### Compactness vs Collusion Resistance in Functional Encryption

Baiyu Li and Daniele Micciancio

##### Abstract

We present two general constructions that can be used to combine any two functional encryption (FE) schemes (supporting a bounded number of key queries) into a new functional encryption scheme supporting a larger number of key queries. By using these constructions iteratively, we transform any primitive FE scheme supporting a single functional key query (from a sufficiently general class of functions) and has certain weak compactness properties to a collusion-resistant FE scheme with the same or slightly weaker compactness properties. Together with previously known reductions, this shows that the compact, weakly compact, collusion-resistant, and weakly collusion-resistant versions of FE are all equivalent under polynomial time reductions. These are all FE variants known to imply the existence of indistinguishability obfuscation, and were previously thought to offer slightly different avenues toward the realization of obfuscation from general assumptions. Our results show that they are indeed all equivalent, improving our understanding of the minimal assumptions on functional encryption required to instantiate indistinguishability obfuscation.

Note: We made some corrections to the security proof of the PRODUCT constructions (including the secret-key version), and added a secret-key version of our transformation (in the appendix)

Available format(s)
Category
Public-key cryptography
Publication info
A minor revision of an IACR publication in TCC 2016
Keywords
Functional encryptionreductioncompactcollusion resistance
Contact author(s)
baiyu @ cs ucsd edu
History
2017-04-10: last of 5 revisions
See all versions
Short URL
https://ia.cr/2016/561

CC BY

BibTeX

@misc{cryptoeprint:2016/561,
author = {Baiyu Li and Daniele Micciancio},
title = {Compactness vs Collusion Resistance in Functional Encryption},
howpublished = {Cryptology ePrint Archive, Paper 2016/561},
year = {2016},
note = {\url{https://eprint.iacr.org/2016/561}},
url = {https://eprint.iacr.org/2016/561}
}

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