Oygarden, M.
, Smith-Tone, D.
and Verbel, J.
(2021),
On the Effect of Projection on Rank Attacks in Multivariate Cryptography, Cryptology ePrint Archive, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=932164, https://eprint.iacr.org/2021/655
(Accessed April 23, 2024)
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On the Effect of Projection on Rank Attacks in Multivariate Cryptography
Published
Author(s)
Morten Oygarden, , Javier Verbel
Abstract
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.Citation
Cryptology ePrint Archive
Volume
2021
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Pub Type
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Keywords
post-quantum cryptography, multivariate cryptography, minrank
Citation
Created May 19, 2021, Updated November 29, 2022