Disposable-number credit card is a recent approach to contrasting the severe problem of credit card fraud, nowadays constantly growing, especially in credit-card-based e-commerce payments. Whenever the solutions cannot rely on a secure extra communication channel between cardholder and issuer, the only possibility is to generate new numbers on the basis of some common scheme, starting from secret shared initial information. However, in order to make the approach feasible, the computational load both on issuer and customer side should be minimized, also to reduce the cost of user-side devices, keeping yet an adequate security level. In this paper we present a disposable-number credit card scheme meeting the above goals, going a step ahead w.r.t. the state of the art.