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Encyclopedia > 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 several Deep Crack chips.

In cryptanalysis, a brute force attack is a method of defeating a cryptographic scheme by trying a large number of possibilities; for example, exhaustively working through all possible keys in order to decrypt a message. In most schemes, the theoretical possibility of a brute force attack is recognized, but it is set up in such a way that it would be computationally infeasible to carry out. Accordingly, one definition of "breaking" a cryptographic scheme is to find a method faster than a brute force attack. Download high resolution version (1412x1479, 336 KB)DES Cracker circuit board fitted with Deep Crack chips Source: http://www. ... Download high resolution version (1412x1479, 336 KB)DES Cracker circuit board fitted with Deep Crack chips Source: http://www. ... EFF Logo The Electronic Frontier Foundation (EFF) is an international non-profit advocacy and legal organization based in the United States with the stated purpose of being dedicated to preserving free speech rights such as those protected by the First Amendment to the United States Constitution in the context of... The EFFs US\$250,000 DES cracking machine contained over 18,000 custom chips and could brute force a DES key in a matter of days — the photo shows a DES Cracker circuit board fitted with several Deep Crack chips In cryptography, the EFF DES cracker (nicknamed Deep Crack... Close-up of the rotors in a Fialka cipher machine Cryptanalysis (from the Greek kryptÃ³s, hidden, and analÃ½ein, to loosen or to untie) is the study of methods for obtaining the meaning of encrypted information, without access to the secret information which is normally required to do so. ... Cryptography (from Greek kryptós, hidden, and gráphein, to write) is, traditionally, the study of means of converting information from its normal, comprehensible form into an incomprehensible format, rendering it unreadable without secret knowledge — the art of encryption. ... A key is a piece of information that controls the operation of a cryptography algorithm. ...

The selection of an appropriate key length depends on the practical feasibility of performing a brute force attack. By obfuscating the data to be encoded, brute force attacks are made less effective as it is more difficult to determine when one has succeeded in breaking the code. In cryptography, the key size (alternatively key length) is a measure of the number of possible keys which can be used in a cipher. ... Obfuscation refers to the concept of concealing the meaning of communication by making it more confusing and harder to interpret. ...

The brute force attack could be combined with a dictionary attack. In cryptanalysis and computer security, a dictionary attack is a technique for defeating a cipher or authentication mechanism by trying to determine its decryption key or passphrase by searching a large number of possibilities. ...

## Contents

In a brute force attack, the expected number of trials before the correct key is found is equal to half the size of the key space. For example, if there are 264 possible keys, a brute force attack would, on average, be expected to find a key after 263 trials. [1]

For each trial of a candidate key the attacker needs to be able to recognize when he has found the correct key. The most straightforward way is to obtain a few corresponding plaintext and ciphertext pairs, that is, a known-plaintext attack. Alternatively, a ciphertext-only attack is possible by decrypting ciphertext using each candidate key, and testing the result for similarity to plaintext language — for example, English encoded in ASCII. The known-plaintext attack (KPA) is an attack model for cryptanalytic where the attacker has samples of both the plaintext and its encrypted version (ciphertext) and is at liberty to make use of them to reveal further secret information; typically this is the secret key. ... In cryptography, a ciphertext-only attack is a form of cryptanalysis where the attacker is assumed to have access only to a set of ciphertexts. ... The English language is a West Germanic language that originates in England. ... Image:ASCII fullsvg There are 95 printable ASCII characters, numbered 32 to 126. ...

In general, a symmetric key cipher is considered secure if there is no method less expensive (in time, memory requirements, etc) than brute force; Claude Shannon used the term "work factor" for this. A symmetric-key algorithm is an algorithm for cryptography that uses the same cryptographic key to encrypt and decrypt the message. ... Claude Elwood Shannon (April 30, 1916 - February 24, 2001) has been called the father of information theory, and was the founder of practical digital circuit design theory. ...

The COPACOBANA machine is a reprogrammable and cost-optimized hardware for cryptanalytical applications such as exhaustive key search. It was built for US\$10,000 by the Universities of Bochum and Kiel, Germany, and contains 120 low-cost FPGAs.

Ciphers with proven perfect secrecy, such as the one-time pad, cannot be broken by a brute force attack. Excerpt from a one-time pad. ...

