椭圆曲线同源的有效计算研究进展

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.本文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，本文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，提出了本方向可进一步开展的研究工作.

Research Development on Efficient Elliptic Curve Isogenous Computations

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 crytosystems emerge at present such as lattice-based, code-based, hash-based and isogeny-based cryptosystems. Compared with other cryptosystems, the isogeny-based crptosystems have the advantages of short key size. Nevertheless, it does not outperform other cryptosystems in respect of implementation efficiency. Basd 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.