Fully Secure and Succinct Attribute Based Encryption for Circuits from Multi-linear Maps

We propose new fully secure attribute based encryption (ABE) systems for polynomialsize circuits in both key-policy and ciphertext-policy flavors. All the previous ABE systems for circuits were proved only selectively secure. Our schemes are based on asymmetric graded encoding systems in composite-order settings. The assumptions consist of the Subgroup Decision assumptions and two assumptions which are similar to Multi-linear Decisional Diffie-Hellman assumption (but more complex) and are proved to hold in the generic graded encoding model. Both of our systems enjoy succinctness: key and ciphertext sizes are proportional to their corresponding circuit and input string sizes. Our ciphertext-policy ABE for circuits is the first to achieve succinctness, and the first that can deal with unbounded-size circuits (even among selectively secure systems). We develop new techniques for proving co-selective security of keypolicy ABE for circuits, which is the main ingredient for the dual-system encryption framework that uses computational arguments for enforcing full security.