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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 .
The original algorithm uses binary Goppa codes (subfield codes of algebraic geometry codes of a genus-0 curve over finite fields of characteristic 2); these codes can be efficiently decoded, thanks to an algorithm due to Patterson. [4] The public key is derived from the private key by disguising the selected code as a general linear code.
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.
There are no published methods to defeat the system if a large enough key is used. RSA is a relatively slow algorithm. Because of this, it is not commonly used to directly encrypt user data. More often, RSA is used to transmit shared keys for symmetric-key cryptography, which are then used for bulk encryption–decryption.
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).
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).
A key can directly be generated by using the output of a Random Bit Generator (RBG), a system that generates a sequence of unpredictable and unbiased bits. [10] A RBG can be used to directly produce either a symmetric key or the random output for an asymmetric key pair generation.
For example, RSA encryption uses the multiplication of very large prime numbers to create a semiprime number for its public key. Decoding this key without its private key requires this semiprime number to be factored, which can take a very long time to do with modern computers.