### 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.

Available format(s)
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
See all versions
Short URL
https://ia.cr/2008/099

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}
}

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