Cryptography and Information Theory

This lecture covers the fundamental concepts of cryptography and information theory, including perfect secrecy, Vernam Cipher, group theory, and algorithms for big numbers. It delves into the historical development of cryptography, from ancient methods to modern milestones like Diffie-Hellman and RSA. The instructor discusses the trade-off between security and cost, emphasizing the need for standard cryptographic solutions. Key topics include prime numbers, unique factorization, modulo operations, group homomorphism, and subgroup constructions. The lecture also explores generators, Lagrange's theorem, and the Diffie-Hellman key agreement protocol, highlighting the importance of public-key cryptography.