Fourier-based Function Secret Sharing with General Access Structure

Function secret sharing (FSS) scheme is a mechanism that calculates a function f(x) for x ∈ {0, 1} which is shared among p parties, by using distributed functions fi : {0, 1} → G (1 ≤ i ≤ p), where G is an Abelian group, while the function f : {0, 1} → G is kept secret to the parties. Ohsawa et al. in 2017 observed that any function f can be described as a linear combination of the basis functions by regarding the function space as a vector space of dimension 2 and gave new FSS schemes based on the Fourier basis. All existing FSS schemes are of (p, p)-threshold type. That is, to compute f(x), we have to collect fi(x) for all the distributed functions. In this paper, as in the secret sharing schemes, we consider FSS schemes with any general access structure. To do this, we observe that Fourier-based FSS schemes by Ohsawa et al. are compatible with linear secret sharing scheme. By incorporating the techniques of linear secret sharing with any general access structure into the Fourier-based FSS schemes, we show Fourier-based FSS schemes with any general access structure.