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Kasiki's test and the index of coincidence are used to attack a Vigenère cipher (or other polyalphabetic ciphers with small alphabet and small key size) - they both try to get the length of the keyword. Kasiki's test gets probable prime factors of the keyword length, while the coincidence index test gets us an estimation of the absolute length of the ...

Expected Index of Coincidence usually refers to a language's expected index of coincidence (1.73 for English, or 0.067 if you're not normalising). The formula in question is usually used to determine the length of the key ($t$) given the (measured) $IC$ of received cipher-text. $IC$ is the probability that two randomly-selected letters from the cipher text ...