# Number Theory & Cryptography

Focuses on modular arithmetic, prime numbers, RSA, and cryptographic protocols.## Lab Manual

## NTC Lab Manual

Distributed by Manipal Institute of Technology, Bengaluru.

## Table of Contents

## Caesar's Cipher Encryption

A Java program that encrypts and decrypts text by shifting characters based on a given value.

## Chinese Remainder Theorem

Apply the theorem to solve systems of congruences and find unique solutions.

## Extended Euclidean Algorithm

Calculate the coefficients for the GCD of two given numbers.

## Fermat's Little Theorem

A Java program to verify Fermat's Little Theorem for a given integer and prime number.

## Groups & Rings

Determine if a set of integers forms a mathematical group or ring based on their respective properties.

## (Practice) Modular Arithmetic

Programs for prime factorization and multiplicative inverse.