Cryptography and Number Theory

An introduction to Number Theory and its application to cryptography. The topics in number theory include congruences, residues, Fermat's Theorem, Chinese Remainder Theorem, primality tests, and Galois Fields. Some simple ciphers and their history will be discussed followed by a careful study of currently employed protocols and standards such as Diffie-Hellman, elgamal, RSA, ECC, and AES. If time permits more experimental topics such as Quantum and Algebraic Cryptography, and zero knowledge proofs will be introduced.