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The HQC encryption framework is a general code-based encryption scheme forwhich decryption returns a noisy version of the plaintext. Any instantiation ofthe scheme will therefore use an error-correcting procedure relying on a fixedauxiliary code. Unlike the McEliece encryption framework whose security isdirectly related to how well one can hide the structure of an error-correctingcode, the security reduction of the HQC encryption framework is independent ofthe nature of the auxiliary decoding procedure which is publicly available.What is expected from it is that the decoding algorithm is both efficient andhas a decoding failure rate which can be easily modelized and analyzed. Theoriginal error-correction procedure proposed for the HQC framework was to usetensor products of BCH codes and repetition codes. In this paper we consideranother code family for removing the error vector deriving from the generalframework: the concatenation of Reed-Muller and Reed-Solomon codes. We denotethis instantiation of the HQC framework by HQC-RMRS. These codes yield betterdecoding results than the BCH and repetition codes: overall we gain roughly17\% in the size of the key and the ciphertext, while keeping a simplemodelization of the decoding error rate. The paper also presents a simplifiedand more precise analysis of the distribution of the error vector output by theHQC protocol.

HQC-RMRS, an instantiation of the HQC encryption framework with a more efficient auxiliary error-correcting code