Introduction to Public Key Cryptography

Number Theory · Axiom Academy

LESSON Introduction to Public Key Cryptography The revolutionary concept of asymmetric encryption that transformed secure communication 1. The Key Distribution Problem Traditional symmetric encryption uses a single secret key for both encryption and decryption. This creates a critical vulnerability: how do two parties exchange this secret key without an eavesdropper intercepting it? The Problem: In a world with n users, symmetric encryption requires n(n-1)/2 unique shared keys. With 1000 users, that's nearly 500,000 keys to manage securely! The foundation of public key cryptography rests on mathematical functions that are easy to compute in one direction but computationally infeasible to reverse without special information. Analogy: Mixing paint colors is easy (forward), but separating mixed paint back into original colors is practically impossible (reverse). Number theory provides mathematical versions of this concept. A trapdoor function is a special one-way function that becomes easy to reverse if you possess secret information (the "trapdoor"). This is the crucial insight that enables public key cryptography. Example: Multiplication is easy: 89 × 97 = 8,633. Factoring is hard: finding that 8,633 = 89 × 97 requires work. But if you know one factor (the trapdoor), finding the other is trivial. 4. Public and Private Key Pairs

This is the written version of the interactive lesson above. See the full Number Theory course.