Public-key cryptosystems

The key agreement protocol provides a way for previously unacquainted parties to agree on a secret key. However, there are times when one party wants to unilaterally send a private message to another party without first interacting with the other party. Public-key encryption, first proposed by Diffie and Hellman in the early 1970s, provides a way to accomplish this.

In traditional (one-key) cryptography, the same key is used to encrypt a message as to decrypt it. Public-key cryptography discards this convention, and allows one (public) key to be used for encryption and another (the secret key) for decryption.

The set-up for public key cryptography is as follows. Every person intending to receive encrypted messages privately chooses a secret key and calculates a corresponding public key. All the public keys are made publically available. If I want to send an encrypted message to someone, I look up her public key and use it to encrypt a message to her; only she is able to decrypt it.

The idea of having different keys for encryption and decryption seems simple, but it represented a startling break with the past. It is worth considering why the discovery was so late in coming; after all, traditional cryptography has been used for a few thousand years. Why did the idea of two different keys not arise earlier?