Abstract

In this paper we show that solving systems coming from the public key of the Unbalanced Oil and Vinegar (UOV) signature scheme is on average at least as hard as solving a certain quadratic system with completely random quadratic part. In providing lower bounds on direct attack complexity we rely on the empirical fact that complexity of solving a non-linear polynomial system is determined by the homogeneous part of this system of the highest degree. Our reasoning explains, in particular, the results on solving the UOV systems presented by J.-C. Faugere and L. Perret at the SCC conference in 2008.

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