MSc (Mathematics and Computing) Programme:Number Theory and Cryptography

Semester I

Real Analysis – I
Linear Algebra
Complex Analysis
Fundamentals of Computer Science and C Programming
Discrete Mathematical Structure
Differential Equations


Semester II

Real Analysis –II
Advanced Abstract Algebra
Computer Oriented Numerical Methods
Data Structures
Data Based Management Systems
Operating Systems


Semester III

Topology
Computer Based Optimization Techniques
Computer Networks
Mechanics
Seminar


Semester IV

Functional Analysis
Dissertation


Number Theory and Cryptography

Divisibility: Greatest common divisor, Fundamental theorem of Arithmetic, Congruence, Residue classes and reduced residue classes, Euler’s theorem, Fermat’s theorem, Wilson Theorem, Chinese Remainder theorem with applications.

Polynomial Congruences: Primitive roots, Indices and their applications, Quadratic residues, Legendre Symbol, Euler’s criterion, Gauss’s Lemma, Quadratic reciprocity law, Jacobi symbol.

Arithmetic Functions: Mobius inversion formula, Diophantine equations x2 + y2 = z2 and its applications to xn + yn = zn when n = 4.

Farey Series: Continued fractions, approximations of reals by rationals, Pell’s equation

Introduction to Cryptography: Encryption schemes, cryptanalysis, Block ciphers, stream ciphers, Affine ciphers, DES and AES algorithms,

Public Key Encryption: RSA cryptosystem, Rabin Encryption, Diffie-Hellman Key Exchange, ElGamal Encryption, Cryptographic Hash functions,