The Birthday Paradox and Hash Collisions: Understanding Probability in Cryptography

This article explores the birthday paradox (birthday problem) in probability theory and connects it to hash collisions in cryptography. It explains how with just 23 people in a room, there's a 50% chance of a shared birthday, and extends this mathematical principle to explain why hash functions can have collisions, why encryption systems have vulnerabilities, and the mathematical foundations that make both the surprising birthday result and cryptographic security work — and sometimes fail.