They underpin numerous Internet standards, such as Transport Layer Security (TLS), S/MIME, PGP, and GPG. Public key algorithms are fundamental security primitives in modern cryptosystems, including applications and protocols which offer assurance of the confidentiality, authenticity and non-repudiability of electronic communications and data storage. Anyone with the sender's corresponding public key can combine that message with a claimed digital signature if the signature matches the message, the origin of the message is verified (i.e., it must have been made by the owner of the corresponding private key). A sender can combine a message with a private key to create a short digital signature on the message. With public-key cryptography, robust authentication is also possible. This scheme has the advantage of not having to manually pre-share symmetric keys (a fundamentally difficult problem) while gaining the higher data throughput advantage of symmetric-key cryptography. With the client and server both having the same symmetric key, they can safely use symmetric key encryption (likely much faster) to communicate over otherwise-insecure channels. The server can then send this encrypted symmetric key over an insecure channel to the client only the client can decrypt it using the client's private key (which pairs with the public key used by the server to encrypt the message). This allows, for instance, a server program to generate a cryptographic key intended for a suitable symmetric-key cryptography, then to use a client's openly-shared public key to encrypt that newly generated symmetric key. In such a system, any person can encrypt a message using the intended receiver's public key, but that encrypted message can only be decrypted with the receiver's private key. Effective security requires keeping the private key private the public key can be openly distributed without compromising security. The generation of such key pairs depends on cryptographic algorithms which are based on mathematical problems termed one-way functions. Each pair consists of a public key (which may be known to others) and a private key (which may not be known by anyone except the owner). ![]() Public-key cryptography, or asymmetric cryptography, is a cryptographic system that uses pairs of keys. 2) Using Alice's public key, Bob can verify that Alice sent the message and that the message has not been modified. 1) Alice signs a message with her private key. ![]() ![]() In this example the message is digitally signed by encrypting its hash value with Alice's private key, but the message itself is not encrypted.
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