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Leveraging Linear Decryption: Rate-1 Fully-Homomorphic Encryption and Time-Lock Puzzles

  • Zvika Brakerski
  • Nico Döttling
  • Sanjam Garg
  • Giulio Malavolta
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11892)

Abstract

We show how to combine a fully-homomorphic encryption scheme with linear decryption and a linearly-homomorphic encryption schemes to obtain constructions with new properties. Specifically, we present the following new results.

  1. (1)

    Rate-1 Fully-Homomorphic Encryption: We construct the first scheme with message-to-ciphertext length ratio (i.e., rate) \(1-\sigma \) for \(\sigma = o(1)\). Our scheme is based on the hardness of the Learning with Errors (LWE) problem and \(\sigma \) is proportional to the noise-to-modulus ratio of the assumption. Our building block is a construction of a new high-rate linearly-homomorphic encryption.

    One application of this result is the first general-purpose secure function evaluation protocol in the preprocessing model where the communication complexity is within additive factor of the optimal insecure protocol.

     
  2. (2)

    Fully-Homomorphic Time-Lock Puzzles: We construct the first time-lock puzzle where one can evaluate any function over a set of puzzles without solving them, from standard assumptions. Prior work required the existence of sub-exponentially hard indistinguishability obfuscation.

     
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Copyright information

© International Association for Cryptologic Research 2019

Authors and Affiliations

  • Zvika Brakerski
    • 1
  • Nico Döttling
    • 2
  • Sanjam Garg
    • 3
  • Giulio Malavolta
    • 4
  1. 1.Weizmann Institute of ScienceRehovotIsrael
  2. 2.CISPA Helmholtz Center for Information SecuritySaarbrückenGermany
  3. 3.University of California, BerkeleyBerkeleyUSA
  4. 4.Simons Institute for the Theory of ComputingBerkeleyUSA

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