5th Alphabet.—Probable vowels, D, L, U; probable common consonants, C, H, I.

Now this cipher may have been made up from five distinct alphabets with letters chosen at random but it is much more likely to have been prepared with a cipher disk or equivalent, having the regular alphabet on the fixed disk and the mixed alphabet on the movable disk. An equivalent form of apparatus (not using the mixed alphabet in question) is one like this:

FixedAlphabet of Text
ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ
PCJVRQZBAODFSUTMXIYHLGEN
Movable Alphabet ofCipher

Here A of the plain text is enciphered by S and the other letters come as they will. If we move the cipher alphabet one space to the left, A will be enciphered by U and the whole sequence of the alphabet will be changed.

We will therefore use some such form as the above and see if we can insert our letters, as they are determined, in such a way as to have each of the cipher slips identical. We may start thus:

ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ
1st Alphabet t x
2d ol qei ms d c u
3d ol qei ms d c u
4th ol qei ms d c u
5th d c u ol qei ms
6th ol qei ms d c u

In the 1st alphabet, T and X are placed as A and E respectively on the basis of frequency. In the 2d and 6th alphabets, O and E are placed as A and E respectively on the basis of frequency. In the 4th alphabet, E and S are placed as A and E, and in the 5th, D, U and L are placed as A, E and O for the same reason. We now have an excess of E’s and a deficiency of A’s, which will be corrected if, in the 3d alphabet, we place L, I and C as A, E and O respectively. As a check, this gives us TOLEDO as the key word.

In the second alphabet, O is four letters to the left of E; we may place O four letters to the left of E in the fourth and it comes under V. Note that in the fourth frequency table O (= V) does not occur. In the same way in the fourth alphabet, S is four letters to the right of E; placing it in the same position with respect to E in the second and sixth, we have S under I. We have already noted that S probably represents a vowel in these two alphabets. In this way, we may add D and U to the third alphabet from their position in the fifth with respect to L and we may add I and O to the fifth from their position in the third with respect to L. In every case we check results from the frequency tables and find nothing unlikely in the results.

Now in the second and sixth, let us try Q, D and U as D, N and R respectively. We may add these letters to the third, fourth and fifth alphabets by the method of observing the number of letters to the right or left of some letter already fixed. We now add L to the second, third, fourth and sixth from its position with reference to D and U in the fifth. M is probably D in the fourth and we may add it to each of the alphabets, except the first, in the same way. The table is now complete as shown.

Let us try these letters on the first line of the message and see if some other letters will be self-evident.