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. © 2009 Springer.
CITATION STYLE
Lauter, K. E., & Stange, K. E. (2008). The elliptic curve discrete logarithm problem and equivalent hard problems for elliptic divisibility sequences. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5381 LNCS, pp. 309–327). https://doi.org/10.1007/978-3-642-04159-4_20
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