研究成果

学術論文誌

  • Optimal Multiple Assignments Based on Integer Programming in Secret Sharing Schemes with General Access Structures
    著者
    M. Iwamoto, H. Yamamoto, and H. Ogawa
    雑誌名
    IEICE Transactions on Fundamentals
    E90–A
    1
    ページ
    101–112
    出版社
    IEICE
    発行年
    2021
    Abstract

    It is known that for any general access structure, a secret sharing scheme (SSS) can be constructed from an (m,m)-threshold scheme by using the so-called cumulative map or from a (t,m)-threshold SSS by a modified cumulative map. However, such constructed SSSs are not efficient generally. In this paper, a new method is proposed to construct a SSS from a (t,m)-threshold scheme for any given general access structure. In the proposed method, integer programming is used to derive the optimal (t,m)-threshold scheme and the optimal distribution of the shares to minimize the average or maximum size of the distributed shares to participants. From the optimality, it can always attain lower coding rate than the cumulative maps because the cumulative maps cannot attain the optimal distribution in many cases. The same method is also applied to construct SSSs for incomplete access structures and/or ramp access structures.