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In cryptography, key stretching techniques are used to make a possibly weak key, typically a password or passphrase, more secure against a brute-force attack by increasing the resources (time and possibly space) it takes to test each possible key. Passwords or passphrases created by humans are often short or predictable enough to allow password cracking, and key stretching is intended to make such attacks more difficult by complicating a basic step of trying a single password candidate. Key stretching also improves security in some real-world applications where the key length has been constrained, by mimicking a longer key length from the perspective of a brute-force attacker.
There are several ways to perform key stretching. One way is to apply a cryptographic hash function or a block cipher repeatedly in a loop. For example, in applications where the key is used for a cipher, the key schedule in the cipher may be modified so that it takes a specific length of time to perform. Another way is to use cryptographic hash functions that have large memory requirements – these can be effective in frustrating attacks by memory-bound adversaries.
Key stretching leaves an attacker with two options:
If the attacker uses the same class of hardware as the user, each guess will take the similar amount of time to process as it took the user (for example, one second). Even if the attacker has much greater computing resources than the user, the key stretching will still slow the attacker down while not seriously affecting the usability of the system for any legitimate user. This is because the user's computer only has to compute the stretching function once upon the user entering their password, whereas the attacker must compute it for every guess in the attack.
This process does not alter the original key-space entropy. The key stretching algorithm is deterministic, allowing a weak input to always generate the same enhanced key, but therefore limiting the enhanced key to no more possible combinations than the input key space. Consequently, this attack remains vulnerable if unprotected against certain time-memory tradeoffs such as developing rainbow tables to target multiple instances of the enhanced key space in parallel (effectively a shortcut to repeating the algorithm). For this reason, key stretching is often combined with salting.
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. This increases the attacker's workload by a factor of 65,000, approximately 216, which means the enhanced key is worth about 16 additional bits in key strength.
Moore's law asserts that computer speed doubles roughly every 2 years. Under this assumption, every 2 years one more bit of key strength is plausibly brute-forcible. This implies that 16 extra bits of strength is worth about 16×2 = 32 years later cracking, but it also means that the number of key stretching rounds a system uses should be doubled about every 2 years to maintain the same level of security (since most keys are more secure than necessary, systems that require consistent deterministic key generation will likely not update the number of iterations used in key stretching. In such a case, the designer should take into consideration how long they wish for the key derivation system to go unaltered and should choose an appropriate number of hashes for the lifespan of the system).
CPU-bound hash functions are still vulnerable to hardware implementations. Such implementations of SHA-1 exist using as few as 5,000 gates, and 400 clock cycles. With multi-million gate costing less than $100, an attacker can build a fully Loop unrolling hardware cracker for about $5,000. Such a design, clocked at 100 Hertz can test about 300,000 keys/second. The attacker is free to choose a good price/speed compromise, for example a 150,000 keys/second design for $2,500. The key stretching still slows down the attacker in such a situation; a $5,000 design attacking a straight SHA-1 hash would be able to try 300,000÷216 ≈ 4.578 keys/second.
Similarly, modern consumer can speed up hashing considerably. For example, in a benchmark, a
, PBKDF2-HMAC-SHA1 with 1,000 iterations costs 2,002 SHA-1 hashes at a speed of 5,164.9 kH/s which comes to 10,340,129,800 SHA-1 hashes per second.
To defend against the hardware approach, memory-bound cryptographic functions have been developed. These functions access a lot of memory in a way that makes caching ineffective. Since large amounts of low latency memory are expensive, potential attackers are discouraged from pursuing such attacks.
Modern password-based key derivation functions, such as PBKDF2, use a cryptographic hash, such as SHA-2, a longer salt (e.g. 64 bits) and a high iteration count. The U.S. National Institute of Standards and Technology (NIST) recommends a minimum iteration count of 10,000. "For especially critical keys, or for very powerful systems or systems where user-perceived performance is not critical, an iteration count of 10,000,000 may be appropriate.”
In 2009, a memory-intensive key strengthening algorithm, scrypt, was introduced with the intention of limiting the use of custom, highly parallel hardware to speed up key testing.
In 2013, a Password Hashing Competition was held to select an improved key stretching standard that would resist attacks from graphics processors and special purpose hardware. The winner, Argon2, was selected on July 1, 2015. Password Hashing Competition
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