About Low DFR for QC-MDPC Decoding

Nicolas Sendrier (1) , Valentin Vasseur (1, 2)

1 COSMIQ - Cryptologie symétrique, cryptologie fondée sur les codes et information quantique
2 UPCité - Université Paris Cité

McEliece-like code-based key exchange mechanisms using QC-MDPC codes can reach IND-CPA security under hardness assumptions from coding theory, namely quasi-cyclic syndrome decoding and quasi-cyclic codeword finding. To reach higher security requirements, like IND-CCA security, it is necessary in addition to prove that the decoding failure rate (DFR) is negligible, for some decoding algorithm and a proper choice of parameters. Getting a formal proof of a low DFR is a difficult task. Instead, we propose to ensure this low DFR under some additional security assumption on the decoder. This assumption relates to the asymptotic behavior of the decoder and is supported by several other works. We define a new decoder, Backflip, which features a low DFR. We evaluate the Backflip decoder by simulation and extrapolate its DFR under the decoder security assumption. We also measure the accuracy of our simulation data, in the form of confidence intervals, using standard techniques from communication systems.

Mots clés: Public key cryptography; Code based cryptography; Post-quantum cryptography; QC-MDPC codes; Bit flipping algorithm; BIKE

Domaines: Cryptographie et sécurité [cs.CR]; Théorie de l'information [cs.IT]

Nicolas Sendrier, Valentin Vasseur. About Low DFR for QC-MDPC Decoding. PQCrypto 2020 - Post-Quantum Cryptography 11th International Conference, Sep 2020, Paris / Virtual, France. pp.20--34, ⟨10.1007/978-3-030-44223-1_2⟩. ⟨hal-03139672⟩