Two novel applications of bilinear groups to ABE encryption

Bilinear groups are often used to create Attribute-Based Encryption (ABE) algorithms. In particular, they have been used to create an ABE system with multi authorities, but limited to the ciphertext-policy instance. Here, for the first time, we propose two multi-authority key-policy ABE systems. In our first proposal, the authorities may be set up in any moment and without any coordination. A party can simply act as an ABE authority by creating its own public parameters and issuing private keys to the users. A user can thus encrypt data choosing both a set of attributes and a set of trusted authorities, maintaining full control unless all his chosen authorities collude against him. In our second system, the authorities are allowed to collaborate to achieve shorter keys and parameters, enhancing the efficiency of encryption and decryption. We prove our systems secure under algebraic assumptions on the bilinear groups: the bilinear Diffie-Hellmann assumption and an original variation of the former.