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In this paper we study recent reaction attacks against QC-LDPC and QC-MDPCcode-based cryptosystems, which allow an opponent to recover the privateparity-check matrix through its distance spectrum by observing a sufficientlyhigh number of decryption failures. We consider a special class of codes, knownas monomial codes, to form private keys with the desirable property of having aunique and complete distance spectrum. We verify that for these codes theproblem of recovering the secret key from the distance spectrum is equivalentto that of finding cliques in a graph, and use this equivalence to prove thatcurrent reaction attacks are not applicable when codes of this type are used inthe McEliece cryptosystem.

Hindering reaction attacks by using monomial codes in the McEliece cryptosystem