The Elliptic Curve Discrete Logarithm Problem and Equivalent Hard Problems for Elliptic Divisibility Sequences

Kristin Lauter and Katherine Stange

2008

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.

Publication type | Article |

Published in | Selected Areas in Cryptography 2008 |

URL | http://eprint.iacr.org/2008/099 |

Publisher | Springer Verlag |

- Computing endomorphism rings of Jacobians of genus 2 curves over finite fields
- Fast Elliptic Curve Arithmetic and Improved Weil Pairing Evaluation
- Private Computation on Encrypted Genomic Data

> Publications > The Elliptic Curve Discrete Logarithm Problem and Equivalent Hard Problems for Elliptic Divisibility Sequences