A family of hash functions is called “correlation intractable” if it is hard to find, given a random function in the family, an inputoutput pair that satisfies any “sparse” relation, namely any relation that is hard to satisfy for truly random functions. Indeed, correlation intractability is a strong and natural random-oracle-like property. However, it was widely considered unobtainable. In fact for some parameter settings, unobtainability has been demonstrated [26]. 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 [13].
CITATION STYLE
Canetti, R., Chen, Y., & Reyzin, L. (2016). On the correlation intractability of obfuscated pseudorandom functions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9562, pp. 389–415). Springer Verlag. https://doi.org/10.1007/978-3-662-49096-9_17
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