Unit – I
Origins of Cryptography- Issues - Codes and ciphers - Preliminary ideas of factoring and testing - gcd and its complexity.
Unit – II
Symmetric Key Cryptosystems- Block ciphers - Substitution ciphers - DES and Feistel ciphers and the problem of breaking them - The field Z/pZ - Euler's φ function.
Unit – III
Stream Ciphers- Linear feedback shift registers and associated results - Geffe generator - Diffe-Hellman key exchange - Bit commitment using symmetric key.
Unit – IV
Public-key Cryptosystems- Discrete logarithm - RSA and Miller-Rabin - Authentication - Digital signatures - Merkle-Hellman Knapsack public key cipher.
Unit – V
Factoring and other topics- Pollard ρ-heuristic - Pollard p-1 algorithm - Quadratic sieve algorithm - Zero-knowledge proof idea - Recent developments.