Bernoulli numbers and the probability of a birthday surprise

Authors:
Boaz Tsaban
Affiliations:
Department of Mathematics and Computer Science, Bar-Ilan University, Ramat-Gan 52900, Israel
Venue:
Discrete Applied Mathematics
Year:
2003

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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.