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

Authors:
Hilder Vitor Lima Pereira
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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 fast bootstrapping methods 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.
Video from PKC 2021
BibTeX
@article{pkc-2021-30962,
  title={Bootstrapping fully homomorphic encryption over the integers in less  than one second},
  booktitle={Public-Key Cryptography - PKC 2021},
  publisher={Springer},
  author={Hilder Vitor Lima Pereira},
  year=2021
}