Fourier-based Function Secret Sharing with General Access Structure

TL;DR

This paper extends Fourier-based function secret sharing schemes to support general access structures by integrating linear secret sharing techniques, moving beyond the traditional (p,p)-threshold models.

Contribution

It introduces a novel method to incorporate general access structures into Fourier-based FSS schemes using linear secret sharing techniques.

Findings

Supports any general access structure in Fourier-based FSS.

Maintains security and efficiency of secret sharing.

Extends applicability of FSS beyond threshold schemes.

Abstract

Function secret sharing (FSS) scheme is a mechanism that calculates a function f(x) for x in {0,1}^n which is shared among p parties, by using distributed functions f_i:{0,1}^n -> G, where G is an Abelian group, while the function f:{0,1}^n -> 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^n 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 f_i(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.