Attribute based encryption scheme is widely used to share sensitive data in cloud storage environment because it can realize fine-grained access control. Aiming at the problem of user revocation and high cost of decryption in cloud storage environment, a multi-authority attribute based encryption scheme with efficient user revocation and outsourcing decryption was proposed. It supports large universe. Each authority manages a specific set of attributes and distributes attribute keys to users

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... h corresponding attributes, avoiding the problem that a single authority may easily become a system bottleneck. The user revocation algorithm of the scheme can realize the efficient revocation of the authorized users, ensuring the forward security of ciphertext. It's proved to be statically-secure under random oracle and the efficiency analysis shows that it reduces user decryption cost greatly