A non-uniform birthday problem with applications to discrete logarithms

We consider a generalisation of the birthday problem that arises in the analysis of algorithms for certain variants of the discrete logarithm problem in groups. More precisely, we consider sampling coloured balls and placing them in urns, such that the distribution of assigning balls to urns depends...

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Bibliographic Details
Published in:Discrete Applied Mathematics Vol. 160; no. 10-11; pp. 1547 - 1560
Main Authors: Galbraith, Steven D., Holmes, Mark
Format: Journal Article
Language:English
Published: Elsevier B.V 01.07.2012
Subjects:
Algorithms
Birthday paradox
Color
Colour
Discrete logarithm problem
Logarithms
Mathematical analysis
Paradoxes
Placing
Probabilistic analysis of randomised algorithms
Sampling
Birthday paradox
Probabilistic analysis of randomised algorithms
Discrete logarithm problem
ISSN:0166-218X, 1872-6771
Online Access:Get full text
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Summary:We consider a generalisation of the birthday problem that arises in the analysis of algorithms for certain variants of the discrete logarithm problem in groups. More precisely, we consider sampling coloured balls and placing them in urns, such that the distribution of assigning balls to urns depends on the colour of the ball. We determine the expected number of trials until two balls of different colours are placed in the same urn. As an aside we present an amusing “paradox” about birthdays.
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ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2012.02.019