Simulation-based secure functional encryption in the random oracle model

One of the main lines of research in functional encryption (FE) has consisted in studying the security notions for FE and their achievability. This study was initiated by [Boneh et al. TCC'11, O'Neill - ePrint'10] where it was first shown that for FE the indistinguishability-based (IND) security notion is not sufficient in the sense that there are FE schemes that are provably IND-Secure but concretely insecure. For this reason, researchers investigated the achievability of Simulation-based (SIM) security, a stronger notion of security. Unfortunately, the above-mentioned works and others [e.g., Agrawal et al. - CRYPTO' 13] have shown strong impossibility results for SIM-Security. One way to overcome these impossibility results was first suggested in the work of Boneh et al. where it was shown how to construct, in the Random Oracle (RO) model, SIM-Secure FE for restricted functionalities and was asked the generalization to more complex functionalities as a challenging problem in the area. Subsequently, [De Caro et al. CRYPTO' 13] proposed a candidate construction of SIM-Secure FE for all circuits in the RO model assuming the existence of an IND-Secure FE scheme for circuits with RO gates. To our knowledge there are no proposed candidate IND-Secure FE schemes for circuits with RO gates and they seem unlikely to exist. We propose the first constructions of SIM-Secure FE schemes in the RO model that overcome the current impossibility results in different settings. We can do that because we resort to the two following models:In the public-key setting we assume a bound on the number of queries but this bound only affects the running-times of our encryption and decryption procedures. We stress that our FE schemes in thismodel are SIM-Secure and have ciphertexts and tokens of constant-size, whereas in the standard model, the current SIM-Secure FE schemes for general functionalities [De Caro et al., Gorbunov et al. - CRYPTO' 12] have ciphertexts and tokens of size growing as the number of queries.In the symmetric-key setting we assume a timestamp on both ciphertexts and tokens. In this model, we provide FE schemes with short ciphertexts and tokens that are SIM-Secure against adversaries asking an unbounded number of queries.Both results also assume the RO model, but not functionalities with RO gates and rely on extractability obfuscation [Boyle et al. - TCC' 14] (and other standard primitives) secure only in the standard model.