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Public-Key Encryption from Homogeneous CLWE

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Theory of Cryptography (TCC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13748))

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Abstract

The homogeneous continuous LWE (hCLWE) problem is to distinguish samples of a specific high-dimensional Gaussian mixture from standard normal samples. It was shown to be at least as hard as Learning with Errors, but no reduction in the other direction is currently known.

We present four new public-key encryption schemes based on the hardness of hCLWE, with varying tradeoffs between decryption and security errors, and different discretization techniques. Our schemes yield a polynomial-time algorithm for solving hCLWE using a Statistical Zero-Knowledge oracle.

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Notes

  1. 1.

    A distinguishing problem is in class \(\mathcal {C}\) if there is an algorithm in \(\mathcal {C}\) that accepts at least 2/3 of the yes instances and rejects at least 2/3 of the no instances.

  2. 2.

    In the body of the paper we use the notation \(1/\gamma ' = \gamma /(\beta ^2 + \gamma ^2)\) for the period of the hCLWE hidden direction. As the difference between \(1/\gamma '\) and \(1/\gamma \) is small we make no distinction between the two in this overview.

  3. 3.

    By relying on discretized encryption instead we can prove the stronger claim of coNISZK membership [GSV99] and improve the sample complexity. Details will be spelled out in the final version.

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Acknowledgements

We are grateful to Devika Sharma and Luca Trevisan for their insight and advice and to an anonymous reviewer for helpful comments.

This work was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 101019547). The first author was additionally supported by RGC GRF CUHK14209920 and the fourth author was additionally supported by ISF grant No. 1399/17, project PROMETHEUS (Grant 780701), and Cariplo CRYPTONOMEX grant.

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Authors and Affiliations

  1. Chinese University of Hong Kong, Hong Kong, China

    Andrej Bogdanov

  2. Institute of Science and Technology Austria, Klosterneuburg, Austria

    Miguel Cueto Noval & Charlotte Hoffmann

  3. Bocconi University, Milan, Italy

    Alon Rosen

  4. Reichman University, Herzliya, Israel

    Alon Rosen

Authors
  1. Andrej Bogdanov
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  2. Miguel Cueto Noval
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  3. Charlotte Hoffmann
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  4. Alon Rosen
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Corresponding author

Correspondence to Miguel Cueto Noval .

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Editors and Affiliations

  1. Ruhr University Bochum, Bochum, Germany

    Eike Kiltz

  2. Massachusetts Institute of Technology, Cambridge, MA, USA

    Vinod Vaikuntanathan

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Bogdanov, A., Cueto Noval, M., Hoffmann, C., Rosen, A. (2022). Public-Key Encryption from Homogeneous CLWE. In: Kiltz, E., Vaikuntanathan, V. (eds) Theory of Cryptography. TCC 2022. Lecture Notes in Computer Science, vol 13748. Springer, Cham. https://doi.org/10.1007/978-3-031-22365-5_20

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  • DOI: https://doi.org/10.1007/978-3-031-22365-5_20

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