Origins, computer arithmetic and complexity- what is cryptography, a history of factoring and primality testing, computer arithmetic and complexity, Symmetric-key cryptosystems- an introduction to congruences, block ciphers, DES cryptanalysis, successor AES, stream ciphers, Public-key crypto-systems- exponentiation, discrete logs, public key cryptography, authentication, knapsacks, Primality Testing- an introduction to primitive roots, true primality tests, probabilistic primality tests, Agrawal algorithm,

Factoring- three algorithms, the number field sieve, Advanced topics – elliptic curves and cryptography, zero knowledge, quantum cryptography.