An efficient public key functional encryption for inner product evaluations

As many services have changed from offline to online, a lot of personal information including user private data has been collected by and exchanged with various service providers. An issue raised in this process is that personal information can be exploited by multiple unwanted entities without the data owner’s knowledge. To solve this problem, functional encryption was proposed. It is suitable for data protection because even if a third-party uses the owner’s secret key for a function f, it cannot retrieve the original message x from the ciphertext. This means that information about x cannot be published, but is exposed only as f(x), the result of the function f. However, previous pairing-based public key functional encryption schemes for inner product evaluations (FE-IPE) cannot be practical solutions yet because they require too much computation, communication and storage overheads. In this paper, we propose an efficient pairing-based public key FE-IPE that requires only n (i.e., the dimension of vectors for function and message) exponentiation plus two pairing computations for decryption with smaller sized public parameters, secret keys and ciphertexts. And this scheme supports fully collusion resistance. The proposed scheme is proven selectively secure against chosen-plaintext attacks in the standard model under the external Diffie–Hellman assumption.