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Integerwise Functional Bootstrapping on TFHE

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Information Security (ISC 2020)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12472))

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Abstract

We propose a new technique for implementing an arbitrary 1-variable function during a bootstrapping procedure based on an integerwise variant of the fully homomorphic encryption scheme TFHE. The integerwise TFHE was implicit in the original TFHE paper (Asiacrypt’ 2016), and Bourse et al. provided an explicit form (CRYPTO’ 2018). However, the modified integerwise TFHE scheme can perform only the homomorphic evaluations of the integer addition and the sign function, and thus, the application of the scheme is restricted.

Our scheme has diverse functionalities of the integerwise TFHE scheme. Based on our bootstrapping procedure, we propose several useful basic functions: homomorphic equality testing, multiplication by a binary number and a division algorithm. We also derive empirical results that show that our division algorithm is approximately \(3.4\)x faster than the fastest division algorithm in the literature based on fully homomorphic encryption schemes, with a runtime less than 1 s for each 4-bit integer division task.

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Notes

  1. 1.

    Precisely, although we can perform binary multiplication on \({m_{\mathrm {int}}}= -B\) or B, which is equivalent to \({m_{\mathrm {int}}}= 0\), we omit \(-B\) from the space of input \({m_{\mathrm {int}}}\) for simplicity.

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Acknowledgements

We would like to thank Benjamin Curtis and Rachel Player for their comments on early versions of the paper.

Author information

Authors and Affiliations

  1. KDDI Research, Inc., Saitama, Japan

    Hiroki Okada & Shinsaku Kiyomoto

  2. Royal Holloway, University of London, Egham, UK

    Carlos Cid

  3. Simula UiB, Bergen, Norway

    Carlos Cid

Authors
  1. Hiroki Okada
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  2. Shinsaku Kiyomoto
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  3. Carlos Cid
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Corresponding author

Correspondence to Hiroki Okada .

Editor information

Editors and Affiliations

  1. Institute of Cybersecurity and Cryptology, University of Wollongong, Wollongong, NSW, Australia

    Willy Susilo

  2. Singapore Management University, Singapore, Singapore

    Robert H. Deng

  3. Institute of Cybersecurity and Cryptology, University of Wollongong, Wollongong, NSW, Australia

    Fuchun Guo

  4. Institute of Cybersecurity and Cryptology, University of Wollongong, Wollongong, NSW, Australia

    Yannan Li

  5. Informatics, Petra Christian University, Surabaya, Indonesia

    Rolly Intan

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Okada, H., Kiyomoto, S., Cid, C. (2020). Integerwise Functional Bootstrapping on TFHE. In: Susilo, W., Deng, R.H., Guo, F., Li, Y., Intan, R. (eds) Information Security. ISC 2020. Lecture Notes in Computer Science(), vol 12472. Springer, Cham. https://doi.org/10.1007/978-3-030-62974-8_7

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  • DOI: https://doi.org/10.1007/978-3-030-62974-8_7

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