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Upon successful completion of this course a students will:
Module-I (T-4 hr P-2 hr P-0 hr)
Divisibility, Representations of Integers,Computer Operations with Integers,Prime Numbers
Practice-1: Write a program to decide whether an integer is prime using trial division of the integer by all primes not exceeding its square root.
Module-II (T-6 hr P-4 hr P-0 hr)
Greatest common divisor,Euclidean Algorithm,Modified Euclidean Algorithm, Prime factorization,Factorization of Integers
Practice-2: Write a program to find the greatest common divisor of two integers using the Euclidean algorithm.
Practice-3:Find the prime factorization of a positive integer.
Module-III (T-5 hr P-2 hr P-0 hr)
Congruence’s, Properties of Congruence’s,System linear Congruence’s
Chinese Remainder Theorem.
Practice -4: Write a program to solves systems of linear congruence
Module-IV (T-5 hr P-0 hr P-0 hr)
Wilson's Theorem,Fermat's Little Theorem,Pseudo prime, Carmichael number
Module-V (T-4 hr P-2 hr P-0 hr)
Euler's Theorem, Euler Phi-function, Perfect Numbers, Mersenne Primes
Practice -5: Write programs to find values of the Euler phi-function
Module-VI (T-3 hr P-2 hr P-0 hr)
Character Ciphers, Block Ciphers, Exponentiation ciphers, Public-Key Cryptography (RSA Cryptosystem).
Practice-6: Write a program for RSA crypto system/Algorithm.
Module-VII (T-3 hr P-0 hr P-0 hr)
Knapsack ciphers, Some applications to computer science.
Write programs to decide whether an integer is prime using trial division of the integer by all primes not exceeding its square root.
Write programs to find the greatest common divisor of two integers using the Euclidean algorithm
Factorization of Integers
Write program to find the prime factorization of a positive integer.
Write programs to solve systems of linear congruence.
Theorems on Pseudo prime
Write programs to find values of the Euler phi-function
Write programs for RSA Cryptosystem/Algorithm
Kali Prasad Rath received his M.Tech. in Computer Science and & M.Sc. in Mathematics from Berhampur University.This is his 10th year at Centurion University of Technology and Management and his 17th year in teaching profession. He is associated with qualitative study on theory of difference equation.