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Faster Fully Homomorphic Encryption: Bootstrapping in Less Than 0.1 Seconds

  • Ilaria ChillottiEmail author
  • Nicolas Gama
  • Mariya GeorgievaEmail author
  • Malika IzabachèneEmail author
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10031)

Abstract

In this paper, we revisit fully homomorphic encryption (FHE) based on GSW and its ring variants. We notice that the internal product of GSW can be replaced by a simpler external product between a GSW and an LWE ciphertext.

We show that the bootstrapping scheme FHEW of Ducas and Micciancio [11] can be expressed only in terms of this external product. As a result, we obtain a speed up from less than 1 s to less than 0.1 s. We also reduce the 1 GB bootstrapping key size to 24 MB, preserving the same security levels, and we improve the noise propagation overhead by replacing exact decomposition algorithms with approximate ones.

Moreover, our external product allows to explain the unique asymmetry in the noise propagation of GSW samples and makes it possible to evaluate deterministic automata homomorphically as in [13] in an efficient way with a noise overhead only linear in the length of the tested word.

Finally, we provide an alternative practical analysis of LWE based scheme, which directly relates the security parameter to the error rate of LWE and the entropy of the LWE secret key.

Keywords

Fully homomorphic encryption Bootstrapping Lattices LWE GSW 
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Notes

Acknowledgements

This work has been supported in part by the CRYPTOCOMP project.

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Copyright information

© International Association for Cryptologic Research 2016

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques de VersaillesUVSQ, CNRS, Université Paris-SaclayVersaillesFrance
  2. 2.InpherLausanneSwitzerland
  3. 3.GemaltoMeudonFrance
  4. 4.CEA LISTGif-sur-Yvette CedexFrance

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