Solving sparse linear equations over finite fields
IEEE Transactions on Information Theory
Generalized linear threshold scheme
Proceedings of CRYPTO 84 on Advances in cryptology
Proceedings of CRYPTO 84 on Advances in cryptology
Communications of the ACM
IEEE Transactions on Information Theory
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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, l驴tj驴T. After knowing any m shadows, m驴n, and the public shadow, pj, we can easily recover d master keys, K1j, K2j..., and Kdj. Furthermore, if the d master keys have to be changed to Kj+1/1 KJ+1/2..., and Kj+1/d 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.