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Privately Constraining and Programming PRFs, the LWE Way

  • Chris Peikert
  • Sina Shiehian
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10770)

Abstract

Constrained pseudorandom functions allow for delegating “constrained” secret keys that let one compute the function at certain authorized inputs—as specified by a constraining predicate—while keeping the function value at unauthorized inputs pseudorandom. In the constraint-hiding variant, the constrained key hides the predicate. On top of this, programmable variants allow the delegator to explicitly set the output values yielded by the delegated key for a particular set of unauthorized inputs.

Recent years have seen rapid progress on applications and constructions of these objects for progressively richer constraint classes, resulting most recently in constraint-hiding constrained PRFs for arbitrary polynomial-time constraints from Learning With Errors (LWE) [Brakerski, Tsabary, Vaikuntanathan, and Wee, TCC’17], and privately programmable PRFs from indistinguishability obfuscation (iO) [Boneh, Lewi, and Wu, PKC’17].

In this work we give a unified approach for constructing both of the above kinds of PRFs from LWE with subexponential \(\exp (n^{\varepsilon })\) approximation factors. Our constructions follow straightforwardly from a new notion we call a shift-hiding shiftable function, which allows for deriving a key for the sum of the original function and any desired hidden shift function. In particular, we obtain the first privately programmable PRFs from non-iO assumptions.

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Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  1. 1.Computer Science and EngineeringUniversity of MichiganAnn ArborUSA

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