The paper introduces a multi-authority attribute-based encryption (ABE) scheme, which allows multiple independent authorities to monitor attributes and distribute secret keys. Each user is identified by a set of attributes, and decryption is possible if the user has at least a specified number of attributes from each authority. The scheme tolerates an arbitrary number of corrupt authorities and ensures security as long as the required attributes cannot be obtained exclusively from the honest authorities. The authors address the challenge of preventing collusion among users by requiring each user to have a global identifier (GID) that is unique and verifiable by all authorities. A central authority, trusted but not monitoring attributes, plays a crucial role in generating secret keys and ensuring the system's security. The central authority uses pseudorandom functions (PRFs) to split the master secret across multiple authorities, allowing each authority to compute its part independently. The paper also discusses extensions to the basic multiauthority scheme, including allowing the encryptor to specify the number of attributes required from each authority and a variant that supports fine-grained access control using policy-based keys. The scheme is proven secure in the selective identity (SID) model, based on the bilinear Diffie-Hellman (BDH) assumption. Finally, the authors demonstrate how their techniques can be applied to a large universe access structure ABE scheme, extending it to a multiauthority version.The paper introduces a multi-authority attribute-based encryption (ABE) scheme, which allows multiple independent authorities to monitor attributes and distribute secret keys. Each user is identified by a set of attributes, and decryption is possible if the user has at least a specified number of attributes from each authority. The scheme tolerates an arbitrary number of corrupt authorities and ensures security as long as the required attributes cannot be obtained exclusively from the honest authorities. The authors address the challenge of preventing collusion among users by requiring each user to have a global identifier (GID) that is unique and verifiable by all authorities. A central authority, trusted but not monitoring attributes, plays a crucial role in generating secret keys and ensuring the system's security. The central authority uses pseudorandom functions (PRFs) to split the master secret across multiple authorities, allowing each authority to compute its part independently. The paper also discusses extensions to the basic multiauthority scheme, including allowing the encryptor to specify the number of attributes required from each authority and a variant that supports fine-grained access control using policy-based keys. The scheme is proven secure in the selective identity (SID) model, based on the bilinear Diffie-Hellman (BDH) assumption. Finally, the authors demonstrate how their techniques can be applied to a large universe access structure ABE scheme, extending it to a multiauthority version.