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Decentralized Multi-Client Functional Encryption (DMCFE) is a multi-user extension of Functional Encryption (FE) without relying on a trusted third party. However, a fundamental requirement for DMCFE is that the decryptor must collect the partial functional keys and the ciphertexts from all clients. If one client does not generate the partial functional key or the ciphertext, the decryptor cannot obtain any useful information. We found that this strong requirement limits the application of DMCFE in scenarios such as statistical analysis and machine learning. In this paper, we first introduce a...

Functional encryption for inner product (FE-IP) allows an authorized user to obtain the inner product of the vectors embedded in his/her secret key and a ciphertext, respectively. Therefore, it is an elegant tool to implement secure computation over encrypted data. Existing FE-IP schemes mainly considered security and function privacy issues, but did not address the decryption delegation problem. However, in practice, delegating decryption is desirable when an authorized user is unavailable to access the system due to leaving, network problems, etc. In this paper, a delegatable FE-IP (DFE-IP) ...