Efficient Pairing Computation on Genus 2 Curves in Projective Coordinates

被引:0
|
作者
Fan, Xinxin [1 ]
Gong, Guang [1 ]
Jao, David [2 ]
机构
[1] Univ Waterloo, Dept Elect & Comp Engn, Waterloo, ON N2L 3G1, Canada
[2] Univ Waterloo, Dept Combinator Optimizat, Waterloo, ON N2L 3G1, Canada
来源
SELECTED AREAS IN CRYPTOGRAPHY | 2009年 / 5381卷
基金
加拿大自然科学与工程研究理事会;
关键词
Genus 2 hyperelliptic curves; Tate pairing; Miller's algorithm; Projective coordinates; Efficient Implementation; HYPERELLIPTIC CURVES; ABELIAN-VARIETIES; IMPLEMENTATION;
D O I
暂无
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
In recent years there has been much interest in the development and the fast computation of bilinear pairings due to their practical and myriad applications in cryptography. Well known efficient examples are the Weil and Tate pairings and their variants such as the Eta and Ate pairings on the Jacobians of (hyper-)elliptic curves. In this paper, we consider the use of projective coordinates for pairing computations on genus 2 hyperelliptic curves over prime fields. We generalize Chatter-jee et. al's idea of encapsulating the computation of the line function with the group operations to genus 2 hyperelliptic curves, and derive new explicit formulae for the group operations in projective and new coordinates in the context of pairing computations. When applying the encapsulated explicit formulae to pairing computations on supersingular genus 2 curves over prime fields, theoretical analysis shows that our algorithm is faster than previously best known algorithms whenever a field inversion is more expensive than about fifteen field multiplications. We also investigate pairing computations on non-supersingular genus 2 curves over prime fields based on the new formulae, and detail the various techniques required for efficient implementation.
引用
收藏
页码:18 / +
页数:5
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