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Bernoulli numbers and the probability of a birthday surprise
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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. |
BibTeX
@misc{eprint-2003-11852, title={Bernoulli numbers and the probability of a birthday surprise}, booktitle={IACR Eprint archive}, keywords={foundations / birthday paradox, arbitrary precision calculators}, url={http://eprint.iacr.org/2003/137}, note={Discrete Applied Mathematics 127(3) (2003), 657--663 tsaban@math.huji.ac.il 12250 received 16 Jul 2003}, author={Boaz Tsaban}, year=2003 }