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Computing discrete logarithms
in real quadratic congruence function fields
of large genus


Authors: Volker Müller, Andreas Stein and Christoph Thiel
Journal: Math. Comp. 68 (1999), 807-822
MSC (1991): Primary 11Y16, 11R29; Secondary 11T71, 11R58, 68Q25, 94A60
DOI: https://doi.org/10.1090/S0025-5718-99-01040-6
MathSciNet review: 1620235
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Abstract | References | Similar Articles | Additional Information

Abstract: The discrete logarithm problem in various finite abelian groups is the basis for some well known public key cryptosystems. Recently, real quadratic congruence function fields were used to construct a public key distribution system. The security of this public key system is based on the difficulty of a discrete logarithm problem in these fields. In this paper, we present a probabilistic algorithm with subexponential running time that computes such discrete logarithms in real quadratic congruence function fields of sufficiently large genus. This algorithm is a generalization of similar algorithms for real quadratic number fields.


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Additional Information

Volker Müller
Affiliation: Technische Universität Darmstadt, Fachbereich Informatik, Alexanderstr. 10, 64283 Darmstadt, Germany
Email: vmueller@cdc.informatik.tu-darmstadt.de

Andreas Stein
Affiliation: Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
Email: astein@cacr.math.uwaterloo.ca

DOI: https://doi.org/10.1090/S0025-5718-99-01040-6
Keywords: Discrete logarithm, class group, subexponential algorithm, real quadratic congruence function field
Received by editor(s): March 25, 1996
Received by editor(s) in revised form: September 10, 1997
Additional Notes: This research was supported by the Deutsche Forschungsgemeinschaft.
Article copyright: © Copyright 1999 American Mathematical Society

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