Quantum security analysis of Wave

Johanna Loyer

Paper 2023/1263

Quantum security analysis of Wave

Johanna Loyer

, French Institute for Research in Computer Science and Automation

Abstract

Wave is a code-based digital signature scheme. Its hardness relies on the unforgeability of the signature and the indistinguishability of its public key, a parity check matrix of a ternary $(U, U+V)$-code. The best known attacks involve solving the Decoding Problem using the Information Set Decoding algorithm (ISD) to defeat these two problems. Our main contribution is the description of a quantum smoothed Wagner’s algorithm within the ISD framework, which improves the forgery attack on Wave in the quantum setting. We also recap the best known key and forgery attacks against Wave in both classical and quantum settings. For each one, we express their time complexity as function of Wave parameters and deduce its claimed security.

Metadata

Available format(s): PDF
Publication info: A minor revision of an IACR publication in CIC 2025
Keywords: Decoding problem Code-based cryptography Information Set Decoding Quantum cryptanalysis
Contact author(s): johanna loyer @ gmail com
History: 2025-12-04: last of 2 revisions; 2023-08-21: received; See all versions
Short URL: https://ia.cr/2023/1263
License: CC BY

BibTeX

@misc{cryptoeprint:2023/1263,
      author = {Johanna Loyer},
      title = {Quantum security analysis of Wave},
      howpublished = {Cryptology {ePrint} Archive, Paper 2023/1263},
      year = {2023},
      url = {https://eprint.iacr.org/2023/1263}
}