2K6 EC 805 (E): SECURE COMMUNICATIONS

Module I: (10 hours)
Rings and fields – Homomorphism- Euclidean domains – Principal Ideal Domains – Unique Factorization Domains — Field extensions- Splitting fields – Divisibility- Euler theorem – Chinese Remainder Theorem – Primality
Module II: (13 hours)
Basic encryption techniques – Concept of cryptanalysis – Shannon’s theory – Perfect secrecy – Block ciphers – Cryptographic algorithms – Features of DES – Stream ciphers – Pseudo random sequence generators – linear complexity – Non-linear combination of LFSRs – Boolean functions
Module III: (14 hours)
Private key and Public key cryptosystems – One way functions – Discrete log problem – Factorization problem – RSA encryption – Diffie Hellmann key exchange – Message authentication and hash functions -Digital signatures – Secret sharing – features of visual cryptography – other applications of cryptography –
Module IV: (15 hours)
Elliptic curves – Basic theory – Weirstrass equation – Group law – Point at Infinity -Elliptic curves over finite fields – Discrete logarithm problem on EC – Elliptic curve cryptography – Diffie Hellmann key exchange over EC – Elgamal encryption over EC – ECDSA

Text Books:
1. Douglas A. Stinson, “Cryptography, Theory and Practice”, 2nd edition, Chapman & Hall, CRC Press Company, Washington
2. William Stallings, “ Cryptography and Network Security”, 3rd edition, Pearson Education
Reference Books:
1. Lawrence C. Washington, “ Elliptic Curves”, Chapman & Hall, CRC Press Company, Washington.
2. David S. Dummit, Richard M. Foote, “ Abstract Algebra”, John Wiley & Sons
3. Evangelos Kranakis, “ Primality and Cryptography”, John Wiley & Sons
4. Rainer A. Ruppel, “ Analysis and Design of Stream Ciphers”, Springer Verlag