Evaluating 2-DNF Formulas on Ciphertexts

Authors: Dan Boneh, Eu-Jin Goh, and Kobbi Nissim.

Abstract:

Let Ψ be a 2-DNF formula on boolean variables x1,…,xn ∈ {0,1}. We present a homomorphic public key encryption scheme that allows the public evaluation of Ψ given an encryption of the variables x1,…,xn. In other words, given the encryption of the bits x1,…,xn, anyone can create the encryption of Ψ(x1,…,xn). More generally, we can evaluate quadratic multi-variate polynomials on ciphertexts provided the resulting value falls within a small set. We present a number of applications of the system:

  • In a database of size n, the total communication in the basic step of the Kushilevitz-Ostrovsky PIR protocol is reduced from √n to ∛n.
  • An efficient election system based on homomorphic encryption where voters do not need to include non-interactive zero knowledge proofs that their ballots are valid. The election system is proved secure without random oracles but still efficient.
  • A protocol for universally verifiable computation.

    • Reference:
    In the Proceedings of Theory of Cryptography Conference 2005.
    BibTex: bib

    Full Paper:
    Last updated on 2 Apr 2006 pdf, ps

    Slides:
    Theory of Cryptography Conference 2005, Stanford Security Forum

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