It is generally realized that the Internet will not be able to offer full-fledged electronic marketplace capabilities without a suitable electronic mechanism for processing payments. The electronic payment mechanism that is presented offers a variety of features that are believed to be particularly appealing in this respect. To participate, an Internet user must interface to his computer a tamper-resistant device with an ordinary 8-bit microprocessor, typically a PCMCIA card, and install some software. Internet service providers do not need special hardware. Payments can be made off-line, and are untraceable and unlinkable. Multiparty security is guaranteed without parties having to trust other parties. Transaction processing speeds are such that even modestly equipped computers would be able to meet the performance levels required by demanding Internet payment applications. One particularly interesting such application is click-and-pay ability when travelling World-Wide-Web links.