of degree 4 or 6. Our pairing computation on Jacobi quartic curves are faster than the pairing computation on Weier-strass curves when j = 1728. The addition steps of our formulae are fewer than the addition steps on Weierstrass curves when j = 0.
引用
收藏
页码：310 / 327
页数：18
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