On the independence heuristic in the dual attack

• Published in: Journal of mathematical cryptology Vol. 19; no. 1; pp. 403 - 15
• Main Authors: Bashiri, Kaveh, Wiemers, Andreas
• Format: Journal Article
• Language: English
• Published: Berlin De Gruyter 03.07.2025; Walter de Gruyter GmbH
• Subjects: 06B99; 94A60; cryptanalysis; dual attack; Estimates; lattices; learning with errors; Quantum computers; Quantum cryptography
• ISSN: 1862-2984; 1862-2976; 1862-2984
• DOI: 10.1515/jmc-2024-0028

Post-quantum cryptography deals with the development and analysis of cryptographic schemes that are assumed to be secure even against attackers with access to a powerful quantum computer. Along the main candidates for quantum-safe solutions are cryptographic schemes, whose security is based on classic lattice problems such as the or the . In this work, we contribute to the analysis of an attack category against these problems called . In recent years, a lot of notable progress was achieved in this topic. Our first contribution is to provide theoretical counterarguments against a so-called independence assumption, which was used in earlier works on this attack, and which was shown in a previous work to be contradicting practical experiments. Then, we provide estimates on the success probability and the cost of the dual attack against the decisional version of the BDD problem. These estimates are derived both rigorously and heuristically. Finally, we also provide experimental evidence that confirms these results.