unit 3 notes and problems very usefull it

1. Cryptography & Network Security @ Unit-3 [Number Theory]
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UNIT-3
Number Theory
UNIT-III Number Theory: Prime and Relatively Prime Numbers, Modular Arithmetic,
Fermat’s and Euler’s Theorems, the Chinese Remainder Theorem, Discrete Logarithms.
Previous Paper Questions:
IV B.Tech I Semester Regular Examinations, December - 2013
1
State and prove Chinese Remainder Theorem.
Define a primitive root. Find all primitive roots of 25
2
Define Euler’s Totient function. Determine ¢(37) and ¢(35
Use Fermat’s theorem to find a number x between 0 and 28 with x85
congruent to 6 modulo
35.
3
State and prove Euler’s theorem
Use Euler’s theorem to find a number a between 0 and 9 such that a is congruent to 71000
modulo 10.
4
State and Prove Fermat’s theorem
Use Fermat’s theorem to find a number x between 0 and 28 with x85
congruent to 6 modulo
29.
IV B.Tech I Semester Supplementary Examinations, May/June - 2014
1
What is the difference between modular arithmetic and ordinary arithmetic?
List three classes of polynomial arithmetic and give examples
2
State Fermat’s theorem and explain with example?
State Euler’s theorem and explain with example?
3 With an example explain the Euclidian algorithm in the process of finding GCD.
4 Describe briefly Chinese remainder theorem with an example.