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Decentralized attribute-based encryption (ABE) is a variant of a multiauthority ABE scheme where each authority can issue secret keys to the user independently without any cooperation and a central authority. This is in contrast to the previous constructions, where multiple authorities must be online and setup the system interactively, which is impractical. Hence, it is clear that a decentralized ABE scheme eliminates the heavy communication cost and the need for collaborative computation in the setup stage. Furthermore, every authority can join or leave the system freely without the necessity of reinitializing the system. In contemporary multiauthority ABE schemes, a user's secret keys from different authorities must be tied to his global identifier (GID) to resist the collusion attack. However, this will compromise the user's privacy. Multiple authorities can collaborate to trace the user by his GID, collect his attributes, then impersonate him. Therefore, constructing a decentralized ABE scheme with privacy-preserving remains a challenging research problem. In this paper, we propose a privacy-preserving decentralized key-policy ABE scheme where each authority can issue secret keys to a user independently without knowing anything about his GID. Therefore, even if multiple authorities are corrupted, they cannot collect the user's attributes by tracing his GID. Notably, our scheme only requires standard complexity assumptions (e.g., decisional bilinear Diffie-Hellman) and does not require any cooperation between the multiple authorities, in contrast to the previous comparable scheme that requires nonstandard complexity assumptions (e.g., q-decisional Diffie-Hellman inversion) and interactions among multiple authorities. To the best of our knowledge, it is the first decentralized ABE scheme with privacy-preserving based on standard complexity assumptions.