Collisions in Fast Generation of Ideal Classes and Points on Hyperelliptic and Elliptic Curves

  • Tanja LangeEmail author
  • Igor Shparlinski


Koblitz curves have been proposed to quickly generate random ideal classes and points on hyperelliptic and elliptic curves. To obtain a further speed-up a different way of generating these random elements has recently been proposed. In this paper we give an upper bound on the number of collisions for this alternative approach. For elliptic Koblitz curves we additionally use the same methods to derive a bound for a modified algorithm. These bounds are tight for cyclic subgroups of prime order, which is the case of most practical interest for cryptography.


Public Key Cryptography Discrete Logarithm Hyperelliptic Curves Koblitz Curves Collisions 


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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Institute for Information Security and CryptologyRuhr-Universität BochumBochumGermany
  2. 2.Department of Computing MacquarieUniversity SydneyAustralia

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