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 ex- tensions, 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.
An Efficient Structural Attack on NIST Submission DAGS
We present an efficient key recovery attack on code based encryption schemes using some quasi-dyadic alternant codes with extension degree 2. This attack permits to break the proposal DAGS recently submitted to NIST.