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An Analysis of the Learning Parity with Noise Assumption Against Fault Attacks

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Smart Card Research and Advanced Applications (CARDIS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10146))

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Abstract

We provide a first security evaluation of LPN-based implementations against fault attacks. Our main result is to show that such implementations inherently have good features to resist these attacks. First, some prominent fault models (e.g. where an adversary flips bits in an implementation) are ineffective against LPN. Second, attacks taking advantage of more advanced fault models (e.g. where an adversary sets bits in an implementation) require significantly more samples than against standard symmetric cryptographic primitives such as block ciphers. Furthermore, the sampling complexity of these attacks strongly suffers from inaccurate fault insertion. Combined with the previous observation that the inner products computed in LPN implementations have an interesting algebraic structure for side-channel resistance via masking, these results therefore suggest LPN-based primitives as interesting candidates for physically secure implementations.

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Notes

  1. 1.

    Intuitively, the independence assumption is reasonable since what we require is that for each key candidate \(\mathbf k ^{*}\) there exists enough plaintexts belonging to \(\mathbb {Z}^d_2 \setminus V(\langle \mathbf x \vert \mathbf k \oplus \mathbf k ^{*}\rangle )\), with \(V(\langle \mathbf x \vert \mathbf k \oplus \mathbf k ^{*}\rangle )\) the hyperplane defined by the equation \(\langle \mathbf x \vert \mathbf k \oplus \mathbf k ^{*}\rangle =0\).

  2. 2.

    Defined as the distance from the uniform probability \(\frac{1}{2}\).

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Acknowledgments

François-Xavier Standaert is a research associate of the Belgian Fund for Scientific Research (F.R.S.-FNRS). This work has been funded in parts by the ERC project 280141 and by the ARC project NANOSEC.

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Authors and Affiliations

  1. ICTEAM/ELEN/Crypto Group, Université catholique de Louvain, Louvain-la-neuve, Belgium

    Francesco Berti & François-Xavier Standaert

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  1. Francesco Berti
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Correspondence to Francesco Berti .

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Editors and Affiliations

  1. Bonn-Rhein-Sieg University of Applied Sciences, St. Augustin, Germany

    Kerstin Lemke-Rust

  2. Cryptography Research Inc. , San Francisco, California, USA

    Michael Tunstall

A Additional figures

A Additional figures

Fig. 8.
figure 8

Inaccurate fault attacks against a \(n=1024\)-bit key with \(\varDelta =8\).

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Berti, F., Standaert, FX. (2017). An Analysis of the Learning Parity with Noise Assumption Against Fault Attacks. In: Lemke-Rust, K., Tunstall, M. (eds) Smart Card Research and Advanced Applications. CARDIS 2016. Lecture Notes in Computer Science(), vol 10146. Springer, Cham. https://doi.org/10.1007/978-3-319-54669-8_15

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