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High-Speed Fully Homomorphic Encryption Over the Integers

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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

A fully homomorphic encryption (FHE) scheme is envisioned as a key cryptographic tool in building a secure and reliable cloud computing environment, as it allows arbitrary evaluation of a ciphertext without revealing the plaintext. However, existing FHE implementations remain impractical due to very high time and resource costs. To the authors’ knowledge, this paper presents the first hardware implementation of a full encryption primitive for FHE over the integers using FPGA technology. A large-integer multiplier architecture utilising Integer-FFT multiplication is proposed, and a large-integer Barrett modular reduction module is designed incorporating the proposed multiplier. The encryption primitive used in the integer-based FHE scheme is designed employing the proposed multiplier and modular reduction modules. The designs are verified using the Xilinx Virtex-7 FPGA platform. Experimental results show that a speed improvement factor of up to 44 is achievable for the hardware implementation of the FHE encryption scheme when compared to its corresponding software implementation. Moreover, performance analysis shows further speed improvements of the integer-based FHE encryption primitives may still be possible, for example through further optimisations or by targeting an ASIC platform.

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Authors and Affiliations

  1. Centre for Secure Information Technologies, Queen’s University Belfast, Belfast, Northern Ireland, UK

    Xiaolin Cao, Ciara Moore, Máire O’Neill, Neil Hanley & Elizabeth O’Sullivan

Authors
  1. Xiaolin Cao
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  2. Ciara Moore
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  3. Máire O’Neill
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  4. Neil Hanley
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  5. Elizabeth O’Sullivan
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Corresponding author

Correspondence to Ciara Moore .

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

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Cao, X., Moore, C., O’Neill, M., Hanley, N., O’Sullivan, E. (2014). High-Speed Fully Homomorphic Encryption Over the Integers. 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_14

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  • DOI: https://doi.org/10.1007/978-3-662-44774-1_14

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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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