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Frequency analysis
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{{short description|Study of the frequency of letters or groups of letters in a ciphertext}} {{Other uses|Frequency analysis (disambiguation)}} [[File:English letter frequency (alphabetic).svg|right|340px|thumbnail|A typical distribution of letters in [[English language]] text. Weak ciphers do not sufficiently mask the distribution, and this might be exploited by a cryptanalyst to read the message.]] In [[cryptanalysis]], '''frequency analysis''' (also known as '''counting letters''') is the study of the [[letter frequencies|frequency of letters]] or groups of letters in a [[ciphertext]]. The method is used as an aid to breaking [[classical cipher]]s. Frequency analysis is based on the fact that, in any given stretch of written language, certain letters and combinations of letters occur with varying frequencies. Moreover, there is a characteristic distribution of letters that is roughly the same for almost all samples of that language. For instance, given a section of [[English language]], {{samp|E}}, {{samp|T}}, {{samp|A}} and {{samp|O}} are the most common, while {{samp|Z}}, {{samp|Q}}, {{samp|X}} and {{samp|J}} are rare. Likewise, {{samp|TH}}, {{samp|ER}}, {{samp|ON}}, and {{samp|AN}} are the most common pairs of letters (termed ''[[bigram]]s'' or ''digraphs''), and {{samp|SS}}, {{samp|EE}}, {{samp|TT}}, and {{samp|FF}} are the most common repeats.<ref>{{ Cite web | last = Singh | first = Simon | author-link = Simon Singh | title = The Black Chamber: Hints and Tips | url = http://www.simonsingh.net/The_Black_Chamber/hintsandtips.html | access-date = 26 October 2010 }}</ref> The nonsense phrase "[[ETAOIN SHRDLU]]" represents the 12 most frequent letters in typical English language text. In some ciphers, such properties of the natural language plaintext are preserved in the ciphertext, and these patterns have the potential to be exploited in a [[ciphertext-only attack]].
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