The final and perhaps the most important aspect of security is providing virtual money or binary cash; from another point of view, this could mean making digital signatures, and therefore electronic checks, possible.
At first sight, this seems impossible. The authority to issue documents such as checks is proved by a signature. Simple as it is, and apparently open to fraud, the system does actually work on paper. We might transfer it literally to the Web by scanning an image of a person's signature and sending that to validate his or her documents. However, whatever security that was locked to the paper signature has now evaporated. A forger simply has to copy the bit pattern that makes up the image, store it, and attach it to any of his or her purchases to start free shopping.
The way to write a digital signature is to perform some action on data provided by the other party that only you could have performed, thereby proving you are who you say.
The ideas of public key (PK) encryption are pretty well known by now, so we will just skim over the salient points. You have two keys: one (your public key) that encrypts messages and one (your private key) that decrypts messages encrypted with your public key (and vice versa). You give the public key to anyone who asks and keep your private key secret. Because the keys for encryption and decryption are not the same, the system is also called asymmetric key encryption.
For instance, let's apply ...