A Class of Weak Keys for the QC-MDPC Cryptosystem

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.