Why the Birthday Paradox Unlocks Hash Collision Risks
The Birthday Paradox reveals a counterintuitive truth: in just 23 people, the chance of two sharing a birthday exceeds 50%, despite only 365 possible dates. This phenomenon arises not from coincidence, but from combinatorial probability—where pairwise matches multiply rapidly as group size grows. Similarly, in computer systems relying on random hashing, uniform input distribution can trigger a hidden surge in collision risks, where distinct inputs map to identical outputs in surprising frequency.
From Randomness to Collision: The Core RiskJust as shared birthdays become statistically likely in small crowds, repeated hashing with uniform randomness accelerates collision chances. The paradox highlights how quickly pairwise matches emerge—not from physical limits,