Recently, e-commerce becomes widespread; hence electronic department stores come into being. As a result, Chan and Chang proposed a scheme for digital gift certificates in 2002. Because it is hard to estimate the number of the clients of the electronic department stores, reducing the computation complexity of the electronic department stores becomes an important issue. Due to the need, we propose two schemes for digital gift certificates. Our proposed schemes are very practical since the computation load is light. So the schemes can be applied to the terminals with low computation power.
