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Cryptographers’ Track at the RSA Conference

CT-RSA 2019: Topics in Cryptology – CT-RSA 2019 pp 83–105Cite as

An Improved RNS Variant of the BFV Homomorphic Encryption Scheme

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11405))

Abstract

We present an optimized variant of the Brakerski/Fan-Vercauteren (BFV) homomorphic encryption scheme and its efficient implementation in PALISADE. Our algorithmic improvements focus on optimizing decryption and homomorphic multiplication in the Residue Number System (RNS), using the Chinese Remainder Theorem (CRT) to represent and manipulate the large coefficients in the ciphertext polynomials. These improvements are based on our original general-purpose techniques for CRT basis extension and scaling that can be applied to many other lattice-based cryptographic primitives. Our variant is simpler and significantly more efficient than the RNS variant proposed by Bajard et al. both in terms of noise growth and the computational complexity of the underlying CRT basis extension and scaling procedures.

S. Halevi—Supported by the Defense Advanced Research Projects Agency (DARPA) and Army Research Office (ARO) under Contract No. W911NF-15-C-0236.

Y. Polyakov—Supported by the Sloan Foundation and Defense Advanced Research Projects Agency (DARPA) and Army Research Office (ARO) under Contracts No. W911NF-15-C-0226 and W911NF-15-C-0233.

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Notes

  1. 1.

    Larger CRT moduli can be supported using “double double” floating-points.

  2. 2.

    A more detailed comparison is presented in the extended version of this paper [12].

  3. 3.

    We ignore the encryption procedure in this section, since it is mostly irrelevant for the current work. For suitable choices, Regev proved that this encryption scheme is CPA-secure under the LWE assumption.

  4. 4.

    Fan and Vercauteren described in [8] a second relinearization procedure, using a technique of Gentry et al. from [10]. We ignore this alternative procedure here.

  5. 5.

    https://bitbucket.org/malb/lwe-estimator.

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Authors and Affiliations

  1. IBM Research, Yorktown Heights, USA

    Shai Halevi

  2. New Jersey Institute of Technology, Newark, USA

    Yuriy Polyakov

  3. New York University, New York, USA

    Victor Shoup

Authors
  1. Shai Halevi
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  2. Yuriy Polyakov
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  3. Victor Shoup
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Corresponding author

Correspondence to Yuriy Polyakov .

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Editors and Affiliations

  1. Mitsubishi Electric Corporation, Kamakura, Japan

    Mitsuru Matsui

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Halevi, S., Polyakov, Y., Shoup, V. (2019). An Improved RNS Variant of the BFV Homomorphic Encryption Scheme. In: Matsui, M. (eds) Topics in Cryptology – CT-RSA 2019. CT-RSA 2019. Lecture Notes in Computer Science(), vol 11405. Springer, Cham. https://doi.org/10.1007/978-3-030-12612-4_5

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  • DOI: https://doi.org/10.1007/978-3-030-12612-4_5

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  • Online ISBN: 978-3-030-12612-4

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