Weighted Secret Sharing Based on the Chinese Remainder Theorem
Lein Harn, Fuyou Miao · 2013
In a), ( nt secret sharing scheme (SS), a dealer divides a secret into n shares in such a way that (a) the secret can be recovered successfully with t or more than t shares, and (b) the secret cannot be recovered with fewer than t shares. In a weighted secret sharing scheme (WSS), each share of a shareholder has a positive weight. The secret can be recovered if the overall weight of shares is equal to or larger than the threshold; but the secret cannot be recovered if the overall weight of shares is smaller than the threshold value. The), ( nt SS is a special type of WSSs in which the weight of all shares is the same. A shareholder having a higher weight needs to keep multiple shares if we adopt a standard), ( nt SS to implement a WSS. In this paper, we propose a WSS based on the Chinese Remainder Theorem (CRT) and the security of our scheme is the same as the), ( nt SS proposed by Asmuth and Bloom. In our proposed WSS, every shareholder including shareholders having higher weights keeps only one share. Furthermore, the modulus associated with shareholders in our proposed scheme is smaller than the modulus in all existing schemes.