Multi-input Functional Encryption in the Private-Key Setting: Stronger Security from Weaker Assumptions

We construct a general-purpose multi-input functional encryption scheme in the private-key setting. Namely, we construct a scheme where a functional key corresponding to a function f enables a user holding encryptions of (x_1, ldots , x_t) to compute (f(x_1, ldots , x_t)) but nothing else. This is achieved starting from any general-purpose private-key single-input scheme (without any additional assumptions) and is proven to be adaptively secure for any constant number of inputs t. Moreover, it can be extended to a super-constant number of inputs assuming that the underlying single-input scheme is sub-exponentially secure. Instantiating our construction with existing single-input schemes, we obtain multi-input schemes that are based on a variety of assumptions (such as indistinguishability obfuscation, multilinear maps, learning with errors, and even one-way functions), offering various trade-offs between security assumptions and functionality. Previous and concurrent constructions of multi-input functional encryption schemes either rely on stronger assumptions and provided weaker security guarantees (Goldwasser et al. in Advances in cryptology—EUROCRYPT, 2014; Ananth and Jain in Advances in cryptology—CRYPTO, 2015), or relied on multilinear maps and could be proven secure only in an idealized generic model (Boneh et al. in Advances in cryptology—EUROCRYPT, 2015). In comparison, we present a general transformation that simultaneously relies on weaker assumptions and guarantees stronger security.