超椭圆曲线上的Ate对变种及其计算的研究  

Variation of Ate pairing on hyperlliptic curves and research of its computation

作　　者：陆卫新 汪学明[1] 

机构地区：[1]贵州大学计算机科学与信息学院,贵州贵阳550025

出　　处：《计算机工程与设计》2014年第5期1578-1582,共5页Computer Engineering and Design

基　　金：国家自然科学基金项目([2011]61163049);贵州省自然科学基金项目(黔科合J字[2011]2197)

摘　　要：对超椭圆曲线上一类非退化的Ate对变种进行研究,使得计算双线性对的Miller算法的循环次数显著减少。通过对此类双线性对与改进Tate对及Ate对的关系的一系列证明,验证了此类双线性对的非退化性;基于广义的Ate对和Vercauteren在椭圆曲线上定义的Ate对,给出了两种超椭圆曲线上的此类双线性对的构造方法;针对此类变种的Miller函数,设计了计算此类变种的Miller算法并对其上的计算进行了详细的研究。The non-degenerate variations of the Ate pairing on hyperelliptic curve is studied, The loop length of Miller＇s algorithm for the computation on bilinear pairing is reduced, the non-degeneracy of the HV pairing is proven by the relationship between this pairing and modified Tate pairing, Ate pairing. And based on generalized Ate pairing and the Ate pairings defined by Vercauteren, two methods of construction of this pairing based on hypereliptic curve are given. And then, contraposing to the Miller function on this paring, a Miller algorithm is designed and its computation is studied in detail.

关 键 词：超椭圆曲线 双线性对 Ate对的变种 Miller函数 Miller算法 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]