Programming Equation Systems of Arithmetization-Oriented Primitives with Constraints

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Arithmetization-Oriented (AO) cryptographic algorithms operate on large finite fields. The most threatening attack on such designs is the Gröbner basis attack, which solves the equation system encoded from the cryptanalysis problem. However, encoding a primitive as a system of equations is not unique, and finding the optimal one with low solving complexity is a formidable challenge. This paper presents an automated tool that transforms the problem into a Mixed-Integer Quadratic Constraint Programming (MIQCP) model. By employing integer variables and constraints, the tool tracks degree propagation and determines strategic variable introduction points. The optimal MIQCP solution yields the most efficient solving complexity, offering the lowest computational burden for the Gröbner basis attack. We construct comprehensive models for the Griffin, Anemoi, and Ciminion permutations. Our experiments demonstrate reduced Gröbner basis attack complexity, surpassing the designers’ bounds. This versatile tool can be leveraged to accurately evaluate the security of new AO designs against Gröbner basis attacks.

Original languageEnglish
Title of host publicationInformation Security and Cryptology - 21st International Conference, Inscrypt 2025, Revised Selected Papers
EditorsRongmao Chen, Robert H. Deng, Moti Yung
PublisherSpringer Science and Business Media Deutschland GmbH
Pages85-106
Number of pages22
ISBN (Print)9789819562022
DOIs
Publication statusPublished - 2026
Externally publishedYes
Event21st International Conference on Information Security and Cryptology, Inscrypt 2025 - Xi'an, China
Duration: 19 Oct 202522 Oct 2025

Publication series

NameLecture Notes in Computer Science
Volume16409 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference21st International Conference on Information Security and Cryptology, Inscrypt 2025
Country/TerritoryChina
CityXi'an
Period19/10/2522/10/25

Keywords

  • Automatic cryptanalysis
  • CICO
  • Griffin
  • Gröbner basis
  • MIQCP

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