Kasiski Examination - How IT Works

How It Works

The Kasiski examination allows a cryptanalyst to deduce the length of the keyword used in the polyalphabetic substitution cipher. Once the length of the keyword is discovered, the cryptanalyst lines up the ciphertext in n columns, where n is the length of the keyword. Then, each column can be treated as the ciphertext of a monoalphabetic substitution cipher. As such, each column can be attacked with frequency analysis.

The Kasiski examination involves looking for strings of characters that are repeated in the ciphertext. The strings should be three characters long or more for the examination to be successful. Then, the distances between consecutive occurrences of the strings are likely to be multiples of the length of the keyword. Thus finding more repeated strings narrows down the possible lengths of the keyword, since we can take the greatest common divisor of all the distances.

The reason this test works is that if a repeated string occurs in the plaintext, and the distance between corresponding characters is a multiple of the keyword length, the keyword letters will line up in the same way with both occurrences of the string. For example, consider the plaintext:

"crypto" is a repeated string, and the distance between the occurrences is 20 characters. We will line up the plaintext with first a six-character keyword "abcdef" (6 does not divide 20) and a five-character keyword "abcde" (5 divides 20).

Notice that the first instance of "crypto" lines up with "abcdef" and the second instance lines up with "cdefab". The two instances will encrypt to different ciphertexts and the Kasiski examination will reveal nothing.

Note that both occurrences of "crypto" now line up with "abcdea". The two instances will encrypt to the same ciphertext and the Kasiski examination will be effective.