Abstract
In a secret sharing scheme, a datumd is broken into shadows which are shared by a set of trustees. The family {P′⊆P:P′ can reconstructd} is called the access structure of the scheme. A (k, n)-threshold scheme is a secret sharing scheme having the access structure {P′⊆P: |P′|≥k}. In this paper, by observing a simple set-theoretic property of an access structure, we propose its mathematical definition. Then we verify the definition by proving that every family satisfying the definition is realized by assigning two more shadows of a threshold scheme to trustees.
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Communicated by Ernest F. Brickell
This work was partly supported by the Telecommunications Advancement Foundation. Also the work of the second author was partly supported by the Grant in Aid for Scientific Research of the Ministry of Education, Science and Culture of Japan under Grant Number YSE (A) 62780017.
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Ito, M., Saito, A. & Nishizeki, T. Multiple assignment scheme for sharing secret. J. Cryptology 6, 15–20 (1993). https://doi.org/10.1007/BF02620229
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DOI: https://doi.org/10.1007/BF02620229