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A Study of the Security of Unbalanced Oil and Vinegar Signature Schemes

  • An Braeken
  • Christopher Wolf
  • Bart Preneel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3376)

Abstract

The Unbalanced Oil and Vinegar scheme (UOV) is a signature scheme based on multivariate quadratic equations. It uses m equations and n variables. A total of v of these are called “vinegar variables”. In this paper, we study its security from several points of view. First, we are able to demonstrate that the constant part of the affine transformation does not contribute to the security of UOV and should therefore be omitted. Second, we show that the case n ≥ 2m is particularly vulnerable to Gröbner basis attacks. This is a new result for UOV over fields of odd characteristic. In addition, we investigate a modification proposed by the authors of UOV, namely to chose coefficients from a small subfield. This leads to a smaller public key. But due to the smaller key-space, this modification is insecure and should therefore be avoided. Finally, we demonstrate a new attack which works well for the case of small v. It extends the affine approximation attack from Youssef and Gong against the Imai-Matsumoto Scheme B for odd characteristic and applies it against UOV. This way, we point out serious vulnerabilities in UOV which have to be taken into account when constructing signature schemes based on UOV.

Keywords

Signature Scheme Basis Attack Birthday Paradox Hide Field Equation Multivariate Quadratic Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • An Braeken
    • 1
  • Christopher Wolf
    • 1
  • Bart Preneel
    • 1
  1. 1.K.U.Leuven, ESAT-COSICLeuven-HeverleeBelgium

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