Everyone who expects to receive a message publishes a key. To send digital cash to someone, you look up the public key and use the algorithm to encrypt the payment. The recipient then uses the private half of the key pair for decryption. Processing time for a reasonably safe digital signature conspires against keeping costs per transaction low. Depending on key length, an average machine can only sign between twenty and fifty messages per second.
Decryption is faster.
One way to factor out the overhead is to use a trustee organization, one that collects batches of small transaction before passing them on to the credit-card organization for processing. First Virtual, an Internet-based banking organization, relies on this approach. One form of verification is secure hash algorithms, which represent a large file of multiple megabytes with a relatively short number consisting of a few hundred bits. The recipient performs the same calculation and compares the two sums to make sure everything arrived correctly. The server poses a question, and the system seeking access offers an answer.