Mathematical Cryptology

This course gives a mathematical introduction to Cryptology, the art and science of making and breaking secret codes. It begins with the oldest recorded codes, and ends with the encryption schemes used to maintain privacy during Internet credit card transactions. Topics covered include the classical monoalphabetic ciphers and their cryptanalysis; polyalphabetic ciphers and their cryptanalysis; perfect cipher systems; public-key cryptology; Diffie-Hellman key exchange, RSA, Knapsack codes, and anonymity. The mathematical subjects include permutations, modular arithmetic, statistics, recurrence relations and elementary number theoretic results.