Abstract
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 \(\textsf{Com}(m;\textbf{r}) := H(m) - \mathcal {R}(\textbf{r})\) is a binding commitment, which is not the case. There is a “folklore” algorithm that can be used to, given any pair of messages, 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.
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Acknowledgements
We thank Charles Bouillaguet for pointing out that the algorithm of Sect. 5 is folklore, and providing us with a reference.
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Beullens, W. (2025). Multivariate Blind Signatures Revisited. In: Eichlseder, M., Gambs, S. (eds) Selected Areas in Cryptography – SAC 2024. SAC 2024. Lecture Notes in Computer Science, vol 15516. Springer, Cham. https://doi.org/10.1007/978-3-031-82852-2_10
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DOI: https://doi.org/10.1007/978-3-031-82852-2_10
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