On-line secret sharing scheme, introduced by Cachin, is a computational variation of secret sharing scheme. It supports dynamic changing of access structures and reusable shares, by grace of public bulletin board. In this paper, first we introduce a formal model of on-line secret sharing scheme, and analyze existing on-line secret sharing schemes. As a result, it is shown that they are all vulnerable by giving concrete attacks. Next, we propose a novel on-line secret sharing scheme which is provably secure.