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Conference Papers Year : 2022

On Codes and Learning With Errors over Function Fields


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.

Dates and versions

hal-03597834 , version 1 (04-03-2022)


Attribution - CC BY 4.0



Maxime Bombar, Alain Couvreur, Thomas Debris-Alazard. On Codes and Learning With Errors over Function Fields. CRYPTO 2022, Aug 2022, Santa Barbara (CA), United States. pp.513-540, ⟨10.1007/978-3-031-15979-4_18⟩. ⟨hal-03597834⟩
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