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

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 Gr¨obner 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 a...

• Type: Conference
• Year: 2005
• Where: CTRSA
• Authors: An Braeken, Christopher Wolf, Bart Preneel
• Keywords: Cryptology, CTRSA 2005, Multivariate Quadratic Equations, Signature Schemes, Vinegar Scheme