Key clustering: Difference between revisions

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{{Orphan|date=February 2009}}

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{{Confusing|date=June 2020}}

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Key or [[hash function]] should avoid ''[[Hash table|clustering]]'', the mapping of two or more keys to consecutive slots. Such clustering may cause the lookup cost to skyrocket, even if the load factor is low and [[hash collision|collisions]] are infrequent. The popular multiplicative hash<ref>{{cite book | first=Donald |last=Knuth |author1-link=Donald Knuth | title = The Art of Computer Programming | volume = 3: ''Sorting and Searching'' | edition = 2nd | publisher = Addison-Wesley | year = 1998 | isbn = 978-0-201-89685-5 | pages = 513–558 }} {{verify source |date=September 2019 |reason=This ref was deleted Special:Diff/902760856 by a bug in VisualEditor and later restored by a bot from the original cite located at Special:Permalink/895004660 cite #3 - verify the cite is accurate and delete this template. [[User:GreenC bot/Job 18]]}}</ref> is claimed to have particularly poor clustering behaviour.<ref>{{Cite web|title = Prime Double Hash Table|url = https://www.concentric.net/~Ttwang/tech/primehash.htm|date = March 1997|accessdate = 2015-05-10|last = Wang|first = Thomas|archiveurl = https://web.archive.org/web/19990903133921/http://www.concentric.net/~Ttwang/tech/primehash.htm|archivedate = 1999-09-03}} {{verify source |date=September 2019 |reason=This ref was deleted Special:Diff/902760856 by a bug in VisualEditor and later restored by a bot from the original cite located at Special:Permalink/895004660 cite #9 - verify the cite is accurate and delete this template. [[User:GreenC bot/Job 18]]}}</ref>

==References==

'''Key clustering''', in [[cryptography]], is two different [[key (cryptography)|keys]] that generate the same [[ciphertext]] from the same [[plaintext]] by using the same [[cipher]] [[algorithm]]. A good cipher algorithm, using different keys on the same plaintext, should generate a different ciphertext irrespective of the key length.

{{Reflist}}

[[Category:Key management]]

If there is a plaintext P, two different keys K1 and K2, and an algorithm A, the two key generate ciphertexts C1 and C2 as follows:

P → A(K1) → C1

P → A(K2) → C2

Key clustering has occurred if C1 and C2 are the same, which should not occur.

==Importance==

If an attacker tries to break a cipher by a [[brute-force attack]], trying all possible keys until it finds the correct key, key clustering makes it easier to attack a particular cipher text. If there are ''n'' possible keys without any key clustering, the attacker needs to try an average of ''n''/2 keys to decrypt it and no more than ''n'' keys. If there are two keys that are clustered, the average number of keys is reduced to ''n''/4 and the maximum is ''n''-1 keys. If three keys cluster, the average attempt is only ''n''/6 attempts.

[[Category:Key management]]

{{crypto-stub}}