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