I'm new to cryptography and I was trying to find key to an intercepted vigenere ciphertext using ciphertext-only attack, I'm following book "cryptography and network security" by Forouzan.
The book introduced some complicated formulas for finding Mutual Index of Coincidence but I didn't get it.
This was mentioned in the text "So in order to find the actual key, we divide the ciphertext into m (key length obtained by Kasiski text) rows, each row is a shift cipher which have been shifted by a key say,Ki.Thus for each row we find the Mutual Index of coincidence with respect to an unencrypted English text. We compute the MI values by varying the keys, Ki from 0 to 25. The values for which the MI values become close to 0.065 will indicate the correct key, Ki. This process is repeated for the m rows to obtain the entire key."
I didn't get what this line means "Thus for each row we find the Mutual Index of coincidence with respect to an unencrypted English text"
Do I need to take second string a character/letter (which is denoted by it's numeric value if we assign numbers 0 to 25 to English alphabets) and find it's MI w.r.t row ?
In "Cryptography Theory and Practice" 4th edition by Douglas R. Stinson and Maura B. Paterson. They use "Mg" values.
Now this book states the following :
"Assuming that we have determined the correct value of m, how do we de-
termine the actual key, K = (k1, k2, . . . , km)? We describe a simple and effec-
tive method now. Let 1 ≤ i ≤ m, and let f0, . . . , f25 denote the frequencies of
A, B, . . . , Z, respectively, in the string yi. Also, let n′ = n/m denote the length of
the string yi. Then the probability distribution of the 26 letters in yi is
f0/n',..., f25/n'
Now, recall that the substring yi is obtained by shift encryption of a subset of
the plaintext elements using a shift ki. Therefore, we would hope that the shifted
probability distribution
fki/n', ..., f(25+ki)/n'
would be “close to” the ideal probability distribution p0, . . . , p25, where subscripts in the above formula are evaluated modulo 26.
Suppose that 0 ≤ g ≤ 25, and define the quantity"
Please, provide me with an example solved either by Mg formula or by Mutual Index of coincidence method.
I'm pretty much lost I can't afford high end institutions
