Dynamic threshold scheme based on the definition of cross-product in an N-dimensional linear space

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, k1j, K2j, …, and Kdj. Furthermore, if the d master keys have to be changed to Kj+11,Kj+½,…,and Kj+1d 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.