🎂 The Birthday Paradox: Math Behind Collisions
Learn why finding collisions is easier than you think—but still impossibly hard
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0 / 5 completed🎂 The Birthday Paradox
Here's a counterintuitive fact: In a room of just 23 people, there's a 50% chance that two share the same birthday! This paradox explains why hash collisions are easier to find than you might think.
🤔 The Classic Birthday Problem
Most people assume you'd need 183 people (half of 365 days) for a 50% collision chance. But mathematics tells a different story!
🎮 Interactive Birthday Simulator
Adjust the number of people and see how collision probability changes:
🔢 Key Birthday Probabilities
🔐 Applying to Hash Functions
The birthday paradox explains why finding hash collisions is easier than brute-forcing a specific hash. Instead of targeting ONE hash, attackers can generate MANY inputs and look for ANY collision.
| Hash Size | Possible Outputs | Collision at ~ | Example |
|---|---|---|---|
| 8 bits | 256 | ~16 | Tiny hash |
| 16 bits | 65K | ~256 | Very weak |
| 32 bits | 4.3B | ~65K | CRC32 |
| 128 bits | 3.4×10³⁸ | ~2⁶⁴ | MD5 (broken) |
| 256 bits | 1.2×10⁷⁷ | ~2¹²⁸ | SHA-256 (secure) |
💡 Key Insights
For n-bit hash, collisions appear after ~2^(n/2) attempts. SHA-256 (256 bits) requires ~2^128 attempts for collision.
Doubling hash size from 128 to 256 bits increases collision resistance from 2^64 to 2^128 - that's 18 quintillion times harder!
With 2^128 attempts needed and billions of hashes per second, finding a SHA-256 collision would take longer than the age of the universe.