MTL730: Cryptography

3 Credits (3-0-0)

Overlaps with: COL759

Applying the corresponding algorithms programmes. (laboratory/ design activities could also be included) Classical cryptosystems, Preview from number theory, Congruences and residue class rings, DES- security and generalizations, Prime number generation. Public Key Cryptosystems of RSA, Rabin, etc. their security and cryptanalysis.

Primality, factorization and quadratic sieve, efficiency of other factoring algorithms.

Finite fields: Construction and examples. Diffie-Hellman key exchange.

Discrete logarithm problem in general and on finite fields. Cryptosystems based on Discrete logarithm problem such as MasseyOmura cryptosystems. Algorithms For finding discrete logarithms, their analysis. Polynomials on finite fields and Their factorization/ irreducibility and their application to coding theory.

Elliptic curves, Public key cryptosystems particularly on Elliptic curves. Problems of key exchange, discrete logarithms and the elliptic curve logarithm problem.

Implementation of elliptic curve cryptosystems. Counting of points on Elliptic Curves over Galois Fields of order 2m. Other systems such as Hyper Elliptic Curves And cryptosystems based on them. Combinatorial group theory: investigation of groups on computers, finitely presented groups, coset enumeration. Fundamental problems of combinatorial group theory. Coset enumeration, Nielsen and Tietze transformations. Braid Group cryptography.

Cryptographic hash functions. Authentication, Digital Signatures, Identification, certification infrastructure and other applied aspects.