Public-key cryptography, also called asymmetric cryptography, uses a pair of mathematically linked keys instead of one shared secret. A public key, which can be published openly, is used to encrypt messages or verify signatures; the matching private key, kept secret by its owner, is used to decrypt those messages or create signatures. What one key does, only the other can undo, and knowing the public key does not let an attacker derive the private one.
This design solves the key-distribution problem that limits symmetric encryption. Two people who have never met, and whose every message may be observed, can still communicate securely: each publishes a public key, and anyone can encrypt a message that only the intended holder of the private key can read. There is no need to share a secret in advance.
The idea was introduced by Whitfield Diffie and Martin Hellman in their 1976 paper “New Directions in Cryptography,” published in the IEEE Transactions on Information Theory. They argued that the theories of communication and computation were finally providing the tools to solve long-standing cryptographic problems, and they described both public-key encryption and a method for two parties to agree on a shared key over an insecure channel.
Diffie and Hellman described the concept but did not give a complete practical encryption scheme; that came shortly afterward with RSA, which realized public-key encryption and digital signatures using the difficulty of factoring large numbers. Together these ideas underpin secure web browsing, signed software, and most encrypted communication in use today.