2K6IT 703 NUMBER THEORY AND CRYPTOGRAPHY

Module 1 (14Hrs)
Divisibility – The division algorithms- gcd, lcm, primes- Fundamental theorem of arithmetic- Euler function, Congruence- Complete residue system- Reduced residue system- Euler theorem- Fermatt’s little theorem- Wilson’s theorem- The Chinese reminder theorem- Quadratic Residues – Legendre symbol
Module II (14 Hrs)
Security goals – Attacks – Services and Mechanisms – Techniques – Symmetric key encryption – Introduction – Substitution and Transposition ciphers – Stream and block ciphers –Modern symmetric key ciphers-DES-Structure, Analysis ,Security-AES- Introduction, AES Ciphers .
Module III (15 Hrs)
Asymmetric key Cryptography – Introduction – RSA cryptosystem – Rabin cryptosystem – Elgamal Cryptosystem – Elliptic Curve Cryptosystem Message Integrity – Message Authentication – Hash Functions – SHA 512 – Digital Signature – Digital Signature Schemes –Entity authentication , Introduction.
Module IV (11 Hrs)
E mail Security – PGP & S/MIME – Transport layer Security – SSL & TLS – Network layer security – IP Sec

Text books
1. An Introduction to the theory of numbers. Ivan Niven, Herbert S Zuckerman, Hugh L Montgomery Wiely Student Edition
2. Cryptography and Network Security, Behrouz A. Forouzan, Tata McGraw-Hill

Reference books
1 Elementary Theory of Numbers- C Y Hsuing – Allied publishers Tom M Apostol Introduction to analytic Number Theory – Springer International Student Edition
2. Niven I., Zuckerman H.S. and Montgomery H. L., An Introduction to the Theory of Numbers, John Wiley and Sons.
2. Stallings W., Cryptography and Network Security: Principles and Practice, Pearson Education Asia.
3. Mano W., Modern Cryptography: Theory & Practice, Pearson Education.
4. D. A. Burton, Elementary Number Theory, 6/e, Tata McGraw Hill.
5. Delfs H. and Knebel H., Introduction to Cryptography: Principles and Applications, Springer.