Public-Key Cryptography and Number Theory Fundamentals

Public-key cryptography forms the invisible backbone of modern digital security, protecting everything from web traffic to financial transactions. This text-based course guides you step by step through the essential number theory and mathematical frameworks that make asymmetric encryption work. By following clear explanations and practical walkthroughs, you will develop a solid mathematical intuition for modern cryptographic systems and understand both how they protect sensitive data and where potential weaknesses lie. What you'll learn: - Understand foundational number theory concepts including modular arithmetic, quadratic residues, and the Euclidean algorithm - Master prime number generation and probabilistic primality testing using the Miller-Rabin test - Explore the construction and mathematical mechanics of the RSA cryptosystem - Analyze common cryptographic vulnerabilities, mathematical attack vectors, and implementation pitfalls in RSA - Examine the Rabin cryptosystem and its provable equivalence to the integer factorization problem - Apply modern security best practices and understand current standards in asymmetric cryptography The course begins with foundational definitions, core terminology, and basic modular arithmetic before progressing into encryption algorithms, primality proofs, and attack analysis. Designed specifically for beginners, this course requires no advanced mathematical background to get started. Start reading today to build your foundation in modern cryptographic theory.