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Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key . [ 1 ] [ 2 ] Key pairs are generated with cryptographic algorithms based on mathematical problems termed one-way functions .
Asymmetric keys differ from symmetric keys in that the algorithms use separate keys for encryption and decryption, while a symmetric key’s algorithm uses a single key for both processes. Because multiple keys are used with an asymmetric algorithm, the process takes longer to produce than a symmetric key algorithm would.
In a key transport scheme, encrypted keying material that is chosen by the sender is transported to the receiver. Either symmetric key or asymmetric key techniques can be used in both schemes. [11] The Diffie–Hellman key exchange and Rivest-Shamir-Adleman (RSA) are the most two widely used key exchange algorithms. [12]
The idea of an asymmetric public-private key cryptosystem is attributed to Whitfield Diffie and Martin Hellman, who published this concept in 1976. They also introduced digital signatures and attempted to apply number theory. Their formulation used a shared-secret-key created from exponentiation of some number, modulo a prime number.
Private (resp. public) ephemeral key agreement keys are the private (resp. public) keys of asymmetric key pairs that are used a single key establishment transaction to establish one or more keys (e.g., key wrapping keys, data encryption keys, or MAC keys) and, optionally, other keying material (e.g., initialization vectors).
Like most public key systems, the ElGamal cryptosystem is usually used as part of a hybrid cryptosystem, where the message itself is encrypted using a symmetric cryptosystem, and ElGamal is then used to encrypt only the symmetric key. This is because asymmetric cryptosystems like ElGamal are usually slower than symmetric ones for the same level ...
The method was followed shortly afterwards by RSA, an implementation of public-key cryptography using asymmetric algorithms. Expired US patent 4200770 [7] from 1977 describes the now public-domain algorithm. It credits Hellman, Diffie, and Merkle as inventors.
Symmetric-key cryptography, where a single key is used for both encryption and decryption. Symmetric-key cryptography refers to encryption methods in which both the sender and receiver share the same key (or, less commonly, in which their keys are different, but related in an easily computable way).