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Index of Coincidence

Tool to compute coincidence index. Index of Coincidence is a cryptanalysis technique studying the probability of finding repeating letters in an encrypted text. A text in English language has a coincidence index of 0.0667.

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Index of Coincidence - dCode

Tag(s) : Cryptanalysis

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Index of Coincidence

Cryptanalysis using Index of Coincidence

Message to Analyse

To be, or not to be, that is the question—
Whether 'tis Nobler in the mind to suffer
The Slings and Arrows of outrageous Fortune,
Or to take Arms against a Sea of troubles,
And by opposing end them? To die, to sleep—
No more; and by a sleep, to say we end
The Heart-ache, and the thousand Natural shocks
That Flesh is heir to? 'Tis a consummation
Devoutly to be wished. To die, to sleep,
To sleep, perchance to Dream; Aye, there's the rub,
For in that sleep of death, what dreams may come,
When we have shuffled off this mortal coil,
Must give us pause. There's the respect
That makes Calamity of so long life:
For who would bear the Whips and Scorns of time,
The Oppressor's wrong, the proud man's Contumely,
The pangs of despised Love, the Law’s delay,
The insolence of Office, and the Spurns
That patient merit of the unworthy takes,
When he himself might his Quietus make
With a bare Bodkin? Who would these Fardels bear,
To grunt and sweat under a weary life,
But that the dread of something after death,
The undiscovered Country, from whose bourn
No Traveler returns, Puzzles the will,
And makes us rather bear those ills we have,
Than fly to others that we know not of.
Thus Conscience does make Cowards of us all,
And thus the Native hue of Resolution
Is sicklied o'er, with the pale cast of Thought,
And enterprises of great pitch and moment,
With this regard their Currents turn awry,
And lose the name of Action. Soft you now,
The fair Ophelia. Nymph, in all thy Orisons
Be thou all my sins remembered.
William Shakespeare - Hamlet

➠ Frequency Analysis

Answers to Questions

How to use Index of Coincidence?

For a given ciphered message, the value for the index of coincidence allows to filter the list of ciphering methods to use. It is one of the first cryptanalysis technique.

If the Index of coincidence is high (close to $ 0.070 $), i.e. similar to plain text, then the message has probably been crypted using a transposition cipher (letters were shuffled) or a monoalphabetic substitution (a letter can be replaced by only one other).

If the Index of coincidence is low (close to $ 0.0385 $), i.e. similar to a random text, then the message has probably been crypted using a polyalphabetic cipher (a letter can be replaced by multiple other ones).

The more the coincidence count is low, the more alphabets have been used.

Example: Vigenere cipher with a key of length 4 to 8 letters have an IC of about $ 0.045 \pm 0.05 $

How to calculate a coincidence index?

Index of coincidence uses the formula:

$$ IC = \sum_{i=A}^{i=Z} \frac{n_{i}(n_{i}-1)}{N(N-1)} $$

with $ n_i $ the number of occurrences of the letter $ i $ in the text and $ N $ the total number of letters.

What are values of IC among languages?

For an non encrypted text, coincidence indexes are

English	0.0667	French	0.0778
German	0.0762	Spanish	0.0770
Italian	0.0738	Russian	0.0529

What is a random text?

A text where each letter has the same probability of appearance than another, IC is then of $ 1/N $ (where $ N $ is the number of letters in the alphabet)

Example: $ IC = 0.0385 $ for $ N=26 $

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Source code

dCode retains ownership of the source code of the script Index of Coincidence online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be given for free. So if you need to download the online Index of Coincidence script for offline use, check contact page !

Questions / Comments

Summary

Cryptanalysis using Index of Coincidence

How to use Index of Coincidence?
How to calculate a coincidence index?
What are values of IC among languages?
What is a random text?

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