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Black-Box Proof of Knowledge of Plaintext and Multiparty Computation with Low Communication Overhead

  • Steven Myers
  • Mona Sergi
  • abhi shelat
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7785)

Abstract

We present a 2-round protocol to prove knowledge of a plaintext corresponding to a given ciphertext. Our protocol is black-box in the underlying cryptographic primitives and it can be instantiated with almost any fully homomorphic encryption scheme.

Since our protocol is only 2 rounds it cannot be zero-knowledge [GO94]; instead, we prove that our protocol ensures the semantic security of the underlying ciphertext.

To illustrate the merit of this relaxed proof of knowledge property, we use our result to construct a secure multi-party computation protocol for evaluating a function f in the standard model using only black-box access to a threshold fully homomorphic encryption scheme. This protocol requires communication that is independent of |f|; while Gentry [Gen09a] has previously shown how to construct secure multi-party protocols with similar communication rates, the use of our novel primitive (along with other new techniques) avoids the use of complicated generic white-box techniques (cf. PCP encodings [Gen09a] and generic zero-knowledge proofs [AJLA + 12, LATV11].)

In this sense, our work demonstrates in principle that practical TFHE can lead to reasonably practical secure computation.

Keywords

Fully Homomorphic Encryption Threshold Encryption Secure Multi-Party Computation Communication and Round Complexity Proof Of Knowledge 

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Copyright information

© International Association for Cryptologic Research 2013

Authors and Affiliations

  • Steven Myers
    • 1
  • Mona Sergi
    • 2
  • abhi shelat
    • 2
  1. 1.Indiana UniversityBloomingtonUSA
  2. 2.University of VirginiaCharlottesvilleUSA

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