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.
CITATION STYLE
Pereira, H. V. L. (2021). Bootstrapping Fully Homomorphic Encryption over the Integers in Less than One Second. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 12710 LNCS, pp. 331–359). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-75245-3_13
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