Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Improved Cryptanalysis of HFEv- via Projection



Jintai Ding, Ray Perlner, Albrecht R. Petzoldt, Daniel Smith-Tone


The HFEv- signature scheme is one of the most studied multivariate schemes and one of the major candidates for the upcoming standardization of post-quantum digital signature schemes. In this paper, we propose three new attack strategies against HFEv-, each of them using the idea of projection. Especially our third attack is very effective and is, for some parameter sets, the most efficient known attack against HFEv-. Furthermore, our attack requires much less memory than direct and rank attacks. By our work, we therefore give new insights in the security of the HFEv- signature scheme and restrictions for the parameter choice of a possible future standardized HFEv- instance.
Proceedings Title
PQCrypto 2018: The Ninth International Conference on Post-Quantum Cryptography
Conference Dates
April 9-11, 2018
Conference Location
Fort Lauderdale, FL, US


Multivariate Cryptography, HFEv-, MinRank, Grobner Basis, Projection


Ding, J. , Perlner, R. , Petzoldt, A. and Smith-Tone, D. (2018), Improved Cryptanalysis of HFEv- via Projection, PQCrypto 2018: The Ninth International Conference on Post-Quantum Cryptography, Fort Lauderdale, FL, US, [online],, (Accessed May 24, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created March 31, 2018, Updated October 12, 2021