Combinatorial Construction of Repairable Threshold Key Sharing Schemes

Abstract

In this paper, we use two types of designs to construct repairable threshold schemes, and calculate information rate and communication complexity of the schemes to analyze their performance. Firstly, SB(2λ + 1, λ, 4λ + 3) is used to construct the (3, 4λ + 3, 2λ + 1)−RTS, which is based on (3λ + 3, 4λ + 4)−Shamir threshold scheme. Secondly, the mutually orthogonal Latin squares are constructed, and a RTD(q, 1; q 2) is obtained by them. Further, the RB(q, 1; q 3) is obtained through filling hole method. (2, n, q)−RTS based on (q, 2q − 1, q 3)−Ramp threshold scheme and (3, n, q)−RTS based on (2q, 3q − 3, q 3)−Ramp threshold scheme are constructed by RB(q, 1; q 3), where 2q 2 ≤ n ≤ q 2 (q 2 + q + 1). Finally , the information rate and the communication complexity of three repairable threshold schemes are calculated, and the performance of these schemes is analyzed. Compared with the existing schemes, the results show that (2, n, q)−RTS and (3, n, q)−RTS constructed by RB(q, 1; q 3) have higher information rate and lower communication complexity.