MSc (Mathematics and Computing) Programme:Number Theory and CryptographyThapar University
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Real Analysis – I
Fundamentals of Computer Science and C Programming
Discrete Mathematical Structure
Real Analysis –II
Advanced Abstract Algebra
Computer Oriented Numerical Methods
Data Based Management Systems
Computer Based Optimization Techniques
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,