Editing Key size (section)

== Brute-force attack ==
{{More citations needed section|date=August 2012}}
{{Main article|Brute-force attack}}
Even if a symmetric cipher is currently unbreakable by exploiting structural weaknesses in its algorithm, it may be possible to run through the entire [[space (mathematics)|space]] of keys in what is known as a brute-force attack. Because longer symmetric keys require exponentially more work to brute force search, a sufficiently long symmetric key makes this line of attack impractical.

With a key of length ''n'' bits, there are 2<sup>n</sup> possible keys. This number grows very rapidly as ''n'' increases. The large number of operations (2<sup>128</sup>) required to try all possible 128-bit keys is widely considered [[Large numbers#Computers and computational complexity|out of reach]] for conventional digital computing techniques for the foreseeable future.<ref>{{cite magazine |url=http://www.eetimes.com/document.asp?doc_id=1279619 |title=How secure is AES against brute force attacks? |magazine=EE Times |access-date=2016-09-24}}</ref> However, a [[quantum computer]] capable of running [[Grover's algorithm]] would be able to search the possible keys more efficiently. If a suitably sized quantum computer would reduce a 128-bit key down to 64-bit security, roughly a [[Data Encryption Standard|DES]] equivalent. This is one of the reasons why [[Advanced Encryption Standard|AES]] supports key lengths of 256 bits and longer.{{efn|See the discussion on the relationship between key lengths and [[quantum computing]] attacks at the bottom of this page for more information.}}