We define the Unbounded Inner-Product functionality in the context of Public-Key Functional Encryption, and introduce schemes that realize it under standard assumptions. In an Unbounded Inner-Product Functional Encryption scheme, a public key allows anyone to encrypt unbounded vectors, that are essentially mappings from N∗ to Zp. The owner of the master secret key can generate functional decryption keys for other unbounded vectors. These keys enable one to evaluate the inner product between the

more »

... unbounded vector underlying the ciphertext and the unbounded vector in the functional decryption key, provided certain conditions on the two vectors are met. We build Unbounded Inner-Product Functional Encryption by introducing pairings, using a technique similar to that of Boneh-Franklin Identity-Based Encryption. A byproduct of this is that our scheme can be made Identity-Based "for free". It is also the first Public-Key Inner-Product Functional Encryption Scheme with a constant-size public key (and master secret key), as well constant-size functional decryption keys: each consisting of just one group element.