摘要 : In this paper, coding theorems on the $(t,m)$-threshold scheme for a general source are discussed, where $m$ means the number of the shares and $t$ means a threshold. The $(t,m)$-threshold scheme treated in this paper encrypts $... 展开 In this paper, coding theorems on the $(t,m)$-threshold scheme for a general source are discussed, where $m$ means the number of the shares and $t$ means a threshold. The $(t,m)$-threshold scheme treated in this paper encrypts $n$ source outputs $X^{n}$ to $m$ shares at once and is required to satisfy the two conditions that 1) $X^{n}$ is reproduced from arbitrary $t$ shares, and 2) almost no information of $X^{n}$ is revealed from any $t-1$ shares. It is shown that the $(t,m)$ -threshold scheme must satisfy certain inequalities including the limit inferiors in probability. One of the inequalities is closely related to the minimum length of the fair random bits needed to a dealer for realizing the $(t,m)$-threshold scheme. In addition, it is shown that a certain variation of Shamir''s threshold scheme meets the two conditions. The same approach can be taken to the problems of Shannon''s cipher system with the perfect secrecy and fixed-length source coding with vanishing decoding error probability. It is shown that the same k-ind of inequalities, which indicate the converse coding theorems, hold in both two cases. 收起