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2018 | OriginalPaper | Buchkapitel

Privately Constraining and Programming PRFs, the LWE Way

verfasst von : Chris Peikert, Sina Shiehian

Erschienen in: Public-Key Cryptography – PKC 2018

Verlag: Springer International Publishing

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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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Vorheriges Kapitel Hash Proof Systems over Lattices Revisited

Nächstes Kapitel Learning with Errors and Extrapolated Dihedral Cosets

Our construction was actually developed independently of [13], though not concurrently; we were unaware of its earlier non-public versions.

This property is obtained by composing homomorphic addition and multiplication of \(\mathbf {G}\)-multiples; the extra 1 attached to x is needed to support NOT gates.

We stress that \(\mathsf {LinEval} \) does not need to know \(\mathbf {k}\), which we view as representing a secret linear function that is hidden by \(\mathbf {C}\).

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Titel: Privately Constraining and Programming PRFs, the LWE Way
verfasst von: Chris Peikert
Sina Shiehian
Verlag: Springer International Publishing
Buch: Public-Key Cryptography – PKC 2018
Print ISBN: 978-3-319-76580-8

Electronic ISBN: 978-3-319-76581-5

Copyright-Jahr: 2018
DOI: https://doi.org/10.1007/978-3-319-76581-5_23

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