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Post-quantum cryptography: a study of the decoding of QC-MDPC codes

Abstract : Post-quantum cryptography aims at securing exchanges against an adversary with a quantum computer. One approach considered to achieve post-quantum public key encryption relies on hard problems in coding theory. The key encapsulation mechanism BIKE, submitted to the NIST post-quantum cryptography standardization process, uses QC-MDPC codes whose quasi-cyclicity allows for a compact key representation. However, their decoding algorithms have a non-zero probability of failure (DFR) and this can be a security concern as demonstrated by Guo, Johansson and Stankovski. This work therefore focuses on the implementation and security of BIKE from the decoder's perspective. First, we design new algorithms that drastically reduce the DFR. These algorithms introduce features of soft-decision decoders into hard-decision decoders, thus bringing the performance of the former and preserving the simplicity of the latter. Second, we develop probabilistic models to predict the DFR in areas beyond the reach of simulations. The first model takes into account the regularity of the code, it is very accurate but can only analyze one iteration of a parallel decoder. The second model is based on a Markovian assumption of the behavior of a complete sequential decoder. Finally, we derive a DFR extrapolation method for which we establish confidence intervals. We then evaluate the adequacy of this extrapolation with the structural characteristics of the code that can affect the decoding process with weak keys or error floors.
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Contributor : Valentin Vasseur Connect in order to contact the contributor
Submitted on : Tuesday, June 8, 2021 - 6:51:24 PM
Last modification on : Wednesday, June 8, 2022 - 12:50:08 PM
Long-term archiving on: : Thursday, September 9, 2021 - 8:29:57 PM


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  • HAL Id : tel-03254461, version 1



Valentin Vasseur. Post-quantum cryptography: a study of the decoding of QC-MDPC codes. Cryptography and Security [cs.CR]. Université de Paris, 2021. English. ⟨tel-03254461⟩



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