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Mathematics of Computation

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Obstacles to the torsion-subgroup attack on the decision Diffie-Hellman Problem

Authors: Neal Koblitz and Alfred J. Menezes
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Journal: Math. Comp. 73 (2004), 2027-2041
MSC (2000): Primary 94A60, 11T71, 14G50
Published electronically: February 25, 2004
MathSciNet review: 2059749
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Abstract: Cheng and Uchiyama show that if one is given an elliptic curve, depending on a prime $p$, that is defined over a number field and has certain properties, then one can solve the Decision Diffie-Hellman Problem (DDHP) in $\mathbb{F}_p^*$ in polynomial time. We show that it is unlikely that an elliptic curve with the desired properties exists.

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Additional Information

Neal Koblitz
Affiliation: Department of Mathematics, Box 354350, University of Washington, Seattle, Washington 98195

Alfred J. Menezes
Affiliation: Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1 Canada

Keywords: Discrete logarithm, Diffie-Hellman Problem, elliptic curve, torsion point, modular curve
Received by editor(s): May 29, 2002
Received by editor(s) in revised form: May 3, 2003
Published electronically: February 25, 2004
Article copyright: © Copyright 2004 American Mathematical Society