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International Conference on Post-Quantum Cryptography

PQCrypto 2021: Post-Quantum Cryptography pp 195–214Cite as

Implementation of Lattice Trapdoors on Modules and Applications

Part of the Lecture Notes in Computer Science book series (LNSC,volume 12841)

Abstract

We develop and implement efficient Gaussian preimage sampling techniques on module lattices, which rely on the works of Micciancio and Peikert in 2012, and Micciancio and Genise in 2018. The main advantage of our implementation is its modularity, which makes it practical to use for signature schemes, but also for more advanced constructions using trapdoors such as identity-based encryption. In particular, it is easy to use in the ring or module setting, and to modify the arithmetic on \(\mathcal R_q\) (as different schemes have different conditions on q).

Relying on these tools, we also present two instantiations and implementations of proven trapdoor-based signature schemes in the module setting: GPV in the random oracle model and a variant of it in the standard model presented in Bert et al. in 2018. For that last scheme, we address a security issue and correct obsolescence problems in their implementation by building ours from scratch. To the best of our knowledge, this is the first efficient implementation of a lattice-based signature scheme in the standard model. Relying on that last signature, we also present the implementation of a standard model IBE in the module setting. We show that while the resulting schemes may not be competitive with the most efficient NIST candidates, they are practical and run on a standard laptop in acceptable time, which paves the way for practical advanced trapdoor-based constructions.

Keywords

  • Lattice-based cryptography
  • Trapdoors
  • Gaussian preimage sampling
  • Module lattices
  • Signature scheme
  • Identity-based encryption

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Acknowledgements

This work was supported by the European Union PROMETHEUS project (Horizon 2020 Research and Innovation Program, grant 780701). Lucas Prabel is funded by the Direction Générale de l’Armement (Pôle de Recherche CYBER).

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Authors and Affiliations

  1. Univ Rennes, CNRS, IRISA, Rennes, France

    Pauline Bert, Gautier Eberhart, Lucas Prabel, Adeline Roux-Langlois & Mohamed Sabt

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  1. Pauline Bert
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  2. Gautier Eberhart
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  3. Lucas Prabel
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  4. Adeline Roux-Langlois
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Correspondence to Lucas Prabel .

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  1. Seoul National University, Seoul, Korea (Republic of)

    Jung Hee Cheon

  2. Inria, Paris, France

    Jean-Pierre Tillich

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Bert, P., Eberhart, G., Prabel, L., Roux-Langlois, A., Sabt, M. (2021). Implementation of Lattice Trapdoors on Modules and Applications. In: Cheon, J.H., Tillich, JP. (eds) Post-Quantum Cryptography. PQCrypto 2021. Lecture Notes in Computer Science(), vol 12841. Springer, Cham. https://doi.org/10.1007/978-3-030-81293-5_11

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