[Resource Topic] 2023/1064: Decoding Quasi-Cyclic codes is NP-complete

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Decoding Quasi-Cyclic codes is NP-complete

Authors: Ernesto Dominguez Fiallo, Pablo Freyre Arrozarena, Luis Ramiro Piñeiro


We prove that the problem of decoding a Quasi-Cyclic (QC) code is NP-hard, and the corresponding decision problem is NP-complete. Our proof is based on a new characterization of quasi-cyclic codes closely related to linear random codes. We also discuss the cryptographic significance of this result.

ePrint: https://eprint.iacr.org/2023/1064

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