期刊
ADVANCES IN CRYPTOLOGY - CRYPTO 2022, PT II
卷 13508, 期 -, 页码 513-540出版社
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1007/978-3-031-15979-4_18
关键词
Code-based cryptography; Search to decision reductions; LWE; Function fields; Carlitz modules
资金
- French Agence Nationale de la Recherche through ANR JCJC COLA [ANR-21-CE39-0011]
- ANR BARRACUDA [ANR-21-CE39-0009BARRACUDA]
- Agence Nationale de la Recherche (ANR) [ANR-21-CE39-0011] Funding Source: Agence Nationale de la Recherche (ANR)
We propose a function field version of the structured decoding problem for linear codes in the lattice-based cryptography setting. This new framework provides another perspective on structured codes such as quasi-cyclic codes and strengthens the connection between lattice-based and code-based cryptography.
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 multiparty computation and to an authentication protocol.
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