Multi-Input Quadratic Functional Encryption From Pairings

We construct the first multi-input functional encryption (MIFE) scheme for quadratic functions from pairings. Our construction supports polynomial number of users, where user i, for i is an element of (sic)n(sic), encrypts input x(i) is an element of Z(m) to obtain ciphertext CTi, the key generator provides a key SKc for vector c is an element of Z((mn)2) and decryption, given CT1, . . . , CTn and SKc, recovers < c, x circle times x > and nothing else. We achieve indistinguishability-based (selective) security against unbounded collusions under the standard bilateral matrix Diffie-Hellman assumption. All previous MIFE schemes either support only inner products (linear functions) or rely on strong cryptographic assumptions such as indistinguishability obfuscation or multi-linear maps.