Cryptographic Primitives: Theory and Practice

This lecture covers the fundamental cryptographic primitives including finite fields, Zn rings, Zp fields, Chinese Remainder Theorem, random variables, expected value, variance, arithmetic with big numbers, modular arithmetic, algorithms, birthday effect, generic attacks, easy problems, membership problem, hard problems, non-polynomial algorithms, Turing reduction, symmetric encryption, security models, chosen ciphertext security, adaptive security, decryption security, and the relationship between decryption security and key recovery security.