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

Authors:
Kristin E. Lauter
Katherine E. Stange
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URL: http://eprint.iacr.org/2008/099
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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-R\"{u}ck and Shipsey EDS attacks on the elliptic curve discrete logarithm problem in the cases where these apply.
BibTeX
@misc{eprint-2008-17776,
  title={The Elliptic Curve Discrete Logarithm Problem and Equivalent Hard Problems for Elliptic Divisibility Sequences},
  booktitle={IACR Eprint archive},
  keywords={foundations / elliptic curve discrete logarithm problem},
  url={http://eprint.iacr.org/2008/099},
  note={ katestange@gmail.com 14095 received 5 Mar 2008, last revised 4 Aug 2008},
  author={Kristin E. Lauter and Katherine E. Stange},
  year=2008
}