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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 new primitive named Robust Decentralized Multi-Client Functional Encryption (RDMCFE), a notion generalized from DMCFE that aims to tolerate the problem of negative clients leading to nothing for the decryptor, where negative clients represent participants that are unable or unwilling to compute the partial functional key or the ciphertext. Conversely, a client is said to be a positive one if it i

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