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

Elisa Gorla; Daniela Mueller; Christophe Petit

Paper 2020/1376

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

Elisa Gorla, 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.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Journal of Symbolic Computation
DOI: 10.1016/j.jsc.2020.07.011
Keywords: multivariate cryptography Groebner bases HFE (fake) Weil descent last fall degree solving degree
Contact author(s): elisa gorla @ unine ch
History: 2020-11-10: received
Short URL: https://ia.cr/2020/1376
License: CC BY

BibTeX

@misc{cryptoeprint:2020/1376,
      author = {Elisa Gorla and Daniela Mueller and Christophe Petit},
      title = {Stronger bounds on the cost of computing Groebner bases for HFE systems},
      howpublished = {Cryptology ePrint Archive, Paper 2020/1376},
      year = {2020},
      doi = {10.1016/j.jsc.2020.07.011},
      note = {\url{https://eprint.iacr.org/2020/1376}},
      url = {https://eprint.iacr.org/2020/1376}
}