Multi-input Functional Encryption for Unbounded Arity Functions

The notion of multi-input functional encryption (MI-FE) was recently introduced by Goldwasser et al. [EUROCRYPT’14] as a means to non-interactively compute aggregate information on the joint private data of multiple users. A fundamental limitation of their work, however, is that the total number of users (which corresponds to the arity of the functions supported by the MI-FE scheme) must be a priori bounded and fixed at the system setup time. In this work, we overcome this limitation by introducing the notion of unbounded input MI-FE that supports the computation of functions with unbounded arity. We construct such an MI-FE scheme with indistinguishability security in the selective model based on the existence of public-coin differing-inputs obfuscation for turing machines and collisionresistant hash functions. Our result enables several new exciting applications, including a new paradigm of on-the-fly secure multiparty computation where new users can join the system dynamically. ? University of California, Los Angeles and Center for Encrypted Functionalities. Email: [email protected] ?? University of California, Los Angeles and Center for Encrypted Functionalities. Email: [email protected] ? ? ? Johns Hopkins University. Email: [email protected] Supported in part by a DARPA/ARL Safeware Grant W911NF-15-C-0213 and NSF CNS-1414023 † University of California, Los Angeles and Center for Encrypted Functionalities. Email: [email protected] Research supported in part from a DARPA/ONR PROCEED award, a DARPA/ARL SAFEWARE award, NSF Frontier Award 1413955, NSF grants 1228984, 1136174, 1118096, and 1065276, a Xerox Faculty Research Award, a Google Faculty Research Award, an equipment grant from Intel, and an Okawa Foundation Research Grant. This material is based upon work supported by the Defense Advanced Research Projects Agency through the U.S. Office of Naval Research under Contract N00014-11-1-0389. The views expressed are those of the author and do not reflect the official policy or position of the Department of Defense, the National Science Foundation, or the U.S. Government.