Prime Numbers and Primality Testing

This lecture covers the concepts of prime numbers, primality testing, and RSA cryptography. It explains the Chinese Remainder Theorem, Euler's Totient Function, Carmichael numbers, the Miller-Rabin primality test, and the generation of prime numbers. The instructor discusses the significance of the Fermat test, Carmichael numbers, and the correctness of RSA. The lecture also delves into the implementation of primality tests, the Miller-Rabin criterion, and the ElGamal vs. RSA comparison.