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A Verifiable Shuffle for the GSW Cryptosystem

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Financial Cryptography and Data Security (FC 2018)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10958))

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Abstract

We provide the first verifiable shuffle specifically for fully homomorphic schemes. A verifiable shuffle is a way to ensure that if a node receives and sends encrypted lists, the content will be the same, even though no adversary can trace individual list items through the node. Shuffles are useful in e-voting, traffic routing and other applications.

We build our shuffle on the ideas and techniques of Groth’s 2010 shuffle, but make necessary modifications for a less ideal setting where the randomness and ciphertexts admit no group structure.

The protocol relies heavily on the properties of the so-called gadget matrices, so we have included a detailed introduction to these.

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Notes

  1. 1.

    See Alperin-Sheriff and Peikert [2] for a justification of this algorithm.

  2. 2.

    An anonymous reviewer pointed out that it is important to ensure that a malicious mix server cannot mark the ciphertexts, typically by using randomness of different size, resulting in more noise. This may lead to a DoS attack unless one employ bootstrapping, but should not compromise secrecy since only the decryption service can measure noise.

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Acknowledgements

The author wishes to thank Jens Groth for his useful comments to an early version of this manuscript, as well as to the anonymous reviewers.

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Authors and Affiliations

  1. Norwegian University of Science and Technology, Trondheim, Norway

    Martin Strand

Authors
  1. Martin Strand
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Correspondence to Martin Strand .

Editor information

Editors and Affiliations

  1. Hebrew University, Jerusalem, Israel

    Aviv Zohar

  2. Technion – Israel Institute of Technology, Haifa, Israel

    Ittay Eyal

  3. University of Melbourne, Parkville, VIC, Australia

    Vanessa Teague

  4. Concordia University, Beaconsfield, QC, Canada

    Jeremy Clark

  5. Computer Science and Mathematics, Stirling University, Stirling, UK

    Andrea Bracciali

  6. Mathematical Institute, University of Oxford, Oxford, UK

    Federico Pintore

  7. Department of Mathematics, University of Trento, Trento, Italy

    Massimiliano Sala

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Strand, M. (2019). A Verifiable Shuffle for the GSW Cryptosystem. In: Zohar, A., et al. Financial Cryptography and Data Security. FC 2018. Lecture Notes in Computer Science(), vol 10958. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-58820-8_12

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  • DOI: https://doi.org/10.1007/978-3-662-58820-8_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-58819-2

  • Online ISBN: 978-3-662-58820-8

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