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 recognised, 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.
The selection of an appropriate key length depends on the practical
feasibility of performing a brute force attack.
Symmetric ciphers
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. For example, if there are 264 possible keys, a brute force attack would, on average, be expected to find a key
after 263 trials.
For each trial of a candidate key the attacker needs to be able to recognise 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 similiarity to plaintext language — for example, English encoded in ASCII.
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. Nearly all ciphers lack a mathematical proof of
security in this sense, although the one time pad has been proven to
provide perfect secrecy.
Symmetric ciphers with keys of length up to 64 bits have been broken by brute force attacks. DES, a widely-used block cipher which uses 56-bit keys, was
broken by custom hardware in 1998 (see EFF DES cracker), and a message encrypted with RC5 using a 64-bit key
was broken more recently. In addition, it is commonly speculated that government intelligence agencies (such as the US NSA) can successfully attack a symmetric key cipher with long
key lengths, such as a 64-bit key, using brute force. For applications requiring long term security, 128 bits is, as of 2004, currently thought a sufficient key length for new systems using symmetric
key algorithms. NIST has recommended that 80-bit designs be phased out by 2015.
If keys are generated in a weak way, for example, derived from a guessable-password, it is be possible to exhaustively search
over a much smaller set, for example, keys generated from passwords in a dictionary. See password cracking for more information.
Asymmetric algorithms
For asymmetric cryptography, a brute force attack
usually involves tackling some difficult problem, such a large integer factorisation or calculating a discrete logarithm.
The situation with regard to asymmetric key
algorithms is more complicated and depends on the individual encryption algorithm. Thus, the currently breakable key length
for the RSA algorithm is at least 512 bits (i.e., it has
been done publicly), and recent research developments suggest that 1024 bits might be breakable in the near to medium term
future. For most elliptic curve asymmetric
algorithms, the largest currently breakable key length is believed to be rather shorter, perhaps as little as 128 bits or so. A
message encrypted with a 109 bit key by an elliptic curve encryption algorithm was publicly broken by brute force key search in
early 2003. At this writing (as of 2004), 128 bit key lengths seem the minimum reasonable for elliptic curve algorithms, and 1024
bits for such asymmetric key algorithms as RSA.
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 1565925203).
- 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).
External links
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