Function-Hiding Multi-Client Inner-Product Functional Encryption Without Pairings for Large Space

Multi-client functional encryption (MCFE) is an extension of functional encryption (FE) in the multi-user setting and serves as a generalization of multi-input functional encryption (MIFE). The necessity of hiding function when it contains sensitive information, coupled with the widespread application of inner product (IP) in the descriptive statistics, has led to extensive research on function-hiding MCFE for IP. However, these works all rely on pairings and impose serious restrictions on the size of supported messages, as they all use inefficient decryption involving the extraction of discrete logarithms. On the other hand, although Abdalla et al. (CRYPTO 2018) introduced the first inner-product MIFE scheme for large message space as a special case of MCFE, it is not function-hiding. Consequently, existing inner-product MCFE schemes either exclusively support large space or solely achieve function-hiding, with no solution simultaneously achieving both properties. This paper employs an incremental construction strategy to design the function-hiding inner-product MCFE scheme, which does not require pairings. This leads to two main advances. First, we achieve the function hiding for inner-product MIFE even for messages of super-polynomial size. Second, we obtain the first function-hiding inner-product MCFE for large space, where the length of the message is of super-polynomial size.