Topics in cryptography and computational complexity

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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)?