Editing Cryptanalysis (section)

===Computational resources required===
{{See also|Time/memory/data tradeoff attack}}
Attacks can also be characterised by the resources they require. Those resources include:<ref>{{Cite journal|last=Hellman|first=M.|date=July 1980|title=A cryptanalytic time-memory trade-off|journal=IEEE Transactions on Information Theory|language=en-US|volume=26|issue=4|pages=401–406|doi=10.1109/tit.1980.1056220|s2cid=552536 |issn=0018-9448|url=http://www-ee.stanford.edu/~hellman/publications/36.pdf |archive-url=https://ghostarchive.org/archive/20221010/http://www-ee.stanford.edu/~hellman/publications/36.pdf |archive-date=2022-10-10 |url-status=live}}</ref>
* Time – the number of ''computation steps'' (e.g., test encryptions) which must be performed.
* Memory – the amount of ''storage'' required to perform the attack.
* Data – the quantity and type of ''plaintexts and ciphertexts'' required for a particular approach.

It is sometimes difficult to predict these quantities precisely, especially when the attack is not practical to actually implement for testing. But academic cryptanalysts tend to provide at least the estimated ''order of magnitude'' of their attacks' difficulty, saying, for example, "SHA-1 collisions now 2<sup>52</sup>."<ref>{{Citation | last1 = McDonald | first1 = Cameron | last2 = Hawkes | first2 = Philip | last3 = Pieprzyk | first3 = Josef | author3-link = Josef Pieprzyk | title =SHA-1 collisions now 2<sup>52</sup> | url = http://eurocrypt2009rump.cr.yp.to/837a0a8086fa6ca714249409ddfae43d.pdf | access-date = 4 April 2012}}</ref>

[[Bruce Schneier]] notes that even computationally impractical attacks can be considered breaks: "Breaking a cipher simply means finding a weakness in the cipher that can be exploited with a complexity less than brute force. Never mind that brute-force might require 2<sup>128</sup> encryptions; an attack requiring 2<sup>110</sup> encryptions would be considered a break...simply put, a break can just be a certificational weakness: evidence that the cipher does not perform as advertised."<ref name="schneier"/><!-- Birthday attacks; man in the middle / time-memory tradeoff -->