整体检测门限秘密共享欺诈者方案

Scheme of Whole Detecting Cheaters in Threshold Secret Sharing

对门限秘密共享欺诈者的检测,目前很少有整体检测法。利用线性方程组解的性质,在能获得比门限个数多一个参与者的条件下,不需其他任何信息,只需执行一次运算,就可整体判断有无欺诈者。该方案是一个完备的秘密共享方案,信息率为1,1个欺诈者欺诈成功的概率为0,2个及多个欺诈者欺诈成功的概率不超过1/p(p为大素数)。

So far, methods of whole detecting cheaters in threshold secret sharing are few. If another participant can join in the t participants, t＋1 participants in total, according to the scheme proposed in this paper, the existence of cheaters can be checked out only calculating equations once, requiring no other information. This scheme is a perfect sharing scheme. Its information rate is 1. The probability of one cheater＇s success is 0 and it is less than l/p （where p is a large prime） for two or three cheaters in probability of success.