Post-quantum cryptography from isogenies

正如我们今天所知，公钥加密是互联网安全的基础，它允许双方安全通信，而无需事先交换机密密钥材料。目前广泛使用的所有公钥密码系统都是基于分解大整数的问题，或者是计算某个组中的离散对数的问题。在1994年的一篇开创性论文中，肖尔表明，这两个问题在量子计算机上都很容易解决，量子计算机利用量子力学来执行比任何经典计算机都快的计算。从那时起，关于构建的主题已经做了很多工作

Public-key cryptography is the foundation of internet security as we know it today, allowing for two parties to communicate securely without the need to exchange confidential key material in advance. All public key cryptosystems in widespread use today are based on either the problem of factoring large integers, or the problem of computing discrete logarithms in some group. In a seminal paper from 1994, Shor showed that both of these problems would be easy to solve on a quantum computer, one which uses quantum mechanics to perform calculations faster than any classical computer can achieve. Since then, much work has been done on the topic of constructing