Paper 2019/1490

Cryptanalysis of The Lifted Unbalanced Oil Vinegar Signature Scheme

Jintai Ding and Joshua Deaton and Kurt Schmidt and Vishakha and Zheng Zhang

Abstract

In 2017, Ward Beullens et al. submitted Lifted Unbalanced Oil and Vinegar (LUOV), a signature scheme based on the famous multivariate public key cryptosystem (MPKC) called Unbalanced Oil and Vinegar (UOV), to NIST for the competition for post-quantum public key scheme standardization. The defining feature of LUOV is that, though the public key $\mathcal{P}$ works in the extension field of degree $r$ of $\mathbb{F}_2$, the coefficients of $\mathcal{P}$ come from $\mathbb{F}_2$. This is done to significantly reduce the size of $\mathcal{P}$. The LUOV scheme is now in the second round of the NIST PQC standardization process. In this paper we introduce a new attack on LUOV. It exploits the "lifted" structure of LUOV to reduce direct attacks on it to those over a subfield.