TY - CHAP

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

AU - Koshiba, Takeshi

N1 - Funding Information:
Acknowledgements TK is supported in part by JSPS Grant-in-Aids for Scientific Research (A) JP16H01705 and for Scientific Research (B) JP17H01695.

PY - 2018

Y1 - 2018

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

UR - http://www.scopus.com/inward/record.url?scp=85054768434&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85054768434&partnerID=8YFLogxK

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

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

M3 - Chapter

AN - SCOPUS:85054768434

T3 - Springer Proceedings in Mathematics and Statistics

SP - 417

EP - 428

BT - Springer Proceedings in Mathematics and Statistics

PB - Springer New York LLC

ER -