椭圆曲线同源的有效计算研究进展  

Research Development on Efficient Elliptic Curve Isogenous Computations

作　　者：黄艳[1,2] 张方国 HUANG Yan;ZHANG Fang-Guo(School of Computer Science and Engineering,Sun Yat-Sen University,Guangzhou 510006,China;Guangdong Provincial Key Laboratory of Information Security Technology,Guangzhou 510006,China)

机构地区：[1]中山大学计算机学院,广东广州510006 [2]广东省信息安全技术重点实验室,广东广州510006

出　　处：《软件学报》2021年第4期1151-1164,共14页Journal of Software

基　　金：国家重点研发计划(2017YFB0802500);国家自然科学基金(61672550,61972429);广东省基础与应用基础研究重大项目(2019B030302008)。

摘　　要：由于Shor算法可以在多项式时间内解决大整数分解以及离散对数问题,使得基于这些问题设计的经典的密码体制不再安全.目前涌现出许多后量子密码体制的研究,如基于格、基于编码、基于多变量和基于椭圆曲线同源的密码系统.相比于其他后量子密码体制,基于椭圆曲线同源的密码系统具有密钥尺寸短的优势,然而其实现效率不占优势.以两类基于超奇异椭圆曲线同源的密钥交换协议为基准,根据经典的椭圆曲线标量乘和双线性对的优化技巧,并结合椭圆曲线同源自身的一些特殊性质,分析优化这两类协议的可能性.与此同时,分类回顾了目前椭圆曲线同源的有效计算方面的已有进展,提出了该方向可进一步开展的研究工作.It is well known that Shor’s algorithm can solve the integer factorization problem and the discrete logarithm problem in polynomial time, which makes classical cryptosystems insecure. Hence, more and more post-quantum cryptosystems emerge at present such as lattice-based, code-based, hash-based, and isogeny-based cryptosystems. Compared with other cryptosystems, the isogeny-based cryptosystems have the advantages of short key size. Nevertheless, it does not outperform other cryptosystems in respect of implementation efficiency. Based on two types of key exchange protocols from supersingular elliptic curve isogeny, this paper analyzes the possibility of optimizing two key exchange protocols according to the classical optimizations of elliptic curve scalar multiplication and pairing as well as some characteristics of elliptic curve isogeny. Meanwhile, the paper categorizes and reviews the current progress on efficient isogenous computations, and puts forward the further researches in this direction.

关 键 词：SIDH CSIDH 同源的计算 Montgomery曲线 Edwards曲线 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]