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An attribute based encryption scheme capable of handling multiple authorities was recently proposed by Chase. The scheme is built upon a single-authority attribute based encryption scheme presented earlier by Sahai and Waters. Chase's construction uses a trusted central authority that is inherently capable of decrypting arbitrary ciphertexts created within the system. The authors present a multi-authority attribute based encryption scheme in which only the set of recipients defined by the encrypting party can decrypt a corresponding ciphertext. The central authority is viewed as "Honest-but-curious": on the one hand it honestly follows the protocol, and on the other hand it is curious to decrypt arbitrary ciphertexts thus violating the intent of the encrypting party.
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