Key-homomorphic constrained pseudorandom functions Conference Paper

Author(s): Banerjee, Abishek; Fuchsbauer, Georg; Peikert, Chris; Pietrzak, Krzysztof; Stevens, Sophie
Title: Key-homomorphic constrained pseudorandom functions
Title Series: LNCS
Affiliation IST Austria
Abstract: A pseudorandom function (PRF) is a keyed function F : K × X → Y where, for a random key k ∈ K, the function F(k, ·) is indistinguishable from a uniformly random function, given black-box access. A key-homomorphic PRF has the additional feature that for any keys k, k' and any input x, we have F(k+k', x) = F(k, x)⊕F(k', x) for some group operations +,⊕ on K and Y, respectively. A constrained PRF for a family of setsS ⊆ P(X) has the property that, given any key k and set S ∈ S, one can efficiently compute a “constrained” key kS that enables evaluation of F(k, x) on all inputs x ∈ S, while the values F(k, x) for x /∈ S remain pseudorandom even given kS. In this paper we construct PRFs that are simultaneously constrained and key homomorphic, where the homomorphic property holds even for constrained keys. We first show that the multilinear map-based bit-fixing and circuit-constrained PRFs of Boneh and Waters (Asiacrypt 2013) can be modified to also be keyhomomorphic. We then show that the LWE-based key-homomorphic PRFs of Banerjee and Peikert (Crypto 2014) are essentially already prefix-constrained PRFs, using a (non-obvious) definition of constrained keys and associated group operation. Moreover, the constrained keys themselves are pseudorandom, and the constraining and evaluation functions can all be computed in low depth. As an application of key-homomorphic constrained PRFs,we construct a proxy re-encryption schemewith fine-grained access control. This scheme allows storing encrypted data on an untrusted server, where each file can be encrypted relative to some attributes, so that only parties whose constrained keys match the attributes can decrypt. Moreover, the server can re-key (arbitrary subsets of) the ciphertexts without learning anything about the plaintexts, thus permitting efficient and finegrained revocation.
Keywords: pseudorandom functions; Cryptography; Access control; Arbitrary subsets; Evaluation function; Fine-grained revocation; Homomorphic property; Multilinear maps; Proxy re encryptions; Untrusted server; Function evaluation
Conference Title: TCC: Theory of Cryptography Conference
Volume: 9015
Conference Dates: March 23 - 25, 2015
Conference Location: Warsaw, Poland
Publisher: Springer  
Date Published: 2015-01-01
Start Page: 31
End Page: 60
DOI: 10.1007/978-3-662-46497-7_2
Notes: Research supported by ERC starting grant (259668- PSPC). This material is based upon work supported by the National Science Foundation under CA- REER Award CCF-1054495, by DARPA under agreement number FA8750-11-C-0096, and by the Alfred P. Sloan Foundation. Any opinions, findings, and conclusions or recommenda- tions expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation, DARPA or the U.S. Government, or the Sloan Foundation. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. Research supported by ERC starting grant (259668- PSPC).
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