General Remarks on Transposition Ciphers
It is the consensus of opinion of experts that the transposition cipher is not the best one for military purposes. It does not fulfill the first, second, and third of Kerckhoffs’ requirements as to indecipherability, safety when apparatus and method fall into the hands of the enemy, and dependability on a readily changeable key word.
However, transposition ciphers are often encountered. They are favorites with those who find the substitution ciphers too difficult and too tedious to handle and who believe that their transposition methods are either absolutely indecipherable or sufficiently so for the purpose of concealing the text of a message for the time being. They seem to be particularly popular with secret agents and spies, presumably because special apparatus is rarely necessary in enciphering and deciphering.
Although the number of transposition methods is legion, they can practically all be considered under one of the three cases already discussed. It is surprising how often transposition ciphers prepared by complicated rules, will, on analysis, be seen to be very simple.
To be successful in solving transposition ciphers, one should constantly practice reading backward and up and down columns, so that the common combinations of letters are as quickly identified when seen thus as when encountered in straight text. Combinations like EHT, LLIW, ROF, DNA, etc., should be appreciated immediately as common words written backward.
A study of the table of frequency of digraphs or pairs is also excellent practice and such a table should be at hand when a transposition cipher is under consideration. It assists greatly if Case 2 be encountered and is of considerable use in solving Case 1.
The solution of route ciphers is necessarily one of try and fit, with the knowledge that such ciphers usually are read up and down columns. It is not believed that route ciphers will often be met with at the present day.
Chapter VI
Examination of Substitution Ciphers
When an unknown cipher has been put into the substitution class by the methods already described we may proceed to decide on the variety of substitution cipher which has been used.
There are a few purely mechanical ways of solving some of the simple cases of substitution ciphers but as a general rule some or all of the following determinations must be made:
1. By preparation of a frequency table for the message we determine whether one or more substitution alphabets have been used and, if one only has been used, this table leads to the solution.
2. By certain rules we determine how many alphabets have been used, if there are more than one, and then isolate and analyze each alphabet by means of a frequency table.
3. If the two preceding steps give no results we have to deal with a cipher with a running key, a cipher of the Playfair type, or a cipher where two or more characters are substituted for each letter of the text. Some special cases under this third head will be given but, in general, military ciphers of the substitution class will usually be found to come under the first two heads, on account of the time and care required in the preparation and deciphering of messages by the last named methods and the necessity, in many cases, of using complicated machines for these processes.
Case 4-a.
Message
OBQFO BPBRP QBAML OBHIF PILFQ FJBOX OFLNR BIXOZ EL
From the recurrence of B, F and O, we may conclude that a single substitution alphabet was used for this message. If so and if the alphabet runs in the same order and direction as the regular alphabet, the simplest way to discover the meaning of the message is to take the first two words and write alphabets under each letter as follows, until some line makes sense:
| O B Q F O B P B R P |
| P C R G P C Q C S Q |
| Q D S H Q D R D T R |
| R E T I R E S E U S |
The word RETIRESE occurs in the fourth line, and, if the whole message be handled in this way we find the rest of the fourth line to read USTED POR EL MISMO ITINERARIO QUE MARCHO. The message was enciphered using an alphabet where A = X, B = Y, C = Z, D = A, etc. noting that as this message is in Spanish the letters K and W do not appear in the alphabet.
Case 4-b.
Message
HUJZH UIUPN OZYTS VQXMI SMOMX MQHUD UMREI SESJU AG
This is a message in Spanish. We will handle it as in [case 4-a], setting down the whole message.
| HUJZHUIU | PNOZY | TSV | QX | MISMO | MXMQHUDUMR | EIS | ESJUAG |
| IVLAIVJV | QOPAZ | UTX | RY | A=A | NYNRIVEVNS | FJT | FTLVBH |
| JXMBJXLX | RPQBA | VUY | SZ | OZOSJXFXOT | GLU | GUMXCI | |
| LYNCLYMY | SQRCB | XVZ | TA | PAPTLYGYPU | HMV | HVNYDJ | |
| MZODMZNZ | TRSDC | YXA | UB | QBQUMZHZQV | INX | IXOZEL | |
| NAPENAOA | USTED | ZYB | VC | RCRVNAIARX | JOY | JYPAFM | |
| OBQFOBPB | A=U | AZC | XD | SDSXOBJBSY | LPZ | LZQBGN | |
| PCRGPCQC | BAD | YE | TETYPCLCTZ | MQA | MARCHO | ||
| QDSHQDRD | CBE | ZF | UFUZQDMDUA | NRB | A=S | ||
| RETIRESE | DCF | AG | VGVARENEVB | OSC | |||
| A=Q | EDG | BH | XHXBSFOFXC | PTD | |||
| FEH | CI | YIYCTGPGYD | QUE | ||||
| GFI | DJ | ZJZDUHQHZE | A=O | ||||
| HGJ | EL | ALAEVIRIAF | |||||
| IHL | A=M | BMBFXJSJBG | |||||
| JIM | CNCGYLTLCH | ||||||
| LJN | DODHZMUMDI | ||||||
| MLO | EPEIANVNEJ | ||||||
| NMP | FQFJBOXOFL | ||||||
| ONQ | GRGLCPYPGM | ||||||
| POR | HSHMDQZQHN | ||||||
| A=E | ITINERARIO | ||||||
| A=D |
Here each word of the message comes out on a different line, and noting in each case the letter corresponding to A, we have the word QUEMADOS which is the key. The cipher alphabet changed with each word of the message.
