**A Reaction Attack on the QC-LDPC McEliece Cryptosystem**

*Tomas Fabsic and Viliam Hromada and Paul Stankovski and Pavol Zajac and Qian Guo and Thomas Johansson*

**Abstract: **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.

**Category / Keywords: **public-key cryptography / QC-LDPC McEliece cryptosystem, reaction attack, soft-decision decoding

**Original Publication**** (in the same form): **PQCrypto 2017

**Date: **received 31 May 2017

**Contact author: **tomas fabsic at stuba sk

**Available format(s): **PDF | BibTeX Citation

**Version: **20170601:035716 (All versions of this report)

**Short URL: **ia.cr/2017/494

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