Diffie-Hellman and ElGamal Cryptosystems

This lecture covers the Diffie-Hellman key exchange protocol, the ElGamal cryptosystem, and their applications in cryptography. The instructor explains the key concepts, such as group membership, subgroup generation, and key derivation functions. The lecture also delves into the security aspects of these protocols, including the computational Diffie-Hellman problem and the decisional Diffie-Hellman game. Additionally, the Chinese Remainder Theorem is discussed as a tool to speed up RSA decryption and prove the correctness of RSA. The lecture concludes with a detailed proof of the Chinese Remainder Theorem and its applications in number theory and cryptography.