Cryptology ePrint Archive: Report 2014/720

Adaptively Secure Constrained Pseudorandom Functions

Dennis Hofheinz and Akshay Kamath and Venkata Koppula and Brent Waters

Abstract: A constrained pseudo random function (PRF) behaves like a standard PRF, but with the added feature that the (master) secret key holder, having secret key K, can produce a constrained key, K_f, that allows for the evaluation of the PRF on a subset of the domain as determined by a predicate function f within some family F. While previous constructions gave constrained PRFs for poly-sized circuits, all reductions for such functionality were based in the selective model of security where an attacker declares which point he is attacking before seeing any constrained keys.

In this paper we give new constrained PRF constructions for circuits that have polynomial reductions to indistinguishability obfuscation in the random oracle model. Our solution is constructed from two recently emerged primitives: an adaptively secure Attribute-Based Encryption (ABE) for circuits and a Universal Parameters as introduced by Hofheinz et al. Both primitives are constructible from indistinguishability obfuscation (iO) (and injective pseudorandom generators) with only polynomial loss.

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Date: received 14 Sep 2014, last revised 8 Jan 2015

Contact author: dennis hofheinz at kit edu, kamath@cs utexas edu, kvenkata@cs utexas edu, bwaters@cs utexas edu