Modular Arithmetic-Divisibility
Numbers
Divisibility
Remainders
Problems
Divisibility Tests
Modular Arithmetic-Modular Arithmetic
Modular Arithmetic
Applications
Modular Subtraction and Division
Euclid's Algorithm-Euclid's Algorithm
Greatest Common Divisor
()
Euclid’s Algorithm
()
Greatest Common Divisor: Code
Extended Euclid’s Algorithm
()
Extended Euclid's Algorithm: Code
Slides
Euclid's Algorithm-Applications
Least Common Multiple
()
Diophantine Equations: Examples
()
Diophantine Equations: Theorem
()
Modular Division
()
Slides
Building Blocks for Cryptography-Integer Factorization
Introduction
Prime Numbers
Factoring: Existence
Factoring: Uniqueness
Unique Factoring: Consequences
Building Blocks for Cryptography-Chinese Remainder Theorem
Remainders for Two Modulo Values
Chinese Remainder Theorem
Building Blocks for Cryptography-Modular Exponentiation
Modular Exponentiation
Fast Modular Exponentiation
Fermat's Little Theorem
Euler's Theorem
Cryptography-One-time Pad
Cryptography
Secure Communication
Substitution Ciphers
One-time Pad
Many Time Pad Attack
Cryptography-RSA Cryptosystem
RSA Cryptosystem
Attacks and Vulnerabilities
Randomness Generation