Fourier-based function secret sharing with general access structure

    Research output: Chapter in Book/Report/Conference proceedingChapter

    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 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.

    Original languageEnglish
    Title of host publicationSpringer Proceedings in Mathematics and Statistics
    PublisherSpringer New York LLC
    Pages417-428
    Number of pages12
    Volume253
    DOIs
    Publication statusPublished - 2018 Jan 1

    Fingerprint

    Access Structure
    Secret Sharing
    Secret Sharing Scheme
    Dimension of a vector space
    Function Space
    Abelian group
    Basis Functions
    Linear Combination

    Keywords

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

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Koshiba, T. (2018). Fourier-based function secret sharing with general access structure. In 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.

    Springer Proceedings in Mathematics and Statistics. Vol. 253 Springer New York LLC, 2018. p. 417-428.

    Research output: Chapter in Book/Report/Conference proceedingChapter

    Koshiba, T 2018, Fourier-based function secret sharing with general access structure. in 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
    Koshiba T. Fourier-based function secret sharing with general access structure. In Springer Proceedings in Mathematics and Statistics. Vol. 253. Springer New York LLC. 2018. p. 417-428 https://doi.org/10.1007/978-981-13-2095-8_32
    Koshiba, Takeshi. / Fourier-based function secret sharing with general access structure. Springer Proceedings in Mathematics and Statistics. Vol. 253 Springer New York LLC, 2018. pp. 417-428
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