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2020•Unpublished venueRequires access

A Class of Weak Keys for the QC-MDPC Cryptosystem

Nuh Aydın, Bahattin Yıldız, Suleyman Uludag

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Abstract

The quasi-cyclic moderate-density parity-check code (QC-MDPC) cryptosystem is one of the recent variants of the original McEliece code-based cryptosystem, that has also been part of the BIKE cryptosystem, which has been submitted to NIST as a post-Quantum cryptosystem candidate. We show that in certain cases the secret key can be recovered from the public key by means of a polynomial factorization. This leads to the concept of "weak keys" for the cryptosystem. Even though the probability of choosing a weak key at random is low, we are able to find weak keys quite easily. This suggests that avoiding weak keys may be introduced as a condition in the implementation of the cryptosystem.

About this research paper

What this paper is about

The quasi-cyclic moderate-density parity-check code (QC-MDPC) cryptosystem is one of the recent variants of the original McEliece code-based cryptosystem, that has also been part of the BIKE cryptosystem, which has been submitted to NIST as a post-Quantum cryptosystem candidate. We show that in certain cases the secret key can be recovered from the public key by means of a polynomial factorization. This leads to the concept of "weak keys" for the cryptosystem. Even though the probability of choosing a weak key at random is low, we are able to find weak keys quite easily. This suggests that avoiding weak keys may be introduced as a condition in the implementation of the cryptosystem.

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OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

The quasi-cyclic moderate-density parity-check code (QC-MDPC) cryptosystem is one of the recent variants of the original McEliece code-based cryptosystem, that has also been part of the BIKE cryptosystem, which has been submitted to NIST as a post-Quantum cryptosystem candidate. We show that in certain cases the secret key can be recovered from the public key by means of a polynomial factorization. This leads to the concept of "weak keys" for the cryptosystem. Even though the probability of choosing a weak key at random is low, we are able to find weak keys quite easily. This suggests that avoiding weak keys may be introduced as a condition in the implementation of the cryptosystem.

Key concepts: McEliece cryptosystem, Cryptosystem, Hybrid cryptosystem, Computer science, Goldwasser–Micali cryptosystem, NIST, Post-quantum cryptography, Paillier cryptosystem

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