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Public key or asymmetric cryptography is a form of encryption using separate keys for encryption and decryption, neither of which can be derived from the other. Anyone can use the public key to encrypt a message which only the holder of the corresponding private key can decrypt. Alternatively, the holder of a private key can "digitally sign" a message by using it to encrypt a digest of the message, sent with the message itself. A recipient can prove the authorship of the message by successfully decrypting the digest using the author's previously published public key. Public key cryptography is computationally expensive so is often used simply to agree a symmetric encryption key.