RSA Cryptography: Primality Testing and Quadratic Residues

This lecture covers the basics of RSA cryptography, focusing on primality testing and quadratic residues. It explains the Fermat test, Carmichael numbers, the Miller-Rabin test, and the generation of prime numbers. The lecture also delves into the significance of the Fermat test, the Miller-Rabin criterion, and the computation of square roots in finite fields. Additionally, it discusses the Legendre and Jacobi symbols, the Goldwasser-Micali cryptosystem, and the breaking of the Decisional Diffie-Hellman assumption in Z. The presentation concludes with the application of quadratic residuosity in various cryptographic systems.