Guo et al. recently presented a reaction attack against the QC-MDPC McEliece cryptosystem. Their attack is based on the observation that when a bit-flipping decoding algorithm is used in the QC-MDPC McEliece, then there exists a dependence between the secret matrix H and the failure probability of the bit-flipping algorithm. This dependence can be exploited to reveal the matrix H which constitutes the private key in the cryptosystem. It was conjectured that such dependence is present even when a soft-decision decoding algorithm is used instead of a bit-flipping algorithm. This paper shows that a similar dependence between the secret matrix H and the failure probability of a decoding algorithm is also present in the QC-LDPC McEliece cryptosystem. Unlike QC-MDPC McEliece, the secret key in QC-LDPC McEliece also contains matrices S and Q in addition to the matrix H. We observe that there also exists a dependence between the failure probability and the matrix Q. We show that these dependences leak enough information to allow an attacker to construct a sparse parity-check matrix for the public code. This parity-check matrix can then be used for decrypting ciphertexts. We tested the attack on an implementation of the QC-LDPC McEliece using a soft-decision decoding algorithm. Thus we also confirmed that soft-decision decoding algorithms can be vulnerable to leaking information about the secret key.
CITATION STYLE
Fabšič, T., Hromada, V., Stankovski, P., Zajac, P., Guo, Q., & Johansson, T. (2017). A reaction attack on the QC-LDPC mceliece cryptosystem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10346 LNCS, pp. 51–68). Springer Verlag. https://doi.org/10.1007/978-3-319-59879-6_4
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