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Decryption Failure Attacks on IND-CCA Secure Lattice-Based Schemes

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Public-Key Cryptography – PKC 2019 (PKC 2019)

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Abstract

In this paper we investigate the impact of decryption failures on the chosen-ciphertext security of lattice-based primitives. We discuss a generic framework for secret key recovery based on decryption failures and present an attack on the NIST Post-Quantum Proposal ss-ntru-pke. Our framework is split in three parts: First, we use a technique to increase the failure rate of lattice-based schemes called failure boosting. Based on this technique we investigate the minimal effort for an adversary to obtain a failure in three cases: when he has access to a quantum computer, when he mounts a multi-target attack or when he can only perform a limited number of oracle queries. Secondly, we examine the amount of information that an adversary can derive from failing ciphertexts. Finally, these techniques are combined in an overall analysis of the security of lattice based schemes under a decryption failure attack. We show that an attacker could significantly reduce the security of lattice based schemes that have a relatively high failure rate. However, for most of the NIST Post-Quantum Proposals, the number of required oracle queries is above practical limits. Furthermore, a new generic weak-key (multi-target) model on lattice-based schemes, which can be viewed as a variant of the previous framework, is proposed. This model further takes into consideration the weak-key phenomenon that a small fraction of keys can have much larger decoding error probability for ciphertexts with certain key-related properties. We apply this model and present an attack in detail on the NIST Post-Quantum Proposal – ss-ntru-pke – with complexity below the claimed security level.

This paper is the result of a merge of [14] and [21].

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Notes

  1. 1.

    The software is available at https://github.com/danversjp/failureattack.

  2. 2.

    The software is available at https://github.com/atneit/ss-ntru-pke-attack-simulation.

  3. 3.

    The error can occur in both directions. We omit the term \(\left( 1 - \text{ erf }(\frac{q/4 + C_{1}}{\sqrt{2(2N-2)}\sigma ^{2}})\right) \cdot \frac{1}{2}\) as it is negligible compared with \(\left( 1 - \text{ erf }(\frac{q/4 - C_{1}}{\sqrt{2(2N-2)}\sigma ^{2}})\right) \cdot \frac{1}{2}\) for \(C_{1}\) a very big positive integer.

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Acknowledgements

The authors would like to thank Tancrède Lepoint and the anonymous reviewers for their helpful comments. They would also like to thank Andreas Hülsing for interesting discussions. This work was supported in part by the Research Council KU Leuven: C16/15/058, by the European Commission through the Horizon 2020 research and innovation programme Cathedral ERC Advanced Grant 695305, by the Research Council KU Leuven grants C14/18/067 and STG/17/019, by the Norwegian Research Council (Grant No. 247742/070), by the Swedish Research Council (Grant No. 2015-04528), by the Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation, and by the Swedish Foundation for Strategic Research (SSF) project RIT17-0005.

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D’Anvers, JP., Guo, Q., Johansson, T., Nilsson, A., Vercauteren, F., Verbauwhede, I. (2019). Decryption Failure Attacks on IND-CCA Secure Lattice-Based Schemes. In: Lin, D., Sako, K. (eds) Public-Key Cryptography – PKC 2019. PKC 2019. Lecture Notes in Computer Science(), vol 11443. Springer, Cham. https://doi.org/10.1007/978-3-030-17259-6_19

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