Paper 2008/099 Original: eprint.iacr.org/2008/099 ↗
The Elliptic Curve Discrete Logarithm Problem and Equivalent Hard Problems for Elliptic Divisibility Sequences
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.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2008-08-04: last updated
- 2008-03-10: published
- Short URL
- https://ia.cr/2008/099
- License
- https://creativecommons.org/licenses/by/4.0/
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},
url = {https://eprint.iacr.org/2008/099}
}