How does public-key encryption work?

Public-key cryptography encrypts or signs data with two different keys. One, the public key, is made available to anyone. The other, the private key, stays secret. Data encrypted with the public key can only be decrypted with the private key, which is why the method is also called asymmetric cryptography. It is widely used, especially in TLS/SSL, which makes HTTPS possible. [1]

Each person first generates a key pair. The Open University's explanation notes that the program usually asks for random input, such as keyboard typing or mouse movement, so that nobody else can recreate the keys. The two people then swap public keys, which can be sent by email or posted on a key server. [2]

To send a message, the sender uses the recipient's public key to turn readable plaintext into scrambled ciphertext. Only the recipient's matching private key can restore the original. In the standard example, Bob asks Alice for her public key, encrypts with it, and sends the result. Alice decrypts with her private key. Even the sender cannot read the encrypted message afterward. [3] [4]

An eavesdropper, usually called Eve, may hold both the ciphertext and the public key, but that does not help her. The public key cannot undo what it did. The keys are related, yet the value of one cannot easily be worked out from the other, so a leaked public key does not reveal the private key. Eve would have to steal the private key or try brute force, which the Open University source says could take billions of years. [2]

Cryptography textbooks describe a public-key scheme as three algorithms. A key generation algorithm produces a public and a private key. An encryption algorithm takes the public key and a message and outputs a ciphertext. A decryption algorithm takes the private key and the ciphertext and returns the message. Correctness means that decrypting an encrypted message always returns the original. In one textbook's definition, encryption is randomized and decryption is deterministic. [5] [6]

The main advantage is that no secret key has to be shared in advance. Users exchange only public keys, which sidesteps the key distribution problem of symmetric encryption. The costs are that public-key methods are generally far slower than symmetric ones, and traditional techniques need much longer keys for the same protection. The Open University source adds that a newer type of public-key cryptography, elliptic-curve cryptography, is introduced to address this, though the excerpt available here is cut off before explaining how. [2]