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Fully Homomorphic Encryption for Point Numbers

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Information Security and Cryptology (Inscrypt 2016)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10143))

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Abstract

Based on the FV scheme, we construct at first fully homomorphic encryption scheme \(\mathsf {FX}\) that can homomorphically compute addition and multiplication of encrypted fixed point numbers without knowing the secret key. Then, we show that in the \(\mathsf {FX}\) scheme one can efficiently and homomorphically compare magnitude of two encrypted numbers. That is, one can compute an encryption of the greater-than bit that indicates \(x > x'\) or not, given two ciphertexts c and \(c'\) of x and \(x'\), respectively, without knowing the secret key. Finally we show that these properties of the \(\mathsf {FX}\) scheme enables us to construct a fully homomorphic encryption scheme \(\mathsf {FL}\) that can homomorphically compute addition and multiplication of encrypted floating point numbers.

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Acknowledgements

This work was supported by CREST, JST.

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Authors and Affiliations

  1. Graduate School of Information Security, Institute of Information Security, Yokohama, Japan

    Seiko Arita & Shota Nakasato

Authors
  1. Seiko Arita
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  2. Shota Nakasato
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Corresponding author

Correspondence to Seiko Arita .

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Editors and Affiliations

  1. School of Science, Hangzhou Normal University, Hangzhou, China

    Kefei Chen

  2. Institute of Information Engineering, SKLOIS, Beijing, China

    Dongdai Lin

  3. Snapchat Inc., Columbia University, New York, New York, USA

    Moti Yung

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Arita, S., Nakasato, S. (2017). Fully Homomorphic Encryption for Point Numbers. In: Chen, K., Lin, D., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2016. Lecture Notes in Computer Science(), vol 10143. Springer, Cham. https://doi.org/10.1007/978-3-319-54705-3_16

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  • DOI: https://doi.org/10.1007/978-3-319-54705-3_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-54704-6

  • Online ISBN: 978-3-319-54705-3

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