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.