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PGP stands for 'pretty good privacy,' and is an NSA-grade encryption standard based on the RSA/DSA prime number factorization schemes. Luckily, using PGP requires no math whatsoever. What it does require, however, is your own keypair, an understanding of how public key encryption works, and the software to make it all run. Most PGP software will take care of key generation for you, so let me skip to instructions on usage.

A keypair, as you might imagine, consists of two separate keys. The first is called the private key, and allows whoever possesses it to DECRYPT message. The second is called the public key, and allows whoever possesses it to ENCRYPT messages. So, a person generates their very own keypair, and distributes their public key in whatever way they find appropriate (usually by putting it onto a keyserver such as pgp.mit.edu). This way, anybody can encrypt a message so that only they are able to decrypt it.

Now, Let's say that cypherpunk A wants to send a message to cypherpunk B, but he doesn't want it to get read by intelligence agent #1. If both A and B have encryption keys, they are in luck. All that A has to do is write her message (on a computer that hasn't already been hacked by the intelligence agent) and tell her encryption software to encrypt it using B's public key. This message can now be sent via the public network without fear of ISP/Telecom/Government scrutiny.

Luckily PGP software can take care of this process as well, maintaining a list of recipients for whom public keys are known, and using them automatically when they are the recipient of a message.