Another look at non-standard discrete log and Diffie-Hellman problems

We examine several versions of the one-more-discrete-log and one-more-Diffie-Hellman problems. In attempting to evaluate their intractability, we find conflicting evidence of the relative hardness of the different problems. Much of this evidence comes from natural families of groups associated with...

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Bibliographic Details
Published in:Journal of mathematical cryptology 2008-12, Vol.2 (4), p.311-326
Main Authors: Koblitz, Neal, Menezes, Alfred
Format: Article
Language:English
Subjects:
Diffie-Hellman problem
discrete log problem
index calculus
jacobian groups
provable security
Public-Key Cryptography
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Summary:We examine several versions of the one-more-discrete-log and one-more-Diffie-Hellman problems. In attempting to evaluate their intractability, we find conflicting evidence of the relative hardness of the different problems. Much of this evidence comes from natural families of groups associated with curves of genus 2, 3, 4, 5, and 6. This leads to questions about how to interpret reductionist security arguments that rely on these non-standard problems.
ISSN:1862-2976
1862-2984
DOI:10.1515/JMC.2008.014