Coincidence Calculator

Index of Coincidence Formula:

\[ IC = \frac{\sum f_i (f_i - 1)}{N (N - 1)} \]

Index of Coincidence (IC):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Index of Coincidence?

The Index of Coincidence (IC) is a statistical measure used in cryptanalysis to identify the likelihood of coincidental matches between two texts. It measures the probability that two randomly selected letters from a text will be identical.

2. How Does the Calculator Work?

The calculator uses the Index of Coincidence formula:

\[ IC = \frac{\sum f_i (f_i - 1)}{N (N - 1)} \]

Where:

\( IC \) — Index of Coincidence (dimensionless)
\( f_i \) — Frequency of letter i
\( N \) — Total number of letters in the text

Explanation: The formula calculates the probability that any two randomly selected letters from the text will be identical, normalized by the total possible letter pairs.

3. Importance of IC in Cryptanalysis

Details: The Index of Coincidence is crucial for breaking classical ciphers. Different languages have characteristic IC values, and deviations from expected values can reveal information about encryption methods and key lengths.

4. Using the Calculator

Tips: Enter any text in the input field. The calculator will automatically remove non-alphabetic characters and calculate the IC based on letter frequencies. Longer texts provide more accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What are typical IC values for different languages?
A: English text typically has IC ≈ 0.065, random text IC ≈ 0.038, and other languages have characteristic values that aid in cryptanalysis.

Q2: How is IC used to break ciphers?
A: By comparing IC values of ciphertext with expected values for different languages and key lengths, cryptanalysts can determine the encryption method and key size.

Q3: What is the range of possible IC values?
A: IC ranges from 0 (no coincidences) to approximately 0.076 (highly non-uniform distribution like monoalphabetic substitution).

Q4: Does IC work for short texts?
A: IC becomes more reliable with longer texts. For very short texts, the statistic may not be meaningful due to small sample size.

Q5: Can IC detect polyalphabetic ciphers?
A: Yes, polyalphabetic ciphers tend to have IC values closer to random text, while monoalphabetic ciphers preserve the IC of the original language.