# Brute-force attack

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Brute-force attack
The EFF's US\$250,000 DES cracking machine contained over 1,800 custom chips and could brute-force a DES key in a matter of days. The photograph shows a DES Cracker circuit board fitted with 32 Deep Crack chips and some control chips.

In cryptography, a brute-force attack, or exhaustive key search, is a strategy that can, in theory, be used against any encrypted data.[1] Such an attack might be utilized when it is not possible to take advantage of other weaknesses in an encryption system (if any exist) that would make the task easier. It involves systematically checking all possible keys until the correct key is found. In the worst case, this would involve traversing the entire search space.

The key length used in the encryption determines the practical feasibility of performing a brute-force attack, with longer keys exponentially more difficult to crack than shorter ones. Brute-force attacks can be made less effective by obfuscating the data to be encoded, something that makes it more difficult for an attacker to recognise when he/she has cracked the code. One of the measures of the strength of an encryption system is how long it would theoretically take an attacker to mount a successful brute-force attack against it.

Brute-force attacks are an application of brute-force search, the general problem-solving technique of enumerating all candidates and checking each one.

## Theoretical limits

The resources required for a brute-force attack grow exponentially with increasing key size, not linearly. As a result, doubling the key size for an algorithm does not simply double the required number of operations, but rather squares them. Although US export regulations historically restricted key lengths to 56-bit symmetric keys (e.g. Data Encryption Standard), these restrictions are no longer in place, so modern symmetric algorithms typically use computationally stronger 128- to 256-bit keys. The table below illustrates how much more complex a 128-bit key is than a 56-bit key. If a device existed that could brute-force a 56-bit encryption key in one second, it would take that device 149.7 trillion years to brute-force a 128-bit encryption key.

Symmetric key length vs brute-force combinations
Key size in bits[2] Permutations Brute-force time for a device checking 256 permutations per second
8 28 0 milliseconds
40 240 0.015 milliseconds
56 256 1 second
64 264 4 minutes 16 seconds
128 2128 149,745,258,842,898 years
256 2256 50,955,671,114,250,072,156,962,268,275,658,377,807,020,642,877,435,085 years

There is also a physical argument that a 128-bit symmetric key is computationally secure against brute-force attack. The so-called Von Neumann-Landauer Limit implied by the laws of physics sets a lower limit on the energy required to perform a computation of ln(2)kT per bit erased in a computation, where T is the temperature of the computing device in kelvins, k is the Boltzmann constant, and the natural logarithm of 2 is about 0.693. No irreversible computing device can use less energy than this, even in principle.[3] Thus, in order to simply flip through the possible values for a 128-bit symmetric key (ignoring doing the actual computing to check it) would theoretically require 2128 − 1 bit flips on a conventional processor. If it is assumed that the calculation occurs near room temperature (~300 K) the Von Neumann-Landauer Limit can be applied to estimate the energy required as ~1018 joules, which is equivalent to consuming 30 gigawatts of power for one year (30×109 W×365×24×3600 s = 9.46×1017 J). The full actual computation—checking each key to see if you have found a solution—would consume many times this amount.

However, this argument assumes that the register values are changed using conventional set and clear operations which inevitably generate entropy. It has been shown that computational hardware can be designed not to encounter this theoretical obstruction (see reversible computing), though no such computers are known to have been constructed.[citation needed]

Modern GPUs are well-suited to the repetitive tasks associated with hardware-based password cracking

As commercial available successors of governmental ASICs Solution also known as custom hardware attack, today two emerging technologies have proven their capability in the brute-force attack of certain ciphers. One is modern graphics processing unit (GPU) technology,[4] the other is the field-programmable gate array (FPGA) technology. GPUs benefit from their wide availability and price-performance benefit, FPGAs from their energy efficiency per cryptographic operation. Both technologies try to transport the benefits of parallel processing to brute-force attacks. In case of GPUs some hundreds, in the case of FPGA some thousand processing units making them much better suited to cracking passwords than conventional processors. Various publications in the fields of cryptographic analysis have proved the energy efficiency of today’s FPGA technology, for example, the COPACOBANA FPGA Cluster computer consumes the same energy as a single PC (600 W), but performs like 2,500 for certain algorithms. A number of firms provide hardware-based FPGA cryptographic analysis solutions from a single FPGA PCI Express card up to dedicated FPGA computers.[citation needed] WPA and WPA2 encryption have successfully been brute-force attacked by reducing the workload by a factor of 50 in comparison to conventional CPUs[5][6] and some hundred in case of FPGAs.

AES permits the use of 256-bit keys. Breaking a symmetric 256-bit key by brute force requires 2128 times more computational power than a 128-bit key. A device that could check a billion billion (1018) AES keys per second (if such a device could ever be made) would in theory require about 3×1051 years to exhaust the 256-bit key space. Quantum computers are needed to crack such complicated encryptions in a more practical length of time.

