Kristin Lauter and Katherine Stange
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-Rueck and Shipsey EDS attacks on the elliptic curve discrete logarithm problem in the cases where these apply.
In Selected Areas in Cryptography 2008
Publisher Springer Verlag