Kasiski Examination - Superposition

Superposition

Kasiski actually used "superimposition" to solve the Vigenère cipher. He started by finding the key length, as above. Then he took multiple copies of the message and laid them one-above-another, each one shifted left by the length of the key. Kasiski then observed that each column was made up of letters encrypted with a single alphabet. His method was equivalent to the one described above, but is perhaps easier to picture.

Modern attacks on polyalphabetic ciphers are essentially identical to that described above, with the one improvement of coincidence counting. Instead of looking for repeating groups, a modern analyst would take two copies of the message and lay one above another.

Modern analysts use computers, but this description illustrates the principle that the computer algorithms implement.

The generalized method

1. The analyst shifts the bottom message one letter to the left, then two letters to the left, etc., each time going through the entire message and counting the number of times the same letter appears in the top and bottom message.
2. The number of "coincidences" goes up sharply when the bottom message is shifted by a multiple of the key length, because then the adjacent letters are in the same language using the same alphabet.
3. Having found the key length, cryptanalysis proceeds as described above using frequency analysis.