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

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

2008-03-05

arxiv.org/abs/0803.0728v2

Mathematics

Number Theory

18 pages; revised version includes some small mathematical corrections, reformatted

Scientific paper

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.

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