OBJECTIVE: To give an exposure on symmetric key cryptosystems, stream ciphers, public key cryptosystem, factoring and related topics.
1. Preliminaries: Origins of Cryptography — Issues in Cryptography — Codes and Ciphers — review of complexity results — Preliminary ideas of factoring and primality testing — ged and its complexity review of finite fields and cyclic groups.
2. Symmetric Key Cryptosystems: Block Ciphers: Affine Ciphers, Substitution Ciphers, Vigenere, Hill Cipher — DES, Feistel Ciphers and the problem of breaking them, Congruences. Complete Residue Systems — Modular Arithmatic — The field Z/pZ — Euler’s φ Theorem and Fermant Little Theorem — Euler’s V function — Chinese Remander Theorem.
3. Stream Ciphers : Information Theoretic considerations — Linear Feed back Shift Registers and associated results — Geffe generator — One way functions and trapdoor — diffe-Heliman Key exchange — Bit commitment using symmetric key.
4. Public — Key Cryptosystems: Discrete Logarithm, hash functions, RSA and its correctness — Modular Exponentiation — Miller-Rabin-Seifridge Prima Testing El Gamal Crypto System Authentication Digital Signatures — Merkle Knapsack Public Key Cipher
5. Factoring and Other Topics : Pollard p-heuristic — Pollard p I Algorithm. Continued Fraction Factoring Algorithm, Quadratic Sieve Algorithm, Number Field Sieve, Zero — Knowledge Proof Idea — Recent Developments
1. A.J. MENEZES .P. VAN OORSCHOT AND S. VANSTONE, "Handbook of Applied Cryptography", CRC Press