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.

Hindering reaction attacks by using monomial codes in the McEliece cryptosystem / Santini, Paolo; Baldi, Marco; Cancellieri, Giovanni; Chiaraluce, Franco. - ELETTRONICO. - (2018), pp. 951-955. (Intervento presentato al convegno International Symposium on Information Theory tenutosi a Vail, CO, USA nel 17-22 June 2018) [10.1109/ISIT.2018.8437553].

Hindering reaction attacks by using monomial codes in the McEliece cryptosystem

Paolo Santini
;
Marco Baldi;Giovanni Cancellieri;Franco Chiaraluce
2018-01-01

Abstract

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.
2018
978-1-5386-4780-6
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/258706
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