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A Scalable Implementation of Fully Homomorphic Encryption Built on NTRU

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  • First Online:
Financial Cryptography and Data Security (FC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8438))

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Abstract

In this paper we report on our work to design, implement and evaluate a Fully Homomorphic Encryption (FHE) scheme. Our FHE scheme is an NTRU-like cryptosystem, with additional support for efficient key switching and modulus reduction operations to reduce the frequency of bootstrapping operations. Ciphertexts in our scheme are represented as matrices of 64-bit integers. The basis of our design is a layered software services stack to provide high-level FHE operations supported by lower-level lattice-based primitive implementations running on a computing substrate. We implement and evaluate our FHE scheme to run on a commodity CPU-based computing environment. We implemented our FHE scheme to run in a compiled C environment and use parallelism to take advantage of multi-core processors. We provide experimental results which show that our FHE implementation provides at least an order of magnitude improvement in runtime as compared to recent publicly known evaluation results of other FHE software implementations.

Sponsored by the Defense Advanced Research Projects Agency (DARPA) and the Air Force Research Laboratory (AFRL) under Contract No. FA8750-11-C-0098. The views expressed are those of the authors and do not necessarily reflect the official policy or position of the Department of Defense or the U.S. Government. Distribution Statement “A”. (Approved for Public Release, Distribution Unlimited.)

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Acknowledgement

The authors wish to acknowledge the helpful feedback and guidance of Prof. Chris Peikert in preparing the material discussed in this paper.

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Authors and Affiliations

  1. Raytheon BBN Technologies, 10 Moulton St., Cambridge, MA, USA

    Kurt Rohloff & David Bruce Cousins

Authors
  1. Kurt Rohloff
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  2. David Bruce Cousins
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Corresponding author

Correspondence to Kurt Rohloff .

Editor information

Editors and Affiliations

  1. University of Münster, Münster, Germany

    Rainer Böhme

  2. University of Hannover, Hannover, Niedersachsen, Germany

    Michael Brenner

  3. Southern Methodist University CS and Engineering Department, Dallas, Texas, USA

    Tyler Moore

  4. University of Bonn, Bonn, Germany

    Matthew Smith

A Experimental Results

A Experimental Results

Table 3. Encryption Runtime (ms) vs. Depth of computation supported and ring dimension for \(p=2\).
Full size table
Table 4. EvalAdd Runtime (ms) vs. Depth of computation supported and ring dimension for \(p=2\).
Full size table
Table 5. ComposedEvalMult Runtime (ms) vs. Depth of computation and Ring Dim. for \(p=2\).
Full size table
Table 6. Decryption Runtime (ms) vs. Depth of computation supported and Initial Ring Dim. for \(p=2\).
Full size table
Table 7. Bootstrapping Runtime (s) vs. Ring dimension for \(p=2\).
Full size table

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Rohloff, K., Cousins, D.B. (2014). A Scalable Implementation of Fully Homomorphic Encryption Built on NTRU. In: Böhme, R., Brenner, M., Moore, T., Smith, M. (eds) Financial Cryptography and Data Security. FC 2014. Lecture Notes in Computer Science(), vol 8438. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44774-1_18

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  • DOI: https://doi.org/10.1007/978-3-662-44774-1_18

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44773-4

  • Online ISBN: 978-3-662-44774-1

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