Fully Secure Functional Encryption without Obfuscation

Previously known functional encryption (FE) schemes for general circuits relied on indistin-guishability obfuscation, which in turn either relies on an exponential number of assumptions (basically, one per circuit), or a polynomial set of assumptions, but with an exponential loss in the security reduction. Additionally these schemes are proved in an unrealistic selective security model, where the adversary is forced to specify its target before seeing the public parameters. For these constructions, full security can be obtained but at the cost of an exponential loss in the security reduction. In this work, we overcome the above limitations and realize a fully secure functional en-cryption scheme without using indistinguishability obfuscation. Specifically the security of our scheme relies only on the polynomial hardness of simple assumptions on multilinear maps.