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arXiv · 0803.0728

The elliptic curve discrete logarithm problem and equivalent hard problems for elliptic divisibility sequences

Kristin E. Lauter·Katherine E. Stange
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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-Rück and Shipsey EDS attacks on the elliptic curve discrete logarithm problem in the cases where these apply.

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Kristin E. Lauter, Katherine E. Stange. 2008-08-04. The elliptic curve discrete logarithm problem and equivalent hard problems for elliptic divisibility sequences. https://doi.org/10.1007/978-3-642-04159-4_20

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