Public key cryptography is a widely adopted cryptographic system used to encrypt data. Unlike symmetric cryptography, which utilizes a single key, this type of system is considered asymmetric because it relies on a pair of keys. Public key cryptography was originally introduced in the 1970s by cryptographers Whitfield Diffie and Martin Hellman. Such cryptography systems are often referred to as Diffie-Hellman encryption as a way of paying homage to the inventors.
As mentioned, public key cryptography utilizes two keys: one public and one private. Both keys play a role in encrypting a message to protect the data it contains, and decrypting the message so it can be read. In this system, the public key can be shared and distributed freely. The private key, however, is to be kept secret and should only be accessed by whoever owns the key. To provide an additional layer of security, the private key is protected by an encrypted passphrase, which is essentially a stronger version of a password created by the owner of the key.
Both the public and private key are related from a mathematical aspect. Despite this relation, it is mathematically impossible for a private key to derived from a public key. This is because they serve two very distinct purposes. The public key is designed to encrypt the initial message, while the purpose of the private key is to decrypt it. Any message encrypted with a public key can only be only be viewed after being decrypted by the corresponding private key.
How public key cryptography works can be examined using a communication between John and Jane as an example. John generates a key pair and sends the public key to Jane, who uses the key to encrypt the message so that only John can read it. When receiving the message from Jane, John uses his secret key to decrypt and read it. Since John created the key pair, he is the owner of the private key, and therefore the only person able to decrypt and read the message.
Anyone who wants to use public key cryptography to protect communications can easily do so via email. For example, if John wants to keep the communications between he and Jane private, he could simply attach the public key she needs for encryption to the message. Since the key can be shared with anyone, sending it via email is not a security risk. One common example of applications that utilize this system is the popular encryption software known as Pretty Good Privacy® (PGP®).