International Association
for Cryptologic Research

In 2017, Petzoldt, Szepieniec, and Mohamed proposed a blind signature scheme, based on multivariate cryptography. This construction has been expanded on by several other works. This short paper shows that their construction is susceptible to an efficient polynomial-time attack. The problem is that the authors implicitly assumed that for a random multivariate quadratic map $\mathcal{R}:\mathbb{F}_q^m \rightarrow \mathbb{F}_q^m$ and a collision-resistant hash function $H: \{0,1\}^* \rightarrow \mathbb{F}_q^m$, the function $\mathsf{Com}(m;\mathbf{r}) := H(m) - \mathcal{R}(\mathbf{r})$ is a binding commitment. This paper shows that this is not the case. Given any pair of messages, one can efficiently produce a commitment that opens to both of them. We hope that by pointing out that multivariate quadratic maps are not binding, similar problems can be avoided in the future.