Diffie-Hellman Cryptography: Key Exchange & ElGamal

This lecture covers the Diffie-Hellman key exchange and the ElGamal Public-Key Cryptosystem. It explains the concept of discrete logarithm problems, the security of Diffie-Hellman against passive adversaries, and the challenges with subgroups. The lecture delves into the Decisional Diffie-Hellman (DDH) problem, the notion of games in cryptography, and the implications of hard cases in DDH. It also discusses the importance of checking group membership, key distribution issues, and the correct Diffie-Hellman key exchange protocol. The lecture concludes with a detailed explanation of the RFC 2631 method for Diffie-Hellman key agreement and exercises related to group parameter generation and key wrapping.