Topics in cryptography and computational complexity

这个提议涉及密码学和计算复杂性方面的一些问题。 计算复杂性中最基本的问题是试图证明某些计算问题需要大量的、不切实际的计算机时间。 事实上，在密码学的设置中，我们实际上希望对手不能在合理的时间内破坏系统。在这个项目中，我们研究了一些与密码学相关的具体问题。两个人共享会话密钥意味着什么？在各种设置（例如公钥基础设施）中有哪些好方法可以实现这一点？我们如何保护我们的算法不受可能运行在不安全硬件上的影响？构造诸如AES（高级加密系统）之类的“分组密码”的理由是什么？

This proposal is concerned with a number of issues in cryptography and computational complexity. The most basic issues in computational complexity involve trying to show that certain computational problems require enormous, impractical amounts of computer time. In the setting of cryptography, in fact, we actually want it to be the case that an adversary cannot break the system in a reasonable amount of time. In this project we study a number of specific questions related to cryptography. What does it mean for two people to share a session-key, and what are good ways of doing this in various settings, such as a public key infrastructure? How can we protect our algorithms against insecure hardware they might run on? What are the justifications for constructions of "block ciphers" such as AES (Advanced Encryption System)?