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

Thapar UniversityPrice on request

Free

Price on request

Price on request

Price on request

## Important information

- Master
- Patiala

Starts | Location |
---|---|

On request |
PatialaThapar University P.O Box 32, 147004, Punjab, India See map |

## Course programme

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,