### 抄録

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.

元の言語 | English |
---|---|

ホスト出版物のタイトル | Springer Proceedings in Mathematics and Statistics |

出版者 | Springer New York LLC |

ページ | 417-428 |

ページ数 | 12 |

巻 | 253 |

DOI | |

出版物ステータス | Published - 2018 1 1 |

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### ASJC Scopus subject areas

- Mathematics(all)

### これを引用

*Springer Proceedings in Mathematics and Statistics*(巻 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.

研究成果: Chapter

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

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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

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AN - SCOPUS:85054768434

VL - 253

SP - 417

EP - 428

BT - Springer Proceedings in Mathematics and Statistics

PB - Springer New York LLC

ER -