On the independence heuristic in the dual attack - Bashiri Kaveh; Wiemers Andreas (Journal of Mathematical Cryptology)
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 bounded-distance decoding (BDD) problem or the learning with error problem. In this work, we contribute to the analysis of an attack category against these problems called dual attack. 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.