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The Elliptic Curve Discrete Logarithm Problem and Equivalent Hard Problems for Elliptic Divisibility Sequences

  • Kristin E. Lauter
  • Katherine E. Stange
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5381)

Abstract

We define three hard problems in the theory of elliptic divisibility sequences (EDS Association, EDS Residue and EDS Discrete Log), each of which is solvable in sub-exponential time if and only if the elliptic curve discrete logarithm problem is solvable in sub-exponential time. We also relate the problem of EDS Association to the Tate pairing and the MOV, Frey-Rück and Shipsey EDS attacks on the elliptic curve discrete logarithm problem in the cases where these apply.

Keywords

Elliptic Curve Elliptic Curf Hard Problem Prime Order Discrete Logarithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Kristin E. Lauter
    • 1
  • Katherine E. Stange
    • 2
  1. 1.Microsoft ResearchRedmond
  2. 2.Department of MathematicsHarvard UniversityCambridge

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