# Key derivation function

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Key derivation function

:"KDF" redirects here. For the Nazi organization, see Kraft durch Freude"

In cryptography, a key derivation function (or KDF) is a function which derives one or more secret keys from a secret value and/or other known information such as a password or passphrase. Key derivation functions internally often use a cryptographic hash function.

Uses of KDFs

Key derivation functions are often used in conjunction with non-secret parameters to derive one or more keys from a common secret value. Such use may prevent an attacker who obtains a derived key from learning useful information about either the input secret value or any of the other derived keys. A KDF may also be used to ensure that derived keys have other desirable properties, such as avoiding "weak keys" in some specific encryption systems.

Key derivation functions are often used as components of multi-party key-agreement protocols.Examples of such key derivation functions include KDF1, defined in IEEE Std 1363-2000, and similar functions in ANSI X9.42.

Key derivation functions are also used to derive keys from secret passwords or passphrases.

Key derivation functions are also used in applications to derive keys from secret passwords or passphrases, which typically do not have the desired properties to be used directly as cryptographic keys. In such applications, it is generally recommended that the key derivation function be made deliberately slow so as to frustrate brute-force attack or dictionary attack on the password or passphrase input value.

Such use may be expressed as $DK=KDF\left(Key, Salt, Iterations\right)$ where $DK$ is the derived key, $KDF$ is the key derivation function, $Key$ is the original key or password, $Salt$ is a random number which acts as cryptographic salt, and $Iterations$ refers to the number of iterations of a sub-function. The derived key is used instead of the original key or password as the key to the system. The values of the salt and the number of iterations (if it isn't fixed) are stored with the hashed password or sent as plaintext with an encrypted message.

The difficulty of a brute force attack increases with the number of iterations. A practical limit on the iteration count is the unwillingness of users to tolerate a perceptible delay in logging in to a computer or seeing a decrypted message. The use of salt prevents the attackers from precomputing a dictionary of derived keys.

The first deliberately-slow password-based key derivation function was called "crypt" (or "crypt(3)" after its man page), and was invented by Robert Morris in the 1980s to encrypt Unix passwords. While it was a great advance at the time, increases in processor speeds since the PDP-11 era have made brute-force attacks against crypt feasible, and advances in storage have rendered the 12-bit salt inadequate. The crypt function's design also limits the user password to 8 characters, which limits the keyspace and makes strong passphrases impossible.

Modern password-based key derivation functions, such as PBKDF2 (specified in RFC 2898), use a cryptographic hash, such as MD5 or SHA1, more salt (e.g. 64 bits) and a high iteration count (often 1000 or more). There have been proposals to use algorithms that require large amounts of computer memory and other computing resources to make custom hardware attacks more difficult to mount.

References

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