## Cryptology ePrint Archive: Report 2019/731

On the Complexity of Superdetermined'' Minrank Instances

Javier Verbel and John Baena and Daniel Cabarcas and 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.

Category / Keywords: foundations / Minrank problem and Multivariate and Cryptanalysis and HFE

Original Publication (with minor differences): PQC2019

Date: received 19 Jun 2019

Contact author: javerbelh at unal edu co

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2019/731

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