Modern cryptographic systems include symmetric-key algorithms (such as DES and AES) and public-key algorithms (such as RSA). Symmetric-key algorithms use a single shared key; keeping data secret requires keeping this key secret. Public-key algorithms use a public key and a private key. The public key is made available to anyone (often by means of a digital certificate). A sender encrypts data with the public key; only the holder of the private key can decrypt this data.
Since public-key algorithms tend to be much slower than symmetric-key algorithms, modern systems such as TLS and SSH use a combination of the two: one party receives the other's public key, and encrypts a small piece of data (either a symmetric key or some data used to generate it). The remainder of the conversation uses a (typically faster) symmetric-key algorithm for encryption.
Computer cryptography uses integers for keys. In some cases keys are randomly generated using a random number generator (RNG) or pseudorandom number generator (PRNG). A PRNG is a computer algorithm that produces data that appears random under analysis. PRNGs that use system entropy to seed data generally produce better results, since this makes the initial conditions of the PRNG much more difficult for an attacker to guess. In other situations, the key is derived deterministically using a passphrase and a key derivation function.
The simplest method to read encrypted data is a brute force attack—simply attempting every number, up to the maximum length of the key. Therefore, it is important to use a sufficiently long key length; longer keys take exponentially longer to attack, rendering a brute force attack impractical. Currently, key lengths of 128 bits (for symmetric key algorithms) and 1024 bits (for public-key algorithms) are common.
- Distributed key generation: For some protocols, no party should be in the sole possession of the secret key. Rather, during distributed key generation, every party obtains a share of the key. A threshold of the participating parties need to cooperate to achieve a cryptographic task, such as decrypting a message.
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