Cryptology ePrint Archive: Report 2018/1043

Improved Bootstrapping for Approximate Homomorphic Encryption

Hao Chen and Ilaria Chillotti and Yongsoo Song

Abstract: Since Cheon et al. introduced a homomorphic encryption scheme for approximate arithmetic (Asiacrypt 17), it has been recognized as suitable for important real-life usecases of homomorphic encryption, including training of machine learning models over encrypted data. A follow up work by Cheon et al. (Eurocrypt 18) described an approximate bootstrapping procedure for the scheme. In this work, we improve upon the previous bootstrapping result. We improve the amortized bootstrapping time per plaintext slot by two orders of magnitude, from ∼ 1 second to ∼ 0.01 second. To achieve this result, we adopt a smart level-collapsing technique for evaluating DFT-like linear transforms on a ciphertext. Also, we replace the Taylor approximation of the sine function with a more accurate and numerically stable Chebyshev approximation, and design a modified version of the Paterson-Stockmeyer algorithm for fast evaluation of Chebyshev polynomials over encrypted data.

Category / Keywords: Fully Homomorphic Encryption, Bootstrapping

Date: received 28 Oct 2018

Contact author: haoche at microsoft com

Available format(s): PDF | BibTeX Citation

Version: 20181102:005546 (All versions of this report)

Short URL: ia.cr/2018/1043


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