Abstract
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.
P. Santini—The work of Paolo Santini was partially supported by Namirial S.p.A.
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Acknowledgment
The authors wish to thank Tomáš Fabšič for fruitful discussion about the FHZ attack.
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Santini, P., Baldi, M., Chiaraluce, F. (2018). Assessing and Countering Reaction Attacks Against Post-Quantum Public-Key Cryptosystems Based on QC-LDPC Codes. In: Camenisch, J., Papadimitratos, P. (eds) Cryptology and Network Security. CANS 2018. Lecture Notes in Computer Science(), vol 11124. Springer, Cham. https://doi.org/10.1007/978-3-030-00434-7_16
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