The complexity of MinRank

Alessio Caminata; Elisa Gorla

Paper 2019/464

The complexity of MinRank

Alessio Caminata and Elisa Gorla

Abstract

In this note, we leverage some of our previous results to produce a concise and rigorous proof for the complexity of the generalized MinRank Problem in the under-defined and well-defined case. Our main theorem recovers and extends previous results by Faugère, Safey El Din, Spaenlehauer.

Note: Final version. Theorem numbering adjusted to match the published version

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint. MINOR revision.
Keywords: MinRank Problem minors solving degree Castelnuovo-Mumford regularity Groebner bases multivariate cryptography post-quantum cryptography.
Contact author(s): caminata @ dima unige it
History: 2022-03-10: last of 4 revisions; 2019-05-10: received; See all versions
Short URL: https://ia.cr/2019/464
License: CC BY

BibTeX

@misc{cryptoeprint:2019/464,
      author = {Alessio Caminata and Elisa Gorla},
      title = {The complexity of {MinRank}},
      howpublished = {Cryptology {ePrint} Archive, Paper 2019/464},
      year = {2019},
      url = {https://eprint.iacr.org/2019/464}
}