In this paper, we propose a fast signature scheme which realizes short transmissions and minimal on-line computation. Our scheme requires a modular exponentiation as preprocessing (i.e., off-line computation). However, we need to acknowledge the existance of the following remarkable properties: neither multiplication nor modular reduction is used in the actual signature generation (i.e., on-line computation). Our scheme requires only two operations: hashing and addition. Although some fast signature schemes with small on-line computation have been proposed so far. those schemes require multiplication or modular reduction in the online phase. This leads to a large amount of work compared to that of addition. As far as we know, this is the first approach to obtain the fast signature without those two calculus methods.