An Improved RNS Variant of the BFV Homomorphic Encryption Scheme

Shai Halevi; Yuriy Polyakov; Victor Shoup

Paper 2018/117

An Improved RNS Variant of the BFV Homomorphic Encryption Scheme

Shai Halevi, Yuriy Polyakov, and Victor Shoup

Abstract

We present an optimized implementation of the Fan-Vercauteren variant of Brakerski's scale-invariant homomorphic encryption scheme. 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. In particular, we propose efficient procedures for scaling and CRT basis extension that do not require translating the numbers to standard (positional) representation. Compared to the previously proposed RNS design due to Bajard et al., our procedures are simpler and faster, and introduce a lower amount of noise. We implement our optimizations in the PALISADE library and evaluate the runtime performance for the range of multiplicative depths from 1 to 100. For example, homomorphic multiplication for a depth-20 setting can be executed in 62 ms on a modern server system, which is already practical for some outsourced-computing applications. Our algorithmic improvements can also be applied to other scale-invariant homomorphic encryption schemes, such as YASHE.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Published elsewhere. Major revision. CT-RSA 2019
DOI: 10.1007/978-3-030-12612-4_5
Keywords: implementation lattice techniques public-key cryptography quantum cryptography homomorphic encryption Residue Number System
Contact author(s): polyakov @ njit edu
History: 2019-03-06: last of 4 revisions; 2018-01-31: received; See all versions
Short URL: https://ia.cr/2018/117
License: CC BY

BibTeX

@misc{cryptoeprint:2018/117,
      author = {Shai Halevi and Yuriy Polyakov and Victor Shoup},
      title = {An Improved {RNS} Variant of the {BFV} Homomorphic Encryption Scheme},
      howpublished = {Cryptology {ePrint} Archive, Paper 2018/117},
      year = {2018},
      doi = {10.1007/978-3-030-12612-4_5},
      url = {https://eprint.iacr.org/2018/117}
}