Introduction to Number Theory

Math for CS · Axiom Academy

Welcome to the World of Secrets Every time you access your email, buy something online, or send a message, you're relying on number theory. This ancient branch of mathematics has become the foundation of modern cryptography—the science of keeping information secret and secure. Number theory studies the properties of integers and their relationships. What makes it so powerful for cryptography is that certain number-theoretic operations are easy to do in one direction but practically impossible to reverse without special knowledge. This asymmetry is what protects your data. This unit is organized into essential topics: Understanding divisibility, GCD, LCM, and the fundamental theorem of arithmetic Clock arithmetic, congruences, and their remarkable properties Fermat's Little Theorem, Euler's Theorem, and the Extended Euclidean Algorithm RSA, Diffie-Hellman, hashing, and real-world applications Cybersecurity: All encryption relies on number theory. Understand the math, and you understand how to protect and attack systems. Blockchain & Cryptography: Bitcoin, Ethereum, and every cryptocurrency depends on number-theoretic algorithms like ECDSA and hash functions. Computer Science: Whether you're a software engineer, security researcher, or data scientist, number theory will deepen your understanding of how systems work. Problem Solving: Number theory develops powerful mathematical reasoning skills that transfer to algorithm design and optimization.

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