### 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 |

Volume | 253 |

DOIs | |

Publication status | Published - 2018 Jan 1 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

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

**Fourier-based function secret sharing with general access structure.** / Koshiba, Takeshi.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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

}

TY - CHAP

T1 - Fourier-based function secret sharing with general access structure

AU - Koshiba, Takeshi

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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 fi:{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 2n 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 propose Fourier-based FSS schemes with any general access structure.

AB - 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 fi:{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 2n 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 propose Fourier-based FSS schemes with any general access structure.

KW - Access structure

KW - Distributed computation

KW - Fourier basis

KW - Function secret sharing

KW - Linear secret sharing

KW - Monotone span program

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U2 - 10.1007/978-981-13-2095-8_32

DO - 10.1007/978-981-13-2095-8_32

M3 - Chapter

VL - 253

SP - 417

EP - 428

BT - Springer Proceedings in Mathematics and Statistics

PB - Springer New York LLC

ER -