On the Complexity of ``Superdetermined'' Minrank Instances

Javier Verbel; John Baena; Daniel Cabarcas; Ray Perlner; Daniel Smith-Tone

Paper 2019/731

On the Complexity of ``Superdetermined'' Minrank Instances

Javier Verbel, John Baena, Daniel Cabarcas, Ray Perlner, and Daniel Smith-Tone

Abstract

The Minrank (MR) problem is a computational problem closely related to attacks on code- and multivariate-based schemes. In this paper we revisit the so-called Kipnis-Shamir (KS) approach to this problem. We extend previous complexity analysis by exposing non-trivial syzygies through the analysis of the Jacobian of the resulting system, with respect to a group of variables. We focus on a particular set of instances that yield a very overdetermined system which we refer to as ``superdetermined''. We provide a tighter complexity estimate for such instances and discuss its implications for the key recovery attack on some multivariate schemes. For example, in HFE the speedup is roughly a square root.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Published elsewhere. Minor revision. PQC2019
Contact author(s): javerbelh @ unal edu co
History: 2019-06-20: received
Short URL: https://ia.cr/2019/731
License: CC BY

BibTeX

@misc{cryptoeprint:2019/731,
      author = {Javier Verbel and John Baena and Daniel Cabarcas and Ray Perlner and Daniel Smith-Tone},
      title = {On the Complexity of ``Superdetermined'' Minrank Instances},
      howpublished = {Cryptology ePrint Archive, Paper 2019/731},
      year = {2019},
      note = {\url{https://eprint.iacr.org/2019/731}},
      url = {https://eprint.iacr.org/2019/731}
}