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Obfuscation for Evasive Functions

  • Boaz Barak
  • Nir Bitansky
  • Ran Canetti
  • Yael Tauman Kalai
  • Omer Paneth
  • Amit Sahai
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8349)

Abstract

An evasive circuit family is a collection of circuits \(\mathcal{C}\) such that for every input x, a random circuit from \(\mathcal{C}\) outputs 0 on x with overwhelming probability. We provide a combination of definitional, constructive, and impossibility results regarding obfuscation for evasive functions:

  1. 1

    The (average case variants of the) notions of virtual black box obfuscation (Barak et al, CRYPTO ’01) and virtual gray box obfuscation (Bitansky and Canetti, CRYPTO ’10) coincide for evasive function families. We also define the notion of input-hiding obfuscation for evasive function families, stipulating that for a random \(C \in{\mathcal{C}}\) it is hard to find, given \(\mathcal{O}(C)\), a value outside the preimage of 0. Interestingly, this natural definition, also motivated by applications, is likely not implied by the seemingly stronger notion of average-case virtual black-box obfuscation.

     
  2. 2

    If there exist average-case virtual gray box obfuscators for all evasive function families, then there exist (quantitatively weaker) average-case virtual gray obfuscators for all function families.

     
  3. 3

    There does not exist a worst-case virtual black box obfuscator even for evasive circuits, nor is there an average-case virtual gray box obfuscator for evasive Turing machine families.

     
  4. 4

    Let \(\mathcal{C}\) be an evasive circuit family consisting of functions that test if a low-degree polynomial (represented by an efficient arithmetic circuit) evaluates to zero modulo some large prime p. Then under a natural analog of the discrete logarithm assumption in a group supporting multilinear maps, there exists an input-hiding obfuscator for \(\mathcal{C}\). Under a new perfectly-hiding multilinear encoding assumption, there is an average-case virtual black box obfuscator for the family \(\mathcal{C}\).

     

Keywords

Turing Machine Random Oracle Impossibility Result Arithmetic Circuit Auxiliary Input 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© International Association for Cryptologic Research 2014

Authors and Affiliations

  • Boaz Barak
    • 1
  • Nir Bitansky
    • 2
  • Ran Canetti
    • 2
    • 3
  • Yael Tauman Kalai
    • 1
  • Omer Paneth
    • 3
  • Amit Sahai
    • 4
  1. 1.Microsoft ResearchUSA
  2. 2.Tel Aviv UniversityIsrael
  3. 3.Boston UniversityUSA
  4. 4.UCLAUSA

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