A variation of this case is where the cipher alphabet changes according to a key word but the change comes every five letters or every ten letters of the message instead of every word. The text of the message can be picked up in this case with a little study.
Note in using case 4 that if we are deciphering a Spanish message we use the alphabet without K or W as a rule, altho if the letters K or W appear in the cipher it is evidence that the regular English alphabet is used.
Case 5-a.
Message
DNWLW MXYQJ ANRSA RLPTE CABCQ RLNEC LMIWL XZQTT QIWRY ZWNSM BKNWR YMAPL ASDAN
This message contains K and W and therefore we expect the English alphabet to be used. The frequency of occurrence of A, L, N, R and W has lead us to examine it under case [4] but without result. Let us set down the first two words and decipher them with a cipher disk set A to A and then proceed as in case [4].
| Cipher message | DNWLWMXYQJ | |
| Deciphered A to | A | XNEPEODCKR |
| B | YOFQFPEDLS | |
| C | ZPGRGQFEMT | |
| D | AQHSHRGFNU | |
| E | BRITISHGOV | |
The message is thus found to be enciphered with a cipher disk set A to E and the text is: BRITISH GOVERNMENT PLACED CONTRACTS WITH FOLLOWING FIRMS DURING SEPTEMBER.
Case 5-b.
Same as [case 4-b] except that the cipher message must be deciphered by means of a cipher disk set A to A before proceeding to make up the columns of alphabets. The words of the deciphered message will be found on separate lines, the lines being indicated as a rule by a key word which can be determined as in [case 4-b].
The question of alphabetic frequency has already been discussed in considering the mechanism of language. It is a convenient thing to put the frequency tables in a graphic form and to use a similar graphic form in comparing unknown alphabets with the standard frequency tables. For instance the standard Spanish frequency table put in graphic form is here presented in order to compare with it the frequency table for the message discussed in [case 4-a].
| Standard Spanish frequencytable | Table for Message Case4-a | ||||
| A | 111111111111111111111111111 | 27 | A | 1 | 1 |
| B | 11 | 2 | B | 1111111 | 7 |
| C | 111111111 | 9 | C | ||
| D | 1111111111 | 10 | D | ||
| E | 1111111111111111111111111111 | 28 | E | 1 | 1 |
| F | 11 | 2 | F | 11111 | 5 |
| G | 111 | 3 | G | ||
| H | 11 | 2 | H | 1 | 1 |
| I | 111111111111 | 12 | I | 111 | 3 |
| J | 1 | 1 | J | 1 | 1 |
| L | 1111111111 | 10 | L | 111 | 3 |
| M | 111111 | 6 | M | 1 | 1 |
| N | 111111111111 | 12 | N | 1 | 1 |
| O | 1111111111111111 | 16 | O | 111111 | 6 |
| P | 11111 | 5 | P | 111 | 3 |
| Q | 11 | 2 | Q | 111 | 3 |
| R | 111111111111111 | 15 | R | 11 | 2 |
| S | 11111111111111 | 14 | S | ||
| T | 11111111 | 8 | T | ||
| U | 1111111 | 7 | U | ||
| V | 11 | 2 | V | ||
| X | X | 11 | 2 | ||
| Y | 11 | 2 | Y | ||
| Z | 1 | 1 | Z | 1 | 1 |
Our first assumption might be that B = A and F = E but it is evident at once that in that case, S, T, U and V (equal to R, S, T and U) do not occur and a message even this short without R, S, T or U is practically impossible. By trying B = E we find that the two tables agree in a general way very well and this is all that can be expected with such a short message. The longer the message the nearer would its frequency table agree with the standard table. Note that if a cipher disk has been used, the alphabet runs the other way and we must count upward in working with a graphic table. Note also that if, in a fairly long message, it is impossible to coördinate the graphic table, reading either up or down, with the standard table and yet some letters occur much more frequently than others and some do not occur at all, we have a mixed alphabet to deal with. The example chosen for [case 6-a] is of this character. An examination of the frequency table given under that case shows that it bears no graphic resemblance to the standard table. However, as will be seen in [case 7-b], the preparation of graphic tables enables us to state definitely that the same order of letters is followed in each of a number of mixed alphabets.