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2020 | OriginalPaper | Buchkapitel

Constraining and Watermarking PRFs from Milder Assumptions

verfasst von : Chris Peikert, Sina Shiehian

Erschienen in: Public-Key Cryptography – PKC 2020

Verlag: Springer International Publishing

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Abstract

Constrained pseudorandom functions (C-PRFs) let the possessor of a secret key delegate the ability to evaluate the function on certain authorized inputs, while keeping the remaining function values pseudorandom. A constraint-hiding constrained PRF (CHC-PRF) additionally conceals the predicate that determines which inputs are authorized. These primitives have a wealth of applications, including watermarking schemes, symmetric deniable encryption, and updatable garbled circuits.

Recent works have constructed (CH)C-PRFs from rather aggressive parameterizations of Learning With Errors (LWE) with subexponential modulus-noise ratios, even for relatively simple “puncturing” or \(\text {NC}^{1}\) circuit constraints. This corresponds to strong lattice assumptions and inefficient constructions, and stands in contrast to LWE-based unconstrained PRFs and fully homomorphic encryption schemes, which can be based on quasi-polynomial or even (nearly) polynomial modulus-noise ratios.

In this work we considerably improve the LWE assumptions needed for building (constraint-hiding) constrained PRFs and watermarking schemes. In particular, for CHC-PRFs and related watermarking schemes we improve the modulus-noise ratio to \(\lambda ^{O((d+\log \lambda ) \log \lambda )}\) for depth-d circuit constraints, which is merely quasi-polynomial for \(\text {NC}^{1}\) circuits and closely related watermarking schemes. For (constraint-revealing) C-PRFs for \(\text {NC}^{1}\) we do even better, obtaining a nearly polynomial \(\lambda ^{\omega (1)}\) ratio. These improvements are partly enabled by slightly modifying the definition of C-PRFs, in a way that is still compatible with many of their applications. Finally, as a contribution of independent interest we build CHC-PRFs for special constraint classes from generic, weaker assumptions: we obtain bit-fixing constraints based on the minimal assumption of one-way functions, and hyperplane-membership constraints based on key-homomorphic PRFs.

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Titel: Constraining and Watermarking PRFs from Milder Assumptions
verfasst von: Chris Peikert
Sina Shiehian
Verlag: Springer International Publishing
Buch: Public-Key Cryptography – PKC 2020
Print ISBN: 978-3-030-45373-2

Electronic ISBN: 978-3-030-45374-9

Copyright-Jahr: 2020
DOI: https://doi.org/10.1007/978-3-030-45374-9_15

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