### Abstract

Function secret sharing (FSS) scheme is a mechanism that calculates a function f(x) for f(x) for x ∈ {0,1}^{n} which is shared among p parties, by using distributed functions f_{i}:{0,1}^{n}→G(1≤i≤p), 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 propose Fourier-based FSS schemes with any general access structure.

Original language | English |
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Title of host publication | Springer Proceedings in Mathematics and Statistics |

Publisher | Springer New York LLC |

Pages | 417-428 |

Number of pages | 12 |

DOIs | |

Publication status | Published - 2018 |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 253 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Keywords

- Access structure
- Distributed computation
- Fourier basis
- Function secret sharing
- Linear secret sharing
- Monotone span program

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*Springer Proceedings in Mathematics and Statistics*(pp. 417-428). (Springer Proceedings in Mathematics and Statistics; Vol. 253). Springer New York LLC. https://doi.org/10.1007/978-981-13-2095-8_32