Hash Collision Estimation

Estimate collision probability online based on the birthday paradox

Input Parameters

Estimation Results

No collision probability：—
At least one collision probability：—

Introduction
Formula
Examples
Significance

Introduction

Hash collision occurs when different inputs map to the same hash value. The birthday paradox (50% probability that two people in a group of 23 share the same birthday) illustrates that even with a large hash space, when the number of keys reaches the order of √m, the collision probability becomes non-negligible. This tool uses an approximate formula to quickly estimate collision probability, helping developers evaluate the security of hash tables and signature algorithms.

Formula

P ≈ 1 − e^(−n²/(2m))

n: number of keys
m: hash space size
P: probability of at least one collision

Examples

Example: SHA-256 outputs 2^256. If the number of keys is 2^128, P ≈ 1 − e^(−2^−128) ≈ 1 − e^(−1) ≈ 63%, indicating that with 2^128 keys, the collision probability is already close to 63%!

Significance

1. **Evaluate hash table load**: Knowing the collision probability in advance allows dynamic resizing or choosing a larger hash space. 2. **Cryptographic security**: Signature and encryption algorithms require a security level above 2^80, thus a sufficiently large hash space must be selected. 3. **Database indexing**: When designing B+ trees or hash indexes, this model can be used to estimate collisions and optimize storage and query performance.