conference paper
Key-homomorphic constrained pseudorandom functions
LNCS
published
yes
Abishek
Banerjee
author
Georg
Fuchsbauer
author 46B4C3EE-F248-11E8-B48F-1D18A9856A87
Chris
Peikert
author
Krzysztof Z
Pietrzak
author 3E04A7AA-F248-11E8-B48F-1D18A9856A87
Sophie
Stevens
author
KrPi
department
TCC: Theory of Cryptography Conference
Provable Security for Physical Cryptography
project
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.
https://research-explorer.app.ist.ac.at/download/1646/5136/IST-2016-679-v1+1_180.pdf
application/pdfno
Springer2015Warsaw, Poland
eng
10.1007/978-3-662-46497-7_2
901531 - 60
Banerjee A, Fuchsbauer G, Peikert C, Pietrzak KZ, Stevens S. Key-homomorphic constrained pseudorandom functions. 2015;9015:31-60. doi:<a href="https://doi.org/10.1007/978-3-662-46497-7_2">10.1007/978-3-662-46497-7_2</a>
Banerjee, Abishek, Georg Fuchsbauer, Chris Peikert, Krzysztof Z Pietrzak, and Sophie Stevens. “Key-Homomorphic Constrained Pseudorandom Functions.” Lecture Notes in Computer Science. Springer, 2015. <a href="https://doi.org/10.1007/978-3-662-46497-7_2">https://doi.org/10.1007/978-3-662-46497-7_2</a>.
Banerjee A, Fuchsbauer G, Peikert C, Pietrzak KZ, Stevens S. 2015. Key-homomorphic constrained pseudorandom functions. 9015, 31–60.
Banerjee, Abishek, et al. <i>Key-Homomorphic Constrained Pseudorandom Functions</i>. Vol. 9015, Springer, 2015, pp. 31–60, doi:<a href="https://doi.org/10.1007/978-3-662-46497-7_2">10.1007/978-3-662-46497-7_2</a>.
A. Banerjee, G. Fuchsbauer, C. Peikert, K. Z. Pietrzak, and S. Stevens, “Key-homomorphic constrained pseudorandom functions,” vol. 9015. Springer, pp. 31–60, 2015.
Banerjee, A., Fuchsbauer, G., Peikert, C., Pietrzak, K. Z., & Stevens, S. (2015). Key-homomorphic constrained pseudorandom functions. Presented at the TCC: Theory of Cryptography Conference, Warsaw, Poland: Springer. <a href="https://doi.org/10.1007/978-3-662-46497-7_2">https://doi.org/10.1007/978-3-662-46497-7_2</a>
A. Banerjee, G. Fuchsbauer, C. Peikert, K.Z. Pietrzak, S. Stevens, 9015 (2015) 31–60.
16462018-12-11T11:53:14Z2020-01-16T12:36:09Z