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Constrained Pseudorandom Functions from Functional Encryption
عملکرد شبه تصادفی از رمزگذاری تابعی-2019 This paper demonstrates how to design constrained pseudorandom functions
(CPRF) and their various extensions from any public key functional encryption
(FE) with standard polynomial security against arbitrary collusions.
More precisely, we start by presenting a CPRF construction that supports
constraint predicates realizable by arbitrary polynomial-size circuits, based
on polynomially-hard public key FE and one way functions. Next, we augment
our CPRF construction with the verifiability feature, relying only on
a minimal additional assumption, namely, the existence of standard public
key encryption (PKE). Finally, we show how to achieve privacy for the issued
keys in the context of programable pseudorandom functions (PPRF),
which is an enhanced variant of CPRF supporting puncturing constraints,
employing polynomially-hard FE and one way functions. All prior works addressing
the above problems either work for very restricted settings or rely on
highly powerful yet little-understood cryptographic objects such as multilinear
maps or indistinguishability obfuscation (IO). Although, there are known
transformations from FE to IO, the reductions suffer from an exponential security
loss and hence cannot be directly employed to replace IO with FE in
cryptographic constructions at the expense of only a polynomial loss. Thus,
our results open up a new pathway towards realizing numerous variants of
CPRF, which are interesting cryptographic primitives in their own right and,
moreover, have already been shown instrumental in a staggering range of
applications, both in classical as well as in cutting edge cryptography, based
on progressively weaker and well-studied cryptographic building blocks. Our
work can also be interpreted as yet another stepping stone towards establishing
FE as a substitute for IO in cryptographic applications. In order to
achieve our results we build upon the prefix puncturing technique developed
by Garg et al. Keywords: Constrained pseudorandom function | Constrained verifiable pseudorandom function | Private programable pseudorandom function | Functional encryption | Polynomial hardness |
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