The Elliptic Curve Discrete Logarithm Problem and Equivalent Hard Problems for Elliptic Divisibility Sequences Katherine Stange (Brown University) The division polynomials of an elliptic curve satisfy a recurrence relation. Evaluated at a given point on a given elliptic curve, both defined over a field K, the sequence of division polynomials becomes a sequence in K. Such a recurrence sequence is called an elliptic divisibility sequence. 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. This is joint work with Kristin Lauter performed at Microsoft Research.