Abstract
This paper investigates the characterizations of threshold /ramp schemes which give rise to the time-dependent threshold schemes. These schemes are called the “dynamic threshold schemes” as compared to the conventional time-independent threshold scheme. In a (d, m, n, T) dynamic threshold scheme, there are n secret shadows and a public shadow, pj, at time t=tj, 1≤tj≤T. After knowing any m shadows, m≤n, and the public shadow, pj, we can easily recover d master keys, k j1 , K j2 , ..., and K jd . Furthermore, if the d master keys have to be changed to \( K\begin{array}{*{20}c} {j + 1} \\ 1 \\ \end{array} ,K\begin{array}{*{20}c} {j + 1} \\ 2 \\ \end{array} ,...,and\,K\begin{array}{*{20}c} {j + 1} \\ d \\ \end{array} \) for some security reasons, only the public shadow, pj, has to be changed to pj+1. All the n secret shadows issued initially remain unchanged. Compared to the conventional threshold/ramp schemes, at least one of the previous issued n shadows need to be changed whenever the master keys need to be updated for security reasons. A (1, m, n, T) dynamic threshold scheme based on the definition of cross-product in an N- dimensional linear space is proposed to illustrate the characterizations of the dynamic threshold schemes.
This work was sponsored by the National Science Council, Republic of China, under Contract NSC79-0408-E006-02.
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© 1990 Springer-Verlag Berlin Heidelberg
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Laih, CS., Harn, L., Lee, JY., Hwang, T. (1990). Dynamic Threshold Scheme Based on the Definition of Cross-Product in an N-Dimensional Linear Space. In: Brassard, G. (eds) Advances in Cryptology — CRYPTO’ 89 Proceedings. CRYPTO 1989. Lecture Notes in Computer Science, vol 435. Springer, New York, NY. https://doi.org/10.1007/0-387-34805-0_26
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DOI: https://doi.org/10.1007/0-387-34805-0_26
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