Paper 2024/279

Polynomial-Time Key-Recovery Attack on the ${\tt NIST}$ Specification of ${\tt PROV}$

Abstract

In this paper, we present an efficient attack against ${\tt PROV}$, a recent variant of the popular Unbalanced Oil and Vinegar (${\tt UOV}$) multivariate signature scheme, that has been submitted to the ongoing ${\tt NIST}$ standardization process for additional post-quantum signature schemes. A notable feature of ${\tt PROV}$ is its proof of security, namely, existential unforgeability under a chosen-message attack (${\tt EUF-CMA}$), assuming the hardness of solving the system formed by the public-key non-linear equations. We present a polynomial-time key-recovery attack against the first specification of ${\tt PROV}$ (v$1.0$). To do so, we remark that a small fraction of the ${\tt PROV}$ secret-key is leaked during the signature process. Adapting and extending previous works on basic ${\tt UOV}$, we show that the entire secret-key can be then recovered from such a small fraction in polynomial-time. This leads to an efficient attack against ${\tt PROV}$ that we validated in practice. For all the security parameters suggested in by the authors of ${\tt PROV}$, our attack recovers the secret-key in at most $8$ seconds. We conclude the paper by discussing the apparent mismatch between such a practical attack and the theoretical security claimed by ${\tt PROV}$ designers. Our attack is not structural but exploits that the current specification of ${\tt PROV}$ differs from the required security model. A simple countermeasure makes ${\tt PROV}$ immune against the attack presented here and led the designers to update the specification of ${\tt PROV}$ (v$1.1$).