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Title:
On the Correlation Intractability of Obfuscated Pseudorandom Functions
Authors: Ran Canetti, Yilei Chen, Leonid Reyzin
Abstract: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].
ePrint: https://eprint.iacr.org/2015/334
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