Work

ANF-Based Satisfiability for Weil-Descent Cryptographic Attacks

Year: 2025

Type: conference-paper

Abstract: In recent years, SAT solvers have been increasingly used in cryptanalysis, for performing attacks both on symmetric and asymmetric schemes. More specifically, they are employed whenever one needs to compute a valid assignment for a logical formula when running the attack. Most often, these formulae are initially represented in Algebraic Normal Form (ANF). Solvers dedicated to solving such instances translate the input formulae into a conjunction of CNF and XOR clauses and use different techniques such as XOR recovery and manipulation and Gaussian elimination. In this paper, we aim to build a solver able to reason directly on ANF formulae derived from attacks using Weil descent on Semaev polynomials of elliptic curves, while integrating dedicated lazy structures inspired from SAT solvers.

Source: International Conference on Control, Decision and Information Technologies (CoDIT)

DOI: 10.1109/codit66093.2025.11321693

Authors: Anthony Blomme, Sami Cherif, Sorina Ionica, Gilles Dequen

Institutions: Modélisation, information et systèmes, Université d'Artois, Université de Picardie Jules Verne

Language: English

Topic: Polynomial and algebraic computation

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Awards: Algebraic cryptanalysis for post-quantum cryptography, Branching for Satisfiability and Beyond