Frequency Tables
| Colum 1 | Column 2 | Column 3 | Column 4 | Column 5 | |||||
| A | 11 | A | 111111111 | A | 1 | A | 1 | A | 11 |
| B | B | 111 | B | 111 | B | B | 1111111 | ||
| C | 1111111 | C | 1 | C | 111 | C | 1111 | C | |
| D | 11 | D | 11 | D | 1 | D | D | 111 | |
| E | 1111 | E | E | 11 | E | 1111111 | E | ||
| F | 111 | F | F | 111111111 | F | 111 | F | 11111 | |
| G | 111111111 | G | G | 111 | G | 11 | G | 11 | |
| H | 111 | H | 11111 | H | 111 | H | 111 | H | 11 |
| I | 11 | I | 11 | I | 1111111 | I | 11111111111111111 | I | 11 |
| J | 11111 | J | 1 | J | 111111 | J | J | 111111111 | |
| K | 111111 | K | 11111 | K | K | 1 | K | 1 | |
| L | L | 1111111111111111111 | L | 11 | L | 11111 | L | 1 | |
| M | M | M | 1111111 | M | 1111 | M | 111 | ||
| N | 1111111 | N | 111 | N | 1111 | N | N | 11111 | |
| O | 11111 | O | O | 111111111 | O | 1 | O | ||
| P | 1111111 | P | 1111111 | P | 11111111 | P | 1111 | P | |
| Q | 11111 | Q | Q | Q | 11 | Q | 111111 | ||
| R | R | 1 | R | 1 | R | 111111 | R | 1 | |
| S | S | 11111111 | S | 111111 | S | 111111111111 | S | 1111111 | |
| T | 1111111 | T | 111 | T | 11111 | T | 1 | T | 11111111111111 |
| U | 1111111 | U | 111 | U | 111111 | U | U | 1 | |
| V | 11111 | V | V | 11 | V | 11111 | V | ||
| W | 111 | W | 1111 | W | W | 11111 | W | 1111111 | |
| X | 11 | X | X | 1111 | X | 11111111 | X | 111111 | |
| Y | 1111 | Y | 11111 | Y | Y | 111 | Y | 1111111 | |
| Z | Z | 11111 | Z | 111 | Z | Z | 111 | ||
In the table for Column 1, the letter G occurs 9 times. Let us consider it tentatively as E. Then if the cipher alphabet runs regularly and in the direction of the regular alphabet, C (7 times) = A and the cipher alphabet bears a close resemblance to the regular frequency table. Note TUV (= RST) occurring respectively 7, 7, and 5 times and the non-occurrence of B, L, M, R, S, Z, (= Z, J, K, P, Q, and X respectively.)
In the next table, L occurs 19 times and taking it for E with the alphabet running in the same way, A=H. The first word of our message, CT, thus becomes AM when deciphered with these two alphabets and the first two letters of the key are C H.
Similarly in the third table we may take either F or O for E, but a casual examination shows that the former is correct and A=B (even if we were looking for a vowel for the next letter of the keyword).
In the fourth table, I is clearly E and A=E. The fifth table shows T=14 and J=9. If we take T=E we find that we would have many letters which should not occur. On the other hand, if we take J=E then T=O and in view of the many E’s already accounted for in the other columns, this may be all right. It checks as correct if we apply the last three alphabets to the second word of our message, OSB, which deciphers NOW. Using these alphabets to decipher the whole message, we find it to read:
“M. B. Am now safe on board a barge moored below Tower Bridge where no one will think of looking for me. Have good friends but little money owing to action of police. Trust, little girl, you still believe in my innocence although things seem against me. There are reasons why I should not be questioned. Shall try to embark before the mast in some outward bound vessel. Crews will not be scrutinized so sharply as passengers. There are those who will let you know my movements. Fear the police may tamper with your correspondence but later on when hue and cry have died down will let you know all.”
The key to this message is CHBEF which is not intelligible as a word but if put into figures indicating that the 2d, 7th, 1st, 4th, and 5th letter beyond the corresponding letter of the message has been used the key becomes 27145 and we may connect it with the “personal” which appeared in the same paper the day before reading:
“M. B. Will deposit £27 14s 5d tomorrow.”
Case 7-b.
Message
| DDLRM | ERGLM | UJTLL | CHERS | LSOEE | SMEJU |
| ZJIMU | DAEES | DUTDB | GUGPN | RCHOB | EQEIE |
| OOACD | EIOOG | COLJL | PDUVM | IGIYX | QQTOT |
| DJCPJ | OISLY | DUASI | UPFNE | AECOB | OESHO |
| BETND | QXUCY | LUQOY | EHYDU | LXPEQ | FIXZE |
| PDCNZ | ENELQ | MJTSQ | ECFIE | ARNDN | ETSCF |
| IFQSE | TDDNP | UUZHQ | CDTXQ | IRMER | GLXBE |
| IQRXJ | FBSQD | LDSVI | XUMTB | AEQEB | YLECO |
| IYCUD | QTPYS | VOQBL | ULYRO | YHEFM | OYMUY |
| ROYMU | EQBLV | UBREY | GHYTQ | CMUBR | EQTOF |
| VSDDU | DAFFS | CEBSV | TIOYE | TCLQX | DVNLQ |
| XYTSI | MZULX | BAXQR | ECVTD | ETGOB | CCUYF |
| TTNXL | UNEFS | IVIJR | ZHSBY | LLTSI |
On the preliminary determination, we have the following count of letters out of a total of 385:
| A | 8 | L | 23 | J | 9 |
| E | 38 | N | 11 | Q | 22 |
| I | 19 | R | 14 | V | 9 |
| O | 21 | S | 20 | X | 13 |
| U | 24 | T | 21 | Z | 6 |
| Total | 110 | Total | 89 | Total | 59 |
| 28% | 23% | 15% |
Every letter except K and W occurs at least six times. We may say then that it is a substitution cipher, Spanish text, and certainly not Case 4, 5 or 6. We will now analyze it for recurring pairs or groups to determine, if it be Case 7, how many alphabets were used. The following is a complete list of such recurring groups and pairs with the number of letters intervening and the factors thereof. In work of this kind, the groups of three or more letters are always much more valuable than single pairs. For example, the groups, HOBE, OYMU, RMERGL and UBRE show, without question, that six alphabets were used. It is not necessary, as a rule, to make a complete list like the following:
Out of one hundred and one recurring pairs we have fifty with the factors 2×3=6; out of twelve recurring triplets, nine have these factors; and the four recurring groups of four or more letters all have these factors. The percentages are respectively 49.5%, 75% and 100% and we may be certain from this that six alphabets were used. But, before the six frequency tables are made up, there is one more point to be considered; why are there so many recurring groups which do not have six as a factor? The answer is that one or more of the alphabets is repeated in each cycle; that is, a key word of the form HAVANA has been used. If this were the key word, the second, fourth and sixth alphabets would be the same. We will see later that in this example the second and sixth alphabets are the same and this introduces the great number of recurring groups without the factor 6.
We will now proceed to make a frequency table for each alphabet. As the message is written in thirty columns, we take the first, seventh, thirteenth, etc., as constituting the first alphabet; the second, eighth, fourteenth, etc., as constituting the second alphabet and so on. The prefix and suffix letter is noted for each occurrence of each letter. The importance of this will be appreciated when the form of the frequency tables is examined. None bears any resemblance to the normal frequency table except that each is evidently a mixed up alphabet. The numbers after “Prefix” and “Suffix” refer to the alphabet to which these belong, for convenience in future reference.