Outline:
1. Origins of Cryptography – Issues – Codes and Ciphers – review of complexity results – Factoring and primality testing – GCD and its complexity – review of finite fields and cyclic groups.
2. Block Ciphers: Affine Ciphers, Substitution Ciphers, Vigenere, Hill Cipher – DES, Feistel Ciphers and the problem of breaking them, Congruences, Complete Residue Systems – Modular Arithmetic – The field Z/pZ – Euler’s Theorem and Fermat’s Little Theorem – Euler’s Φ function – Chinese Remainder Theorem.
3. Stream Ciphers : Information Theoretic considerations – Linear Feed back Shift Registers and associated results – Geffe generator – One way functions and trapdoor – Diffe-Hellman Key exchange – Bit commitment using symmetric key.
4. Discrete Logarithm, hash functions, RSA and its correctness – Modular Exponentiation – Miller-Rabin-Selfridge Primality Testing – EI Gamal Crypto System – Authentication – Digital Signatures – Merkle-Hellman Knapsack Public Key Cipher.
5. Pollard p-heuristic – Pollard p – I Algorithm, Continued Fraction Factoring Algorithm, Quadratic Sieve Algorithm, Number Field Sieve, Zero – Knowledge Proof Idea – Recent Developments
Books:
1. A.J. Menezes .P. Van Oorschot and S. Vanstone, "Handbook of Applied Cryptography", CRC Press
2. H.Mel and D.Baker, "Cryptography Decrypted", 2001, Addison Wesley
