Public-key cryptography, or asymmetric cryptography, is a cryptographic system that uses pairs of keys: public keys, which may be disseminated widely, and private keys, which are known only to the owner. The generation of such keys depends on cryptographic algorithms based on mathematical problems to produce one-way functions. Effective security only requires keeping the private key private; the public key can be openly distributed without compromising security.
In such a system, any person can encrypt a message using the receiver's public key, but that encrypted message can only be decrypted with the receiver's private key. This allows, for instance, a server to generate a cryptographic key intended for symmetric-key cryptography, then use a client's openly-shared public key to encrypt that newly-generated symmetric key. Now, the server can send this encrypted symmetric key on insecure channels to the client, and only the client can decrypt it using the client's private key pair to the public key used by the server to encrypt this message. With the client and server both having the same symmetric key now, they can safely transition to symmetric key encryption to securely communicate back and forth on otherwise-insecure channels. This has the advantage of not having to manually pre-share symmetric keys, while also gaining the higher data throughput advantage of symmetric-key cryptography over asymmetric key cryptography.
With public-key cryptography, robust authentication is also possible. A sender can combine a message with a private key to create a short digital signature on the message. Anyone with the sender's corresponding public key can combine the same message and the supposed digital signature associated with it to verify whether the signature was valid, i.e. made by the owner of the corresponding private key.
Public key algorithms are fundamental security ingredients in modern cryptosystems, applications and protocols assuring the confidentiality, authenticity and non-repudiability of electronic communications and data storage. They underpin various Internet standards, such as Transport Layer Security (TLS), S/MIME, PGP, and GPG. Some public key algorithms provide key distribution and secrecy (e.g., Diffie–Hellman key exchange), some provide digital signatures (e.g., Digital Signature Algorithm), and some provide both (e.g., RSA). Compared to symmetric encryption, asymmetric encryption is slow for many purposes. Today's cryptosystems (such as TLS, Secure Shell) use both symmetric encryption and asymmetric encryption.
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