基于椭圆曲线中配对的密码学研究综述  

A Survey of Pairings on Elliptic Curve-based Cryptography

作　　者：王辈 胡红钢[1] WANG Bei;HU Hong-Gang(CAS Key Laboratory of Electromagnetic Space Information,School of Information Science and Technology,University of Science and Technology of China,Hefei 230027,China)

机构地区：[1]中国科学技术大学信息科学技术学院中国科学院电磁空间信息重点实验室,合肥230027

出　　处：《密码学报》2022年第2期189-209,共21页Journal of Cryptologic Research

基　　金：国家自然科学基金(61972370)。

摘　　要：近些年,椭圆曲线中的配对在密码学中的应用日趋广泛,对配对的计算效率也有了越来越高的要求.为了提高配对的计算效率,研究者们一方面从理论与算法的角度改进已有的配对,另一方面构造新的更快速的配对.本文对近二十年来配对的发展历程作了详细的综述.与配对有关的快速算法,如配对友好型椭圆曲线的构造、Miller算法的改进等,以及与配对有关的计算困难问题,如双线性Diffie-Hellman问题、双线性求逆问题等,一直是密码学的研究热点.本文结合最新研究成果对它们作简要的综述.In recent years,pairings on elliptic curves have many applications in cryptographic protocols.Hence,the efficiency of the pairing computation is required to be as faster as possible.In order to improve the efficiency of the pairing computation,on one hand,researchers improved the existing pairings in both theory and algorithms;on the other hand,constructions of new faster pairings have been of great interest.This paper presents a detailed survey on the history of pairings in the last two decades.The fast algorithms regarding pairing,such as the construction of pairing-friendly elliptic curves,the improvement of Miller’s algorithm,etc.,and the computationally hard problems regarding pairing,such as the bilinear Diffie-Hellman problem,the bilinear inversion problem,etc.,have been active research issues in cryptography.This paper briefly reviews them based on the latest research results.

关 键 词：椭圆曲线 配对 配对友好型曲线 Miller算法 基于配对的困难问题 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]