Introduction to Computational Number Theory and Cryptography

Modern digital security relies on mathematical problems that are easy to create but incredibly difficult to solve. To understand how our data remains secure, you must grasp the intersection of number theory and computational complexity. This text-based course guides you through the core mathematical principles and algorithmic concepts that power secure modern communication. You will transition from understanding basic modular arithmetic to analyzing the mathematical structures that keep global financial systems and private data secure from computational attacks. What you'll learn: - Understand foundational algebraic structures, prime numbers, and modular arithmetic - Analyze computational complexity classes and their role in modern cryptography - Practice executing key exchange protocols and public-key encryption algorithms - Evaluate the security of cryptographic systems against common mathematical attacks - Explore modern cryptographic paradigms including basic post-quantum security concepts This course begins with essential terminology, basic definitions, and the core mathematical concepts of number theory. You will then progress through the mechanics of classic public-key algorithms, examine how computational complexity guarantees security, and study the future of cryptography. This course is designed for beginners in cryptography, computer science students, and self-taught developers who want to understand the math behind secure systems. No prior background in advanced number theory or cryptography is required. Start reading today to build a strong theoretical foundation in cryptographic mathematics.