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

Stanislav Bulygin; Albrecht Petzoldt; Johannes Buchmann

Paper 2010/420

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

Stanislav Bulygin, 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.

Metadata

Available format(s): PDF PS
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: Multivariate Cryptography UOV Signature Scheme provable security security reduction semi-regular sequence
Contact author(s): Stanislav Bulygin @ cased de
History: 2010-07-30: received
Short URL: https://ia.cr/2010/420
License: CC BY

BibTeX

@misc{cryptoeprint:2010/420,
      author = {Stanislav Bulygin and Albrecht Petzoldt and Johannes Buchmann},
      title = {Towards provable security of the Unbalanced Oil and Vinegar signature scheme under direct attacks},
      howpublished = {Cryptology {ePrint} Archive, Paper 2010/420},
      year = {2010},
      url = {https://eprint.iacr.org/2010/420}
}