## Theoretical limits

The resources required for a brute force attack scale exponentially with increasing key size, not linearly. Doubling key size does not double the required number of operations, but rather squares the number of required operations. Thus, although 56 bit keys, such as those used by the obsolete Data Encryption Standard (DES) are now quite practical to attack by brute force, this is not true of much longer keys, such as those used by the more modern Advanced Encryption Standard (AES), which uses keys of at least 128 bits in length. Image File history File links Question_book-3. ... In mathematics, exponential growth (or geometric growth) occurs when the growth rate of a function is always proportional to the functions current size. ... In cryptography, the key size (alternatively key length) is the size of the digits used to create an encrypted text; it is therefore also a measure of the number of possible keys which can be used in a cipher, and the number of keys which must be tested to break... The Data Encryption Standard (DES) is a cipher (a method for encrypting information) selected as an official Federal Information Processing Standard (FIPS) for the United States in 1976, and which has subsequently enjoyed widespread use internationally. ... In cryptography, the Advanced Encryption Standard (AES), also known as Rijndael, is a block cipher adopted as an encryption standard by the U.S. government. ...

There is a physical argument that a 128 bit key is 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 kelvin, k is the Boltzmann constant, and the natural logarithm of 2 is about .693. No irreversible computing device can use less energy than this, even in principle.[2] Landauers Principle, first argued in 1961 by Rolf Landauer of IBM, holds that any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase in non-information bearing degrees of freedom of... For other uses, see Kelvin (disambiguation). ... The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. ... The natural logarithm, formerly known as the hyperbolic logarithm, is the logarithm to the base e, where e is an irrational constant approximately equal to 2. ...

Thus, in order to simply flip through the possible values for a 128-bit key (ignoring doing the actual computing to check it), one would need a device consuming at a minimum 10 gigawatts (about the equivalent of eight large, dedicated nuclear reactors) running continuously for 100 years.[citation needed] The full actual computation—checking each key to see if you have found a solution—would consume many times this amount.[citation needed] This page lists examples of the power in watts produced by various different sources of energy. ... Core of a small nuclear reactor used for research. ...

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. It should be pointed out that no known such computers have been constructed. The term reversible computing refers to any computational process that is (at least to some close approximation) reversible, i. ...

The amount of time required to break a 128 bit key is also daunting. Each of the 2128 possibilities must be checked. This is an enormous number, 340,282,366,920,938,463,463,374,607,431,768,211,456 in decimal. A device that could check a billion billion keys (1018) per second would still require about 1013 years to exhaust the key space. This is longer than the age of the universe, which is about 13,000,000,000 ($1.3 times 10^{10}$) years. This box:      This article is about scientific estimates of the age of the universe. ...

AES permits the use of 256 bit keys. Breaking a 256 bit key by brute force requires 2128 time more computational power than a 128 bit key. A device that could check a billion billion (1018) AES keys per second would require about $3 times 10^{51}$ years to exhaust the 256 bit key space.

Hence, 128 bit keys are impractical to attack by brute force methods using current technology and resources, and 256 bit keys are not likely to be broken by brute force methods using any obvious future technology.

## 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 bit has a corresponding key bit. 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. Excerpt from a one-time pad. ...

For example, 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.

In cryptography, the key size (alternatively key length) is a measure of the number of possible keys which can be used in a cipher. ... In the Forgotten Realms setting, based on the Dungeons & Dragons role-playing game, Twinkle is Drizzts defensive scimitar; his offensive scimitar is Icingdeath. ... In cryptography and number theory, TWIRL (The Weizmann Institute Relation Locator) is a hypothetical hardware device designed to speed up the sieving step of the general number field sieve integer factorization algorithm. ... 40-bit encryption is a key size for symmetric encryption representing a low-level of security where the key is forty bits in length (five bytes). ... The distributed. ... In cryptography, MD5CRK was a distributed effort (similar to distributed. ... Unicity distance is a term used in cryptography referring to the length of an original ciphertext needed to break the cipher by reducing the number of possible spurious keys to zero in a brute force attack. ... The RSA Factoring Challenge is a challenge put forward by RSA Laboratories on March 18, 1991 to encourage research into computational number theory and the practical difficulty of factoring large integers. ...

## References

• 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), pp74–84.
• 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, pp31–79 (1996).

Results from FactBites:

 PGP Attacks (5523 words) The attack is a passive one where the attacker sits on a network and observes the RSA operations. While the attack is definitely something to be wary of, it is theoretical in nature, and has not been done in practice as of yet. This attack, however exotic it may seem, is not beyond the capability of anyone with some technical know-how and the desire to read PGP encrypted files.
 Brute force attack - Wikipedia, the free encyclopedia (1010 words) In cryptanalysis, a brute force attack is a method of defeating a cryptographic scheme by trying a large number of possibilities; for example, exhaustively working through all possible keys in order to decrypt a message. For symmetric-key ciphers, a brute force attack typically means a brute-force search of the key space; that is, testing all possible keys in order to recover the plaintext used to produce a particular ciphertext. In a brute force attack, the expected number of trials before the correct key is found is equal to half the size of the key space.
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