Cryptology ePrint Archive: Report 2020/995

Bootstrapping fully homomorphic encryption over the integers in less than one second

Hilder Vitor Lima Pereira

Abstract: One can bootstrap LWE-based fully homomorphic encryption (FHE) schemes in less than one second, but bootstrapping AGCD- based FHE schemes, also known as FHE over the integers, is still very slow. In this work we propose a fast bootstrapping method for FHE over the integers, closing thus this gap between these two types of schemes. We use a variant of the AGCD problem to construct a new GSW-like scheme that can natively encrypt polynomials, then, we show how the single-gate bootstrapping method proposed by Ducas and Micciancio (EUROCRYPT 2015) can be adapted to FHE over the integers using our scheme, and we implement a bootstrapping that, using around 400 MB of key material, runs in less than one second in a common personal computer.

Category / Keywords: public-key cryptography / Fully Homomorphic Encryption, AGCD problem, Bootstrapping.

Date: received 17 Aug 2020, last revised 16 Nov 2020

Contact author: hilder vitor at gmail com

Available format(s): PDF | BibTeX Citation

Version: 20201116:153654 (All versions of this report)

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