Introduction to Number Theory and Cryptography

This course introduces elementary number theory and its role in modern cryptography. Number theory studies the additive and multiplicative structures of the integers and the solutions of equations involving them, while cryptography provides methods for secure communication. We will develop fundamental concepts of number theory and modular arithmetic, including divisibility, congruences, and the arithmetic of the integers modulo n, and explore number-theoretic structures and algorithms that are central to cryptographic applications. These ideas are used to motivate and analyze classical and public-key cryptographic schemes, illustrating how mathematical assumptions underpin security. By the end of the course, students will be able to apply number-theoretic reasoning to computational and proof-based problems and to execute and evaluate cryptographic methods in an introductory setting.