Cryptology ePrint Archive: Report 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 \textit{et al.} submitted Lifted Unbalanced Oil and Vinegar (LUOV)\cite{beullens2017field}, 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. We show that this reduces the complexity below the targeted security for the NIST post-quantum standardization competition.

Category / Keywords: public-key cryptography /

Date: received 27 Dec 2019, last revised 20 Jul 2020

Contact author: jintai ding at gmail com, deatonju at mail uc edu, schmidku at mail uc edu, sharmav4 at mail uc edu, zhang2zh at mail uc edu

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Version: 20200720:200332 (All versions of this report)

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