Estimations on the security aspect of Brands´ electronic cash scheme

In Crypto ´93, Stefan Brands (1993) proposed a very efficient off-line electronic cash. Then, the subsequent researchers such as Ernest Foo (1999, 2000), WK Yip (2000) and Yiannis (1998) developed their schemes based upon Brands model (Brands,1993) to improve Brands´ efficiency. In this paper, we demonstrate the feasibility of attacks on Brands scheme´s security aspect. By our attacks presented here, we conclude the security aspect of (Brands, 1993; Boyd et al., 1999; Foo, 2000; Goh and Yip, 2000; Chan et al., 1998) has been defeated by us. Although we address here that Brands´ security aspect need to be further investigated, but the anonymous feature in Brand´s scheme (1993) remain significant contributions to electronic cash, especially for privacy reason.