finding repeated strings. This is a very hard task to perform manually, but computers can make it much easier. However, care is still required, since some repeated strings may just be coincidence, so that some of the repeat distances are misleading. The cryptanalyst has to rule out the coincidences to find the correct length. Then, of course, the monoalphabetic ciphertexts that result must be cryptanalyzed. A cryptanalyst looks for repeated groups of letters and counts the number of letters between the beginning of each repeated group. For instance, if the ciphertext were , the distance between groups is 10. The analyst records the distances for all repeated groups in the text. The analyst next factors each of these numbers. If any number is repeated in the majority of these factorings, it is likely to be the length of the keyword. This is because repeated groups are more likely to occur when the same letters are encrypted using the same key letters than by mere coincidence; this is especially true for long matching strings. The key letters are repeated at multiples of the key length, so most of the distances found in step 1 are likely to be multiples of the key length. A common factor is usually evident. Once the keyword length is known, the following observation of Babbage and Kasiski comes into play. If the keyword is N letters long, then every Nth letter must have been enciphered using the same letter of the keytext. Grouping every Nth letter together, the analyst has N "messages", each encrypted using a one-alphabet substitution, and each piece can then be attacked using frequency analysis. Using the solved message, the analyst can quickly determine what the keyword was. Or, in the process of solving the pieces, the analyst might use guesses about the keyword to assist in breaking the message. Once the interceptor knows the keyword, that knowledge can be used to read other messages that use the same key. Superimposition 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