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Practical homomorphic encryption over the integers for secure computation in the cloud

  • James DyerEmail author
  • Martin Dyer
  • Jie Xu
Regular Contribution
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Abstract

We present novel homomorphic encryption schemes for integer arithmetic, intended primarily for use in secure single-party computation in the cloud. These schemes are capable of securely computing arbitrary degree polynomials homomorphically. In practice, ciphertext size and running times limit the polynomial degree, but this appears sufficient for most practical applications. We present four schemes, with increasing levels of security, but increasing computational overhead. Two of the schemes provide strong security for high-entropy data. The remaining two schemes provide strong security regardless of this assumption. These four algorithms form the first two levels of a hierarchy of schemes, and we also present the general cases of each scheme. We further elaborate how a fully homomorphic system can be constructed from one of our general cases. In addition, we present a variant based upon Chinese Remainder Theorem secret sharing. We detail extensive evaluation of the first four algorithms of our hierarchy by computing low-degree polynomials. The timings of these computations are extremely favourable by comparison with even the best of existing methods and dramatically outperform many well-publicised schemes. The results clearly demonstrate the practical applicability of our schemes.

Keywords

Cryptography Symmetric encryption Homomorphic encryption Computing on encrypted data Secure computation in the cloud 

Notes

Acknowledgements

This work was supported in part by Engineering and Physical Sciences Research Council (EPSRC) research grants EP/I028099/1 and EP/M004953/1 and National Key Research and Development Program of China research Grant 2016YFB1000103. Experimentation conducted on Microsoft Azure was supported by a Microsoft Azure for Research sponsorship.

Compliance with ethical standards

Funding

This study was funded by Engineering and Physical Sciences Research Council (EP/I028099/1 & EP/M004953/1) and National Key Research and Development Program of China (2016YFB1000103). Usage of Microsoft’s Azure cloud was funded by a Microsoft Azure for Research sponsorship.

Ethical approval

Ethical approval: This article does not contain any studies with human participants or animals performed by any of the authors.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.De Montfort UniversityLeicesterUK
  2. 2.School of ComputingUniversity of LeedsLeedsUK

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