Public key encryption, also known as asymmetric encryption, is a cryptographic method that uses a pair of mathematically related keys to secure communication and protect data. The pair consists of a public key and a private key, which are used for encryption and decryption, respectively. Here's how public key encryption works:

1. Key Generation: The process starts with generating a key pair. The user generates a private key, which is kept secret and never shared with anyone. Simultaneously, a corresponding public key is derived from the private key.
2. Public Key Distribution: The public key is made freely available to others and can be shared widely. It's called the "public" key because it can be shared openly without compromising the security of the encryption system.
3. Encryption: To send an encrypted message to someone who possesses the public key, the sender uses the recipient's public key to encrypt the message. The encryption process takes the plaintext message and transforms it into an unreadable ciphertext using the recipient's public key.
4. Transmission: The encrypted ciphertext can now be safely transmitted over insecure channels, such as the internet or email.
5. Decryption: Upon receiving the encrypted message, the recipient uses their private key to decrypt the ciphertext and recover the original plaintext. Only the recipient's private key can successfully decrypt the ciphertext, ensuring the confidentiality of the message.
6. Security: Public key encryption provides a high level of security because even if an attacker intercepts the encrypted message and obtains the public key, they cannot use it to decrypt the message without the corresponding private key.

Public key encryption is often used in various applications, such as secure communication protocols (e.g., HTTPS), digital signatures, and secure file transfer. It allows secure communication between parties who have never directly exchanged secrets or keys, as long as they possess each other's public keys.

One popular algorithm used for public key encryption is the RSA (Rivest-Shamir-Adleman) algorithm. Other widely used algorithms include Diffie-Hellman, DSA (Digital Signature Algorithm), and elliptic curve cryptography (ECC).

Public key encryption provides a powerful and secure method for protecting data and ensuring the confidentiality, integrity, and authenticity of communications in various digital systems.