The regular multivariate quadratic problem
Year: 2025
Type: preprint
Abstract: In this work, we introduce a novel variant of the multivariate quadratic problem, which is at the core of one of the most promising post-quantum alternatives: multivariate cryptography. In this variant, the solution of a given multivariate quadratic system must also be regular, i.e. if it is split into multiple blocks of consecutive entries with the same fixed length, then each block has only one nonzero entry. We prove the NP-completeness of this variant and show similarities and differences with other computational problems used in cryptography. Then we analyze its hardness by reviewing the most common solvers for polynomial systems over finite fields, derive asymptotic formulas for the corresponding complexities and compare the different approaches.
Source: arXiv (Cornell University)
Authors: Joux, Antoine, Mora, Rocco
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6929424313
Cites:
Cited by:
Related to: