Paper 2008/286

One-Up Problem for (EC)DSA

Daniel R. L. Brown

Abstract

The one-up problem is defined for any group and a function from the group to integers. An instance of problem consists of two points in the group. A solution consists of another point satisfying an equation involving the group and the function. The one-up problem must be hard for the security of (EC)DSA. Heuristic arguments are given for the independence of the discrete log and one-up problems. DSA and ECDSA are conjectured to be secure if the discrete log and one-up problems are hard and the hash is collision resistant.