  Code-based public-key cryptosystems based on QC-LDPC and QC-MDPC codes are
promising post-quantum candidates to replace quantum vulnerable classical
alternatives. However, a new type of attacks based on Bob's reactions have
recently been introduced and appear to significantly reduce the length of the
life of any keypair used in these systems. In this paper we estimate the
complexity of all known reaction attacks against QC-LDPC and QC-MDPC code-based
variants of the McEliece cryptosystem. We also show how the structure of the
secret key and, in particular, the secret code rate affect the complexity of
these attacks. It follows from our results that QC-LDPC code-based systems can
indeed withstand reaction attacks, on condition that some specific decoding
algorithms are used and the secret code has a sufficiently high rate.
