An asymptotically perfect secret sharing scheme based on the Chinese Remainder Theorem

Abstract

The secret sharing schemes based on the Chinese Remainder Theorem (CRT) and their applications have attracted many researchers in recent years. In this paper, we propose a weighted threshold secret sharing scheme based on the CRT and prove the scheme is asymptotically perfect. Since all CRT-based secret sharing schemes use special sequences of pairwise coprime integers as its parameters, this paper proposes the first algorithm to generate these integers. Moreover, the correctness of this algorithm is proved by using the prime number theorem. The experimental result shows the effectiveness and the efficiency of our algorithm as well as the space efficiency of our scheme using the sequences of integers generated from our algorithm. Our scheme with the parameter generation algorithm can be used in many applications such as threshold cryptosystems.