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Example of a Key Derivation Function chain as used in the Signal Protocol.The output of one KDF function is the input to the next KDF function in the chain. In cryptography, a key derivation function (KDF) is a cryptographic algorithm that derives one or more secret keys from a secret value such as a master key, a password, or a passphrase using a pseudorandom function (which typically uses a ...
Thus, a program that uses key stretching can use 65,000 rounds of hashes and delay the user for at most one second. Testing a trial password or passphrase typically requires one hash operation. But if key stretching was used, the attacker must compute a strengthened key for each key they test, meaning there are 65,000 hashes to compute per test.
For example, bcrypt cannot be used to derive a 512-bit key from a password. At the same time, algorithms like pbkdf2, scrypt, and argon2 are password-based key derivation functions - where the output is then used for the purpose of password hashing rather than just key derivation. Password hashing generally needs to complete < 1000 ms.
The first iteration of PRF uses Password as the PRF key and Salt concatenated with i encoded as a big-endian 32-bit integer as the input. (Note that i is a 1-based index.) Subsequent iterations of PRF use Password as the PRF key and the output of the previous PRF computation as the input: F(Password, Salt, c, i) = U 1 ^ U 2 ^ ⋯ ^ U c. where:
The salt and hash are then stored in the database. To later test if a password a user enters is correct, the same process can be performed on it (appending that user's salt to the password and calculating the resultant hash): if the result does not match the stored hash, it could not have been the correct password that was entered.
Argon2 is a key derivation function that was selected as the winner of the 2015 Password Hashing Competition. [1] [2] It was designed by Alex Biryukov, Daniel Dinu, and Dmitry Khovratovich from the University of Luxembourg. [3]
Common graphics processing units can try billions of possible passwords each second. Password hash functions that perform key stretching – such as PBKDF2, scrypt or Argon2 – commonly use repeated invocations of a cryptographic hash to increase the time (and in some cases computer memory) required to perform brute-force attacks on stored ...
S/KEY password generation. This step begins with a secret key W. This secret can either be provided by the user, or can be generated by a computer. Either way, if this secret is disclosed, then the security of S/KEY is compromised. A cryptographic hash function H is applied n times to W, thereby producing a hash chain of n one-time passwords ...