Journal of Cryptology

, Volume 1, Issue 3, pp 139–150

Hyperelliptic cryptosystems

  • Neal Koblitz

DOI: 10.1007/BF02252872

Cite this article as:
Koblitz, N. J. Cryptology (1989) 1: 139. doi:10.1007/BF02252872


In this paper we discuss a source of finite abelian groups suitable for cryptosystems based on the presumed intractability of the discrete logarithm problem for these groups. They are the jacobians of hyperelliptic curves defined over finite fields. Special attention is given to curves defined over the field of two elements. Explicit formulas and examples are given, and the problem of finding groups of almost prime order is discussed.

Key words

CryptosystemPublic keyDiscrete logarithmHyperelliptic curveJacobian

Copyright information

© International Association for Cryptologic Research 1988

Authors and Affiliations

  • Neal Koblitz
    • 1
  1. 1.Department of Mathematics GN-50University of WashingtonSeattleU.S.A.