Welcome to the resource topic for
**2003/137**

**Title:**

Bernoulli numbers and the probability of a birthday surprise

**Authors:**
Boaz Tsaban

**Abstract:**

A birthday surprise is the event that, given k uniformly random

samples from a sample space of size n, at least two of them are identical.

We show that Bernoulli numbers can be used to derive arbitrarily exact

bounds on the

probability of a birthday surprise.

This result can be used in arbitrary precision calculators, and it can

be applied to better understand some questions in

communication security and pseudorandom number

generation.

**ePrint:**
https://eprint.iacr.org/2003/137

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