An underlying assumption of a brute-force attack is that the complete keyspace was used to generate keys, something that relies on an effective random number generator, and that there are no defects in the algorithm or its implementation. For example, a number of systems that were originally thought to be impossible to crack by brute force have nevertheless been cracked because the key space to search through was found to be much smaller than originally thought, because of a lack of entropy in their pseudorandom number generators. These include Netscape's implementation of SSL (famously cracked by Ian Goldberg and David Wagner in 1995[7]) and a Debian/Ubuntu edition of OpenSSL discovered in 2008 to be flawed.[8] A similar lack of implemented entropy lead to the breaking of Enigma's code.[9][10]

## Credential recycling

Credential recycling refers to the hacking practice to re-use username and password combinations gathered in previous brute-force attacks. A special form of credential recycling is Pass the hash.[11]

## Unbreakable codes

Certain types of encryption, by their mathematical properties, cannot be defeated by brute force. An example of this is one-time pad cryptography, where every cleartext bit has a corresponding key bit. One-time pads rely on the ability to generate a truly random sequence of key bits. A brute-force attack would eventually reveal the correct decoding, but also every other possible combination of bits, and would have no way of distinguishing one from the other. A small, 100-byte, one-time-pad–encoded string subjected to a brute-force attack would eventually reveal every 100-byte string possible, including the correct answer, but mostly nonsense. Of all the answers given, there is no way of knowing which is the correct one. Nevertheless, the system can be defeated if not implemented correctly, for example if one-time pads are re-used or intercepted.[12]

A similar argument can apply when a *single* plaintext is encrypted by any method where the text is shorter than the key. For example, if the text is a single byte, then (for most types of encryption with large key sizes such as 128 bits) all bytes from "00"-"FF" will appear, with equal probability, as possible plaintexts corresponding to guessed keys.

## Countermeasures

In case of an offline attack where the attacker has access to the encrypted material, he can try key combinations at his leisure without the risk of discovery or interference. However database and directory administrators can take countermeasures against online attacks, for example by limiting the number of attempts that a password can be tried, by introducing time delays between successive attempts, increasing the answer's complexity (e.g. requiring a CAPTCHA answer or verification code sent via cellphone), and/or locking accounts out after unsuccessful logon attempts.[13] Website administrators may prevent a particular IP address from trying more than a predetermined number of password attempts against any account on the site.[14]

## References

1. ^ Christof Paar, Jan Pelzl, Bart Preneel (2010). Understanding Cryptography: A Textbook for Students and Practitioners. Springer. p. 7. ISBN 3642041000.
2. ^ Calculating Bit Strength
3. ^ Rolf Landauer, "Irreversibility and heat generation in the computing process," IBM Journal of Research and Development, vol. 5, pp. 183-191, 1961.
4. ^ Robert David Grahamd (22 June 2011). "Password cracking, mining, and GPUs". erratasec.com. Retrieved 17 August 2011.
5. ^
6. ^
7. ^ John Viega, Matt Messier, Pravir Chandra (2002). Network Security with OpenSSL. O'Reilly. p. 18. ISBN 059600270X. Retrieved 2008-11-25.
8. ^
9. ^ Exploring the Enigma http://plus.maths.org/content/exploring-enigma
10. ^ NSA's How Mathematicians Helped Win WWII http://www.nsa.gov/about/cryptologic_heritage/center_crypt_history/publications/how_math_helped_win.shtml
11. ^ Metasploit Express user guide
12. ^ Robert Reynard (1997). Secret Code Breaker II: A Cryptanalyst's Handbook. Jacksonville, FL: Smith & Daniel Marketing. p. 86. ISBN 1889668060. Retrieved 2008-09-21.
13. ^ Mark Burnett, James C. Foster (2004). Hacking the Code: ASP.NET Web Application Security. Syngress. ISBN 1932266658.
14. ^ Ivan Ristic (2010). Modsecurity Handbook. Feisty Duck. p. 136. ISBN 1907117024.
• Leonard M. Adleman, Paul W. K. Rothemund, Sam Roweis and Erik Winfree, On Applying Molecular Computation To The Data Encryption Standard, in Proceedings of the Second Annual Meeting on DNA Based Computers, Princeton University, June 10–12, 1996.
• Cracking DES — Secrets of Encryption Research, Wiretap Politics & Chip Design by the Electronic Frontier Foundation (ISBN 1-56592-520-3).
• W. Diffie and M.E. Hellman, Exhaustive cryptanalysis of the NBS Data Encryption Standard, Computer 10 (1977), pp 74–84.
• Michael J. Wiener, "Efficient DES Key Search", presented at the rump session of Crypto 93; reprinted in Practical Cryptography for Data Internetworks, W. Stallings, editor, IEEE Computer Society Press, pp 31–79 (1996).

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