Fourier-based Verifiable Function Secret Sharing

Function secret sharing is a cryptographic protocol for secure distribution of a secret function. While the notion of function secret sharing is a conceptual extension of secret sharing schemes, it faces difficulties in its constructions. We demonstrate that if we consider function secret sharing schemes for Fourier basis functions then we can enjoy the linear properties of linear secret sharing schemes to construct function secret sharing schemes. In this paper, we construct a verifiable function secret sharing by using Fourier basis functions, where players can verify if the dealer is cheating.