What is so hard about electronic currency? After all, debit and teller machine cards are in common use over networks. Credit cards are widely used over the telephone network. It turns out that there are several difficult problems to be solved, though the problems vary with the type of currency under discussion. For example, bank debit cards and automatic teller cards work because they have reliable authentication procedures based on both a physical device and knowledge of a private code. Digital currency over the network is more difficult because it is not possible to install physical devices and protect them from tampering on every workstation. Credit cards over the phone network are relatively secure because phone tapping is difficult and costly, and there is no central database connected to the network that contains all of the voice-provided credit card numbers. When a credit card number is transmitted over the Internet in the clear, however, ``sniffing'' it is relatively easy and inexpensive, and following its path may lead to a massive database of valid card numbers.
A variety of schemes are being developed. See the Economics of the Internet Web page for some links to at least 14 different systems! Many of these systems use forms of public key cryptography to encrypt payment records. This is relatively straightforward for, say, credit card numbers, but becomes substantially more difficult if you want to ensure anonymity. See [Chaum92] for a description of one such electronic cash system.