Obfuscating Conjunctions

  • Zvika Brakerski
  • Guy N. Rothblum
Conference paper

DOI: 10.1007/978-3-642-40084-1_24

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8043)
Cite this paper as:
Brakerski Z., Rothblum G.N. (2013) Obfuscating Conjunctions. In: Canetti R., Garay J.A. (eds) Advances in Cryptology – CRYPTO 2013. Lecture Notes in Computer Science, vol 8043. Springer, Berlin, Heidelberg


We show how to securely obfuscate the class of conjunction functions (functions like \(f(x_1, \ldots, x_n) = x_1 \land \lnot x_4 \land \lnot x_6 \land \cdots \land x_{n-2}\)). Given any function in the class, we produce an obfuscated program which preserves the input-output functionality of the given function, but reveals nothing else.

Our construction is based on multilinear maps, and can be instantiated using the recent candidates proposed by Garg, Gentry and Halevi (EUROCRYPT 2013) and by Coron, Lepoint and Tibouchi (CRYPTO 2013). We show that the construction is secure when the conjunction is drawn from a distribution, under mild assumptions on the distribution. Security follows from multilinear entropic variants of the Diffie-Hellman assumption. We conjecture that our construction is secure for any conjunction, regardless of the distribution from which it is drawn. We offer supporting evidence for this conjecture, proving that our obfuscator is secure for any conjunction against generic adversaries.


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Copyright information

© International Association for Cryptologic Research 2013

Authors and Affiliations

  • Zvika Brakerski
    • 1
  • Guy N. Rothblum
    • 2
  1. 1.Stanford UniversityUSA
  2. 2.Microsoft ResearchUSA

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