Paper 2022/269
On Codes and Learning With Errors over Function Fields
, Institut Polytechnique de Paris, Inria Saclay - Île-de-France Research Centre, Inria Saclay - Île-de-France Research Centre, Institut Polytechnique de Paris, Inria Saclay - Île-de-France Research Centre, Institut Polytechnique de ParisAbstract
It is a long standing open problem to find search to decision reductions for structured versions of the decoding problem of linear codes. Such results in the lattice-based setting have been carried out using number fields: Polynomial–LWE, Ring–LWE, Module–LWE and so on. We propose a function field version of the LWE problem. This new framework leads to another point of view on structured codes, e.g. quasi-cyclic codes, strengthening the connection between lattice-based and code-based cryptography. In particular, we obtain the first search to decision reduction for structured codes. Following the historical constructions in lattice–based cryptography, we instantiate our construction with function fields analogues of cyclotomic fields, namely Carlitz extensions, leading to search to decision reductions on various versions of Ring-LPN, which have applications to secure multi party computation and to an authentication protocol.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- A minor revision of an IACR publication in CRYPTO 2022
- DOI
- 10.1007/978-3-031-15979-4_18
- Keywords
- Code-based cryptographySearch to decision reductionsLWEFunction fieldsCarlitz modules
- Contact author(s)
-
maxime bombar @ inria fr
alain couvreur @ inria fr
thomas debris @ inria fr - History
- 2023-10-27: revised
- 2022-03-02: received
- See all versions
- Short URL
- https://ia.cr/2022/269
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2022/269,
author = {Maxime Bombar and Alain Couvreur and Thomas Debris-Alazard},
title = {On Codes and Learning With Errors over Function Fields},
howpublished = {Cryptology ePrint Archive, Paper 2022/269},
year = {2022},
doi = {10.1007/978-3-031-15979-4_18},
note = {\url{https://eprint.iacr.org/2022/269}},
url = {https://eprint.iacr.org/2022/269}
}
