同源密码方案综述

A Survey of Isogeny-Based Cryptographic Schemes

基于超奇异椭圆曲线同源构造的密码体制作为后量子密码的重要分支,因其较小的密钥尺寸和良好的抗量子特性,成为一个很有潜力的发展方向.本文对同源密码进行了简要概述,总结同源密码底层的数学困难问题;整理了近年来基于椭圆曲线同源构造的不同密码方案,分别从两方密钥交换、组密钥交换、数字签名、不经意传输和公钥加密等方面介绍国内外同源密码发展现状;总结了该领域一些需要重点解决的问题,对同源密码未来发展前景进行展望.

Cryptosystems based on supersingular elliptic curve isogenies is a class of the most important post-quantum cryptosystems.Due to their small key size and good post-quantum properties,isogeny-based cryptosystems have become promising candidates in PQC standardization.This paper gives a brief overview of isogeny-based cryptosystems and summarizes the underlying mathematical problems.This paper also classifies recent isogeny-based cryptographic schemes,surveys the current research results,and traces their development in detail following their categories such as two-party key exchange,group key exchange,digital signature,oblivious transfer and public key encryption.Finally,some important problems that need to be solved in this field are summarized,and the future development prospect is discussed.