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On the Effect of Projection on Rank Attacks in Multivariate Cryptography



Morten Oygarden, Daniel Smith-Tone, Javier Verbel


The multivariate scheme HFEv- used to be considered a promising candidate for a post-quantum signature system. First suggested in the early 2000s, a version of the scheme made it to the third round of the ongoing NIST post-quantum standardization process. In late 2020, the system suffered from an efficient rank attack due to Tao, Petzoldt, and Ding. In this paper, we inspect how this recent rank attack is affected by the projection modification. Somewhat analogically, this modification was introduced to secure the signature scheme PFLASH against its predecessor's attacks. We prove upper bounds for the rank of projected HFEv- (pHFEv-) and PFLASH under the new attack, which are tight for the experiments we have performed. We conclude that projection could be a useful tool in protecting against this recent cryptanalysis.
Cryptology ePrint Archive


post-quantum cryptography, multivariate cryptography, minrank


Oygarden, M. , Smith-Tone, D. and Verbel, J. (2021), On the Effect of Projection on Rank Attacks in Multivariate Cryptography, Cryptology ePrint Archive, [online],, (Accessed July 18, 2024)


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Created May 19, 2021, Updated November 29, 2022