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2018 | OriginalPaper | Buchkapitel

Homomorphic Lower Digits Removal and Improved FHE Bootstrapping

verfasst von : Hao Chen, Kyoohyung Han

Erschienen in: Advances in Cryptology – EUROCRYPT 2018

Verlag: Springer International Publishing

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Abstract

Bootstrapping is a crucial operation in Gentry’s breakthrough work on fully homomorphic encryption (FHE), where a homomorphic encryption scheme evaluates its own decryption algorithm. There has been a couple of implementations of bootstrapping, among which HElib arguably marks the state-of-the-art in terms of throughput, ciphertext/message size ratio and support for large plaintext moduli.

In this work, we applied a family of “lowest digit removal” polynomials to design an improved homomorphic digit extraction algorithm which is a crucial part in bootstrapping for both FV and BGV schemes. When the secret key has 1-norm \(h=||s||_1\) and the plaintext modulus is \(t = p^r\), we achieved bootstrapping depth \(\log h + \log ( \log _p(ht))\) in FV scheme. In case of the BGV scheme, we brought down the depth from \(\log h + 2 \log t\) to \(\log h + \log t\).

We implemented bootstrapping for FV in the SEAL library. We also introduced another “slim mode”, which restrict the plaintexts to batched vectors in \(\mathbb {Z}_{p^r}\). The slim mode has similar throughput as the full mode, while each individual run is much faster and uses much smaller memory. For example, bootstrapping takes 6.75 s for vectors over GF(127) with 64 slots and 1381 s for vectors over \(GF(257^{128})\) with 128 slots. We also implemented our improved digit extraction procedure for the BGV scheme in HElib.

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Titel: Homomorphic Lower Digits Removal and Improved FHE Bootstrapping
verfasst von: Hao Chen
Kyoohyung Han
Verlag: Springer International Publishing
Buch: Advances in Cryptology – EUROCRYPT 2018
Print ISBN: 978-3-319-78380-2

Electronic ISBN: 978-3-319-78381-9

Copyright-Jahr: 2018
DOI: https://doi.org/10.1007/978-3-319-78381-9_12

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