A non-uniform birthday problem with applications to discrete logarithms

Steven D.  Galbraith; Mark Holmes

Paper 2010/616

A non-uniform birthday problem with applications to discrete logarithms

Steven D. Galbraith and Mark Holmes

Abstract

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.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Submitted to Discrete Applied Mathematics
Keywords: birthday paradox discrete logarithm problem (DLP)
Contact author(s): s galbraith @ math auckland ac nz
History: 2012-02-14: revised; 2010-12-08: received; See all versions
Short URL: https://ia.cr/2010/616
License: CC BY

BibTeX

@misc{cryptoeprint:2010/616,
      author = {Steven D.  Galbraith and Mark Holmes},
      title = {A non-uniform birthday problem with applications to discrete logarithms},
      howpublished = {Cryptology {ePrint} Archive, Paper 2010/616},
      year = {2010},
      url = {https://eprint.iacr.org/2010/616}
}