Cryptology ePrint Archive: Report 2020/1376

Stronger bounds on the cost of computing Groebner bases for HFE systems

Elisa Gorla and Daniela Mueller and Christophe Petit

Abstract: We give upper bounds for the solving degree and the last fall degree of the polynomial system associated to the HFE (Hidden Field Equations) cryptosystem. Our bounds improve the known bounds for this type of systems. We also present new results on the connection between the solving degree and the last fall degree and prove that, in some cases, the solving degree is independent of coordinate changes.

Category / Keywords: public-key cryptography / multivariate cryptography, Groebner bases, HFE, (fake) Weil descent, last fall degree, solving degree

Original Publication (in the same form): Journal of Symbolic Computation

Date: received 2 Nov 2020

Contact author: elisa gorla at unine ch

Available format(s): PDF | BibTeX Citation

Version: 20201110:120047 (All versions of this report)

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