Hindering reaction attacks by using monomial codes in the McEliece cryptosystem
This addresses security risks in post-quantum cryptography for users of McEliece-based systems, though it is incremental as it builds on existing code structures.
The paper tackles the vulnerability of QC-LDPC and QC-MDPC code-based cryptosystems to reaction attacks by using monomial codes, proving that these attacks are not applicable due to the equivalence of key recovery to finding cliques in a graph.
In this paper we study recent reaction attacks against QC-LDPC and QC-MDPC code-based cryptosystems, which allow an opponent to recover the private parity-check matrix through its distance spectrum by observing a sufficiently high number of decryption failures. We consider a special class of codes, known as monomial codes, to form private keys with the desirable property of having a unique and complete distance spectrum. We verify that for these codes the problem of recovering the secret key from the distance spectrum is equivalent to that of finding cliques in a graph, and use this equivalence to prove that current reaction attacks are not applicable when codes of this type are used in the McEliece cryptosystem.