The elliptic curve discrete logarithm problem and equivalent hard problems for elliptic divisibility sequences
Number Theory
2014-12-30 v2 Algebraic Geometry
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.
Cite
@article{arxiv.0803.0728,
title = {The elliptic curve discrete logarithm problem and equivalent hard problems for elliptic divisibility sequences},
author = {Kristin E. Lauter and Katherine E. Stange},
journal= {arXiv preprint arXiv:0803.0728},
year = {2014}
}
Comments
18 pages; revised version includes some small mathematical corrections, reformatted