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As Is Known, Attribute-based Encryption (ABE) Is Usually Adopted For Cloud Storage, Both For Its Achievement Of Fine-grained Access Control Over Data, And For Its Guarantee Of Data Confidentiality. Nevertheless, Single-authority Attribute-based Encryption (SA-ABE) Has Its Obvious Drawback In That Only One Attribute Authority Can Assign The Users' Attributes, Enabling The Data To Be Shared Only Within The Management Domain Of The Attribute Authority, While Rendering Multiple Attribute Authorities Unable To Share The Data. On The Other Hand, Multi-authority Attribute-based Encryption (MA-ABE) Has Its Advantages Over SA-ABE. It Can Not Only Satisfy The Need For The Fine-grained Access Control And Confidentiality Of Data, But Also Make The Data Shared Among Different Multiple Attribute Authorities. However, Existing MA-ABE Schemes Are Unsuitable For The Devices With Resources-constraint, Because These Schemes Are All Based On Expensive Bilinear Pairing. Moreover, The Major Challenge Of MA-ABE Scheme Is Attribute Revocation. So Far, Many Solutions In This Respect Are Not Efficient Enough. In This Paper, On The Basis Of The Elliptic Curves Cryptography, We Propose An Efficient Revocable Multi-authority Attribute-based Encryption (RMA-ABE) Scheme For Cloud Storage. The Security Analysis Indicates That The Proposed Scheme Satisfies Indistinguishable Under Adaptive Chosen Plaintext Attack Assuming Hardness Of The Decisional Diffie-Hellman Problem. Compared With The Other Schemes, The Proposed Scheme Gets Its Advantages In That It Is More Economical In Computation And Storage.