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

Kristin E.  Lauter; Katherine E.  Stange

Paper 2008/099

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

Kristin E. Lauter and Katherine E. Stange

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.

Note: New version corrects several minor errors.

Metadata

Available format(s): PDF PS
Category: Foundations
Publication info: Published elsewhere. Unknown where it was published
Keywords: elliptic curve discrete logarithm problem
Contact author(s): katestange @ gmail com
History: 2008-08-04: revised; 2008-03-10: received; See all versions
Short URL: https://ia.cr/2008/099
License: CC BY

BibTeX

@misc{cryptoeprint:2008/099,
      author = {Kristin E.  Lauter and Katherine E.  Stange},
      title = {The Elliptic Curve Discrete Logarithm Problem and Equivalent Hard Problems for Elliptic Divisibility Sequences},
      howpublished = {Cryptology ePrint Archive, Paper 2008/099},
      year = {2008},
      note = {\url{https://eprint.iacr.org/2008/099}},
      url = {https://eprint.iacr.org/2008/099}
}