Coding theorems on the threshold scheme for a general source

This paper is concerned with basic properties of the (t, m)-threshold scheme, where m denotes the number of shares and t a threshold. We are interested in the case where a secret information is generated from a source with no assumption on its probabilistic structure. We first give conditions that the (t, m)-threshold scheme must satisfy. Then, we give a theorem which is related to lower bounds on the sizes of shares and the length of random bits needed to a dealer. In addition, we show that the (t, m)-threshold scheme is realized under a certain mild assumption on the source