Private key cryptography suffers from one major drawback: how does the private key get to Alice and Bob in the first place? If Alice generates it, she has to send it to Bob, but it is sensitive information so it should be encrypted. However, keys have not been exchanged to perform the encryption.

Public key cryptography, invented in the 1970s, solves the problem of encrypting messages between two parties without prior agreement on the key.

In public key cryptography, Alice and Bob not only have different keys, they each have two keys. One key is private and must not be shared with anyone. The other key is public and can be shared with anyone.

When Alice wants to send a secure message to Bob, she encrypts the message using Bob's public key and sends the result to Bob. Bob uses his private key to decrypt the message. When Bob wants to send a secure message to Alice, he encrypts the message using Alice's public key and sends the result to Alice. Alice uses her private key to decrypt the message. Eve can eavesdrop on both public keys and the encrypted messages, but she cannot decrypt the messages because she does not have either of the private keys.

The public and private keys are generated as a pair and need longer lengths than the equivalent-strength private key encryption keys. Typical key lengths for the RSA algorithm are 1,024 bits. It is not feasible to derive one member of the key pair from the other.

Public key encryption is slow (100 to 1,000 times slower than private key encryption), so a hybrid technique is usually used in practice. Public key encryption is used to distribute a private key, known as a session key, to another party, and then private key encryption using that private session key is used for the bulk of the message encryption.