Paper 2025/018
On the Independence Assumption in Quasi-Cyclic Code-Based Cryptography
Abstract
Cryptography based on the presumed hardness of decoding codes -- i.e., code-based cryptography -- has recently seen increased interest due to its plausible security against quantum attackers. Notably, of the four proposals for the NIST post-quantum standardization process that were advanced to their fourth round for further review, two were code-based. The most efficient proposals -- including HQC and BIKE, the NIST submissions alluded to above -- in fact rely on the presumed hardness of decoding structured codes. Of particular relevance to our work, HQC is based on quasi-cyclic codes, which are codes generated by matrices consisting of two cyclic blocks. In particular, the security analysis of HQC requires a precise understanding of the Decryption Failure Rate (DFR), whose analysis relies on the following heuristic: given random "sparse" vectors $e_1,e_2$ (say, each coordinate is i.i.d. Bernoulli) multiplied by fixed "sparse" quasi-cyclic matrices $A_1,A_2$, the weight of resulting vector $e_1A_1+e_2A_2$ is very concentrated around its expectation. In the documentation, the authors model the distribution of $e_1A_1+e_2A_2$ as a vector with independent coordinates (and correct marginal distribution). However, we uncover cases where this modeling fails. While this does not invalidate the (empirically verified) heuristic that the weight of $e_1A_1+e_2A_2$ is concentrated, it does suggest that the behavior of the noise is a bit more subtle than previously predicted. Lastly, we also discuss implications of our result for potential worst-case to average-case reductions for quasi-cyclic codes.
Metadata
- Available format(s)
- Category
- Foundations
- Publication info
- Preprint.
- Keywords
- code-based cryptographyring-lpnquasi-cyclic codesworst-case to average-case reduction
- Contact author(s)
-
maxime bombar @ math u-bordeaux fr
n a resch @ uva nl
e wiedijk @ uva nl - History
- 2025-01-06: approved
- 2025-01-05: received
- See all versions
- Short URL
- https://ia.cr/2025/018
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2025/018, author = {Maxime Bombar and Nicolas Resch and Emiel Wiedijk}, title = {On the Independence Assumption in Quasi-Cyclic Code-Based Cryptography}, howpublished = {Cryptology {ePrint} Archive, Paper 2025/018}, year = {2025}, url = {https://eprint.iacr.org/2025/018} }