Mutual Index of Coincidence Calculator

Mutual Index of Coincidence Formula:

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

Mutual Index of Coincidence (IC):

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1. What is Mutual Index of Coincidence?

The Mutual Index of Coincidence is a statistical measure used in cryptanalysis to compare the frequency distributions of two texts. It helps identify potential relationships between ciphertexts, particularly useful for breaking polyalphabetic ciphers like the Vigenère cipher.

2. How Does the Calculator Work?

The calculator uses the Mutual Index of Coincidence formula:

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

Where:

\( IC \) — Mutual Index of Coincidence (dimensionless)
\( f_i \) — Frequency of letters in overlapping positions
\( N \) — Total number of letters in the text

Explanation: The formula measures the probability that two randomly selected letters from different texts will be the same, normalized by the text lengths.

3. Importance in Cryptanalysis

Details: Mutual IC is crucial for determining the period of polyalphabetic ciphers. High mutual IC values between shifted versions of ciphertext suggest the correct key length, enabling cryptanalysts to break the cipher by treating each position as a simple substitution cipher.

4. Using the Calculator

Tips: Enter two texts in the input fields. The calculator will automatically remove non-alphabetic characters and convert to uppercase. For best results, use texts of reasonable length (at least 50 characters each).

5. Frequently Asked Questions (FAQ)

Q1: What is a typical IC value for English text?
A: For standard English text, the Index of Coincidence is approximately 0.065. Values significantly different may indicate ciphertext or non-English language.

Q2: How is Mutual IC different from regular IC?
A: Regular IC compares letters within the same text, while Mutual IC compares letters between two different texts or shifted versions of the same text.

Q3: What does a high Mutual IC value indicate?
A: High Mutual IC suggests the texts are related or encrypted with the same key (for polyalphabetic ciphers), making it useful for determining cipher period.

Q4: Can this be used for modern cryptography?
A: Primarily for classical ciphers. Modern encryption methods like AES are resistant to frequency analysis attacks.

Q5: What are the limitations of this method?
A: Requires sufficient text length for accuracy, and may not work well with very short texts or when the cipher uses strong randomization.