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Computer Security and Cryptography by Alan G. Konheim

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4.6 COINCIDENCE

A coincidence occurs at the ith position in two samples of plaintext

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if image. If the length n of the samples are the same, the kappa-value κ[x(1), x(2)] is the total number of coincidences

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The normalized kappa-value κ*[x(1), x(2)] is the average number of coincidences per letter

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How many coincidences can one expect in typical plaintext? If the plaintext is generated by the language model consisting of independent and identically distributed random variables with distribution as specified in Equation (4.2), then a coincidence occurs at the ith position of two samples X(1) and X(2) plaintext with probability

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The expected number of coincidences is

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where s2 ≈ 0.06875 using the English 1-gram probabilities in Table 4.3. The values of s2 in some languages are given in Table 4.6. We can use the coincidence rate to detect if two samples of ciphertext result from the same or different ...

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