Objective: Explore the underlying mathematical principles that form the basis of cryptographic algorithms.

Introduction to Mathematical Foundations

Key Concepts and Theories

  1. Modular Arithmetic:
    • Fundamental to many cryptographic algorithms.
    • Involves arithmetic with a wrap-around feature at a certain value, known as the modulus.
  2. Prime Numbers and Factoring:
    • The difficulty of factoring large prime numbers forms the basis of algorithms like RSA.
    • Prime numbers are used because their properties make the factoring problem hard.
  3. Elliptic Curves:
    • Used in algorithms like ECC (Elliptic Curve Cryptography).
    • Involves points on a curve and the mathematics of their relationships.
  4. Discrete Logarithms:
    • The discrete logarithm problem is a hard problem used in cryptographic algorithms, including Diffie-Hellman and some forms of ECC.

Hands-on Exercise: Exploring Modular Arithmetic

Practical Application

Further Reading and Resources