Paper 2015/334

On the Correlation Intractability of Obfuscated Pseudorandom Functions

Ran Canetti, Yilei Chen, and Leonid Reyzin


A family of hash functions is called ``correlation intractable'' if it is hard to find, given a random function in the family, an input-output pair that satisfies any ``sparse'' relation, namely any relation that is hard to satisfy for truly random functions. Correlation intractability captures a strong and natural Random Oracle-like property. However, it is widely considered to be unobtainable. Indeed, it was shown that correlation intractable functions do not exist for some length parameters [Canetti, Goldreich and Halevi, J.ACM 04]. Furthermore, no candidate constructions have been proposed in the literature for any setting of the parameters. We construct a correlation intractable function ensemble that withstands all relations with a priori bounded polynomial complexity. We assume the existence of sub-exponentially secure indistinguishability obfuscators, puncturable pseudorandom functions, and input-hiding obfuscators for evasive circuits. The existence of the latter is implied by Virtual-Grey-Box obfuscation for evasive circuits [Bitansky et al, CRYPTO 14].

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A minor revision of an IACR publication in Tcc 2016
Contact author(s)
canetti @ tau ac il
chenyl @ bu edu
reyzin @ cs bu edu
2015-11-17: last of 3 revisions
2015-04-19: received
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      author = {Ran Canetti and Yilei Chen and Leonid Reyzin},
      title = {On the Correlation Intractability of Obfuscated Pseudorandom Functions},
      howpublished = {Cryptology ePrint Archive, Paper 2015/334},
      year = {2015},
      note = {\url{}},
      url = {}
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