Bounded-collusion decentralized ABE with sublinear parameters

In this paper, we propose a decentralized ABE scheme against bounded collusion which means the number of users in the system is a-prior bounded. The scheme enjoys public key and ciphertext of sublinear sizes in the number of users in the system while all prior constructions require linear sizes. Besides, our scheme achieves semi-adaptive security under bilateral k-Lin assumption and SXDH assumption in a pairing group. Keep the same as the previous constructions, the scheme supports monotone span program as a policy and does not rely on the random oracle. Technically, we follow Wang et al.'s “linear secret sharing scheme (LSSS) + inner-product functional encryption (IPFE)” paradigm [PKC'19] and use (an extended variant of) functional encryption for quadratic functions (QFE) in the place of IPFE. By this, we encrypt with sublinear-size random coins and later expand them to linear-size entropy for security proof. Roughly, the use of QFE requires bilateral k-Lin assumption while the entropy expansion relies on SXDH.