  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 a multi-authority key-policy ABE system. In our
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. We prove our system secure under the bilinear Diffie-Hellman
assumption.
