## EC445 Number Theory and Applications in E&C Engg.

### Course Name:

EC445 Number Theory and Applications in E&C Engg.

### Programme:

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### Credits (L-T-P):

### Content:

Basic Number Theory: Prime numbers, Divisibility and GCD, Congruences, Powers, Fermat's Little theorem, Euler's theorem, Euler's totient function, Chinese Remainder theorem, Diophantine equations, Fibonacci Sequence and properties, Lucas Sequences. Alternate Number Systems: Need for alternate number systems, Positional and Non weighted number systems, Residue Number system (RNS), Double base number system(DBNS), Implications on Processor architectures and Implementations. Signal Processing and Number Theory: Review of DFT and circular convolution, Number theory and DFT, Consequences of Euler's theorem for Signal Processing, Groups, Rings and Fields in DSP, Polynomial Theory, Fast Convolution Algorithms, Processor Architectures. Cryptography: Mathematical Background, Encryptions and block ciphers, DES, Prime number generation and primality tests, RSA. Communication Engg: PN sequences, Polynomials and Euclidean algorithm, Generation of PN sequences application of PN sequences.