Generation in Cryptography
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 without actually decrypting it 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.
Generation in Physical Layer
In a rich-fading environment, a wireless channel is characterized by its two end users. By transmitting pilot signals, these two users can estimate the channel between them and use the channel information to generate a key which is secret only to them. The common secret key for a group of users can be generated based on the channel of each pair of users.
A key can also be generated by exploiting the phase fluctuation in a fiber link.
- 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.
- Chan Dai Truyen Thai; Jemin Lee; Tony Q. S. Quek (Feb 2016). "Physical-Layer Secret Key Generation with Colluding Untrusted Relays". IEEE Trans. Wireless Communications. 15 (2): 1517–1530. doi:10.1109/TWC.2015.2491935.
- Chan Dai Truyen Thai; Jemin Lee; Tony Q. S. Quek (Dec 2015). "Secret Group Key Generation in Physical Layer for Mesh Topology". 2015 IEEE Global Communications Conference (GLOBECOM). San Diego. pp. 1–6. doi:10.1109/GLOCOM.2015.7417477.
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