Homomorphic Encryption from Learning with Errors: Conceptually-Simpler, Asymptotically-Faster, Attribute-Based

  • Craig Gentry
  • Amit Sahai
  • Brent Waters
Conference paper

DOI: 10.1007/978-3-642-40041-4_5

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8042)
Cite this paper as:
Gentry C., Sahai A., Waters B. (2013) Homomorphic Encryption from Learning with Errors: Conceptually-Simpler, Asymptotically-Faster, Attribute-Based. In: Canetti R., Garay J.A. (eds) Advances in Cryptology – CRYPTO 2013. Lecture Notes in Computer Science, vol 8042. Springer, Berlin, Heidelberg

Abstract

We describe a comparatively simple fully homomorphic encryption (FHE) scheme based on the learning with errors (LWE) problem. In previous LWE-based FHE schemes, multiplication is a complicated and expensive step involving “relinearization”. In this work, we propose a new technique for building FHE schemes that we call the approximate eigenvector method. In our scheme, for the most part, homomorphic addition and multiplication are just matrix addition and multiplication. This makes our scheme both asymptotically faster and (we believe) easier to understand.

In previous schemes, the homomorphic evaluator needs to obtain the user’s “evaluation key”, which consists of a chain of encrypted secret keys. Our scheme has no evaluation key. The evaluator can do homomorphic operations without knowing the user’s public key at all, except for some basic parameters. This fact helps us construct the first identity-based FHE scheme. Using similar techniques, we show how to compile a recent attribute-based encryption scheme for circuits by Gorbunov et al. into an attribute-based FHE scheme that permits data encrypted under the same index to be processed homomorphically.

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Copyright information

© International Association for Cryptologic Research 2013

Authors and Affiliations

  • Craig Gentry
    • 1
  • Amit Sahai
    • 2
  • Brent Waters
    • 3
  1. 1.IBM ResearchUSA
  2. 2.UCLAUSA
  3. 3.UT AustinUSA

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