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Also known as: IC
A statistic measuring letter coincidence likelihood in text, used to assess randomness and aid cryptanalysis of substitution ciphers.
DESCRIPTION
The index of coincidence (IC) estimates the probability that two randomly selected letters from a text match. Natural languages have characteristic IC values, while random text differs. Cryptanalysts use IC to detect monoalphabetic vs. polyalphabetic ciphers and infer key lengths. It complements entropy and chi-squared frequency tests. Reliable estimation needs sufficient text length and normalization for alphabet size. IC assists in early-stage cipher analysis and language identification.
ALTERNATIVE DEFINITIONS
Wikipedia
The index of coincidence is a measure of how likely it is that two randomly selected letters from a text will be the same.
Defines the statistic via the probability of letter matches.
Practical Cryptography
The index of coincidence (IC) is a statistic used to measure how unevenly letters are distributed in a text.
Emphasizes uneven distribution and text characterization.
University of Maryland
The index of coincidence measures the probability that two randomly selected letters are identical, helping distinguish random text from language.
Educational framing linking IC to language detection and cipher type.
RELATED TERMS
Frequency Analysis Chi-squared Test Vigenère Cipher Kasiski Examination Cryptanalysis N-gram Statistics Substitution Plaintext
COMPETING TERMS
Shannon Entropy Mutual Information
KNOWLEDGE AREAS
Data Security Mathematics Data Science
TARGET AUDIENCE
Cybersecurity Engineer Security Architect Data Scientist IT Auditor
EXTERNAL SOURCES
- Wikipedia - Index of coincidence
- Practical Cryptography - Guide to IC in cryptanalysis
- Crypto StackExchange - Community explanation of IC
- University of Maryland - Lecture notes on cryptanalysis including IC
TOP QUESTIONS
Why is the Index of Coincidence useful in cryptanalysis?
It differentiates random text from natural language and helps detect cipher types and key lengths.
Category: Relevancy
How is the Index of Coincidence computed?
Count letter frequencies and use the IC formula summing n_i(n_i−1)/N(N−1), where n_i are counts and N is total letters.
Category: Requirements
What mistakes occur when using the Index of Coincidence?
Applying IC to very short texts or mixed alphabets yields misleading estimates.
Category: Mistakes
What risks exist in relying solely on the Index of Coincidence?
Sophisticated ciphers or obfuscation can mask IC patterns, requiring complementary tests.
Category: Risks
How does IC compare to Shannon entropy?
Both measure distribution properties; entropy quantifies uncertainty, while IC focuses on coincidence probability.
Category: Alternatives
What is a hot topic around the Index of Coincidence today?
IC remains educational; modern cryptanalysis relies more on computational attacks and information theory.
Category: Topic
Where to start learning the Index of Coincidence?
Study classical cryptography, frequency analysis, and practice with monoalphabetic and Vigenère ciphers.
Category: Requirements
Is the Index of Coincidence still relevant?
It’s relevant for classical ciphers and pedagogy, less so for modern encryption.
Category: Relevancy
What is a misunderstanding about the Index of Coincidence?
Assuming a single IC value universally identifies language; context and alphabet matter.
Category: Misunderstanding