> One way to minimize the problem of multiple spending in an off-line system is to set an upper limit on the value of each payment. This would limit the financial losses to a given merchant due to accepting coins that have been previously deposited. However, this will not prevent someone from spending the same small coin many times in different places.
> In order to prevent multiple spending in off-line payments, we need to rely on physical security. A "tamper-proof" card could prevent multiple spending by removing or disabling a coin once it is spent. Unfortunately, there is no such thing as a truly "tamper-proof" card. Instead, we will refer to a "tamper-resistant" card, which is physically constructed so that it is very difficult to modify its contents.