Cryptology ePrint Archive: Report 2010/420

Towards provable security of the Unbalanced Oil and Vinegar signature scheme under direct attacks

Stanislav Bulygin and Albrecht Petzoldt and Johannes Buchmann

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.

Category / Keywords: public-key cryptography / Multivariate Cryptography, UOV Signature Scheme, provable security, security reduction, semi-regular sequence

Date: received 29 Jul 2010

Contact author: Stanislav Bulygin at cased de

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Version: 20100730:035329 (All versions of this report)

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