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UNIT-3 Number Theory: Fermat's and Euler's Theorems, The Chinese Remainder Theorem, Discrete Logarithms

This document provides an overview of the topics covered in Unit 3 of a cryptography and network security course, which is Number Theory. It includes prime and relatively prime numbers, modular arithmetic, Fermat's and Euler's theorems, the Chinese Remainder Theorem, and discrete logarithms. It also lists previous exam questions related to these topics, such as proving theorems like the Chinese Remainder Theorem, finding primitive roots, using theorems like Fermat's and Euler's to solve congruences, and explaining algorithms like the Euclidean algorithm.

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290 views12 pages

UNIT-3 Number Theory: Fermat's and Euler's Theorems, The Chinese Remainder Theorem, Discrete Logarithms

This document provides an overview of the topics covered in Unit 3 of a cryptography and network security course, which is Number Theory. It includes prime and relatively prime numbers, modular arithmetic, Fermat's and Euler's theorems, the Chinese Remainder Theorem, and discrete logarithms. It also lists previous exam questions related to these topics, such as proving theorems like the Chinese Remainder Theorem, finding primitive roots, using theorems like Fermat's and Euler's to solve congruences, and explaining algorithms like the Euclidean algorithm.

Uploaded by

Anji
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Cryptography & Network Security @ Unit-3 [Number Theory]

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


State and prove Chinese Remainder Theorem.
1
Define a primitive root. Find all primitive roots of 25
Define Euler’s Totient function. Determine ¢(37) and ¢(35
2 Use Fermat’s theorem to find a number x between 0 and 28 with x85congruent to 6 modulo
35.
State and prove Euler’s theorem
3 Use Euler’s theorem to find a number a between 0 and 9 such that a is congruent to 71000
modulo 10.
State and Prove Fermat’s theorem
4 Use Fermat’s theorem to find a number x between 0 and 28 with x85congruent to 6 modulo
29.

IV B.Tech I Semester Supplementary Examinations, May/June - 2014


What is the difference between modular arithmetic and ordinary arithmetic?
1
List three classes of polynomial arithmetic and give examples
State Fermat’s theorem and explain with example?
2
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.

bphanikrishna.wordpress.com CSE Page 1

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