Editing Index of coincidence (section)

{{short description|How often identical letters appear in the same position in two texts}}
{{more footnotes needed|date=March 2009}}
In [[cryptography]], '''coincidence counting''' is the technique (invented by [[William F. Friedman]]<ref>[[William F. Friedman|Friedman, William F.]] (1922). "The index of coincidence and its applications in cryptography." ''Department of Ciphers. Publ 22''. Geneva, Illinois, USA: [[Riverbank Laboratories]]. {{OCLC|55786052}}. The original application ignored normalization.
* [https://www.nsa.gov/portals/75/documents/news-features/declassified-documents/friedman-documents/publications/FOLDER_233/41761039080018.pdf 2nd ed.] (1935). Washington, D.C.: Signals Office, [[War Department]].
*[https://www.cryptomuseum.com/people/friedman/files/TIOC_Aegean_1987.pdf 3rd ed.] (1996). Laguna Hills, Calif.: [[Aegean Park Press]]. {{ISBN|0894121383}}.</ref>) of putting two texts side-by-side and counting the number of times that identical letters appear in the same position in both texts. This count, either as a ratio of the total or normalized by dividing by the expected count for a random source model, is known as the '''index of coincidence''', or '''IC''' or '''IOC'''<ref>{{cite web | url=https://pages.mtu.edu/~shene/NSF-4/Tutorial/VIG/Vig-IOC.html#:~:text=Given%20a%20text%20string%2C%20the,1922%20%5BFRIEDMAN1996%2C%20KULLBACK1976%5D | title=Index of Coincidence }}</ref> or '''IoC'''<ref>{{cite web | url=https://www.dcode.fr/index-coincidence | title=Index of Coincidence Calculator - Online IoC Cryptanalysis }}</ref> for short.

Because letters in a natural language are not [[letter frequency|distributed evenly]], the IC is higher for such texts than it would be for uniformly random text strings. What makes the IC especially useful is the fact that its value does not change if both texts are scrambled by the same single-alphabet [[substitution cipher]], allowing a cryptanalyst to quickly detect that form of encryption.