Cryptology ePrint Archive: Report 2020/1232

On the Existence of Weak Keys for QC-MDPC Decoding

Nicolas Sendrier and Valentin Vasseur

Abstract: We study in this work a particular class of QC-MDPC codes for which the decoding failure rate is significantly larger than for typical QC-MDPC codes of same parameters. Our purpose is to figure out whether the existence of such weak codes impacts the security of cryptographic schemes using QC-MDPC codes as secret keys. A class of weak keys was exhibited in [DGK19]. We generalize it and show that, though their Decoding Failure Rate (DFR) is higher than normal, the set is not large enough to contribute significantly to the average DFR. It follows that with the proper semantically secure transform [HHK17], those weak keys do not affect the IND-CCA status of key encapsulation mechanisms, like BIKE, which are using QC-MDPC codes.

Category / Keywords: public-key cryptography / code-based cryptography, QC-MDPC codes, BIKE, bit flipping algorithm, weak keys

Date: received 6 Oct 2020

Contact author: nicolas sendrier at inria fr, valentin vasseur@inria fr

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Version: 20201009:112722 (All versions of this report)

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