Special Solution for Case 7

When a short message is enciphered with a long key word, the methods of analysis already discussed may fail; first, because there will be no recurring pairs to indicate the number of alphabets used and, second, because there will be so few letters in each alphabet that the methods of Case 6 will not be easily applied.

However, if we know or correctly assume one word, preferably a fairly long one, in the cipher text, a solution is very simple. For example, the following message is believed to refer to reënforcements and to contain that word.

YANZVZNLPPKQFXIJBPWA
NRUQPEPLOMCCWHMI

Let us assume that REINFORCEMENTS is the first word and that it is represented by the cipher group YANZVZNLPPKQFX. We may put the test in this tabular form, using a cipher disk and a Larrabee cipher card to determine the value of A for each letter under these two systems. Any other alphabets suspected may be tried out at the same time.

If

YANZVZNLPPKQFX

equals

REINFORCEMENTS

then, with cipher disk, A equals

PERMANENTBODYP

and, in Vigenere cipher, A equals

HWFMQLWJLDGDMF

It is evident that the guess as to the appearance of the word REINFORCEMENTS was correct, that it is the first word of the message, that the cipher disk was used in preparing the cipher and that the key words are PERMANENT BODY.

This is, of course, an especially favorable case and we will take one less favorable to show how this method can be applied.

Two Mexican chieftains, A and B, have been communicating with the following cipher alphabet:

Plain textABCDEFGHIJLMNOPQRSTUVXYZ
Cipher PCJVRQZBAODFSUTMXIYHLGEN

This alphabet has been determined from many radio messages from A, the superior, to B, his sub-ordinate, who has a force of about 2,000 men near the border. A uses the form ORDENO QUE instead of the more familiar MANDO QUE in all his messages giving orders to B. The following message is received from A by B’s radio station (and other listening stations) and about an hour later there is a good deal of noise and movement as if B’s force were breaking camp.

IIHAHYDXRPEGQGVJJEEEHOBGV
GJCAGXAESAVVXLEIILHMPSQAG
BDGAVGSQAZ

This is a substitution cipher, but it is not Case 6 using the usual alphabet of the communications from A to B and, in fact, is not Case 6 at all. The recurring pairs and triplets point to a key word of ten letters and this would give us but six letters per alphabet if it is Case 7.

The preparations for a move lead us to believe that A has given an order to B and he has, in that case, probably used the expression ORDENO QUE in the message. We will try the first nine letters of the message as in the other example, first preparing a cipher disk or equivalent sliding arrangement having on it the alphabet usually used between these chieftains or A-B cipher.

FixedCipher Alphabet
PCJVRQZBAODFSUTMXIYHLGENPCJVRQZBAODFSUTMXIYHLGEN
ABCDEFGHIJLMNOPQRSTUVXYZ
Sliding Plain TextAlphabet
A-BCipher
IfIequalsOthen A equalsR
IRC
HDX
AER
HNB
YOQ

Clearly there is nothing here and the assumed words, if they occur, are in the middle of the message. We may jump to the combination PEGQGV at once since the preceding letters do not make ORDENO QUE. We try this without result and proceed to EGQGVJ, GQGVJJ, QGVJJE, GVJJEE, VJJEEE, JJEEEH, JEEEHO, EEEHOB, EEHOBG, EHOBGV, HOBGVG, OBGVGJ, BGVGJC, GVGJCA, VGJCAG, all without result. This work requires less time than might be imagined and is the kind of work which can be divided among a number of operators. Now let us come to the next combination GJCAGX. We add the next three letters, AES, against QUE.

If

GJCAGXAES

equals

ORDENOQUE

Then, in the A-B cipher, A equals

ADEROVIVA

The key is found; VIVA_ADERO and a trial of M in the blank space shows correct results. This checks with our theory that a ten letter key word was used and deciphering the message we have:

PARA EL ATAQUE CONTRA TORREON ORDENO QUE SUS TROPAS MARCHEN ESTE NOCHE X.

The reason for breaking camp is now evident.

This method may be used, with some labor, on short words like THE, AND, etc. Parts of the key will appear whenever an assumed word is found in the message and the whole key may be assembled if enough of the parts are available. Even if only part of the key may be so recovered, it will always lead to the ultimate solution of the cipher by trial of the partially recovered key on the message letter by letter.

As an example of recovery of a key by use of short common words, let us refer to the message of Case [7-a]. There are twenty-four groups of three letters each in this message and we will try them against THE, ARE and YOU, assuming that the Vigenere cipher is used.

123456789101112
IfOSBVOIGSWCYYZSZBVJXLDOSYUVDYJLSQAHSI
equalsTHETHETHETHETHETHETHETHETHETHETHETHE
orAREAREAREAREAREAREAREAREAREAREAREARE
orYOUYOUYOUYOUYOUYOUYOUYOUYOUYOUYOUYOU
then A equalsVLXCHENLSJRUGLVIOFEEZVLUBOZFCHZJWOLE
orOBXVXEGBSCHUZBVBEFXUZOBUUEZYSHSZWHBE
orQEHXAOIECEKEBEFDHPZXJQEEWHJAVRUCGJEO
131415161718192021222324
IfBJVSFXDQBAIIOHZIVXJBFESFJSCNLUCTWCSM
equalsTHETHETHETHETHETHETHETHETHETHETHETHE
orAREAREAREAREAREAREAREAREAREAREAREARE
orYOUYOUYOUYOUYOUYOUYOUYOUYOUYOUYOUYOU
then A equalsICRZYTKJXHBEVAVPOTQUBLLBQLYUEQJMSJLI
orBSRSOTDZXAREOQVIETJKBEBBJBYNUQCCSCBI
orDVBURDFCHYUOQTFKHDLNLGELLEIPXAEFCEES

In column 5, we have, for YOU, the key BEF; column 6 gives the same key for ARE; column 10 gives the key FCH for THE and column 15 gives the same key for YOU; column 12 gives the key HBE for ARE and column 16 gives the same key for THE; column 23 gives the key EFC for YOU. The only possible key for the message is a five-letter one made up of the letters BEFCH or EFCHB or FCHBE or CHBEF or HBEFC. If the key in this case were a word, we would have no difficulty in determining it; as it is, there is no real difficulty in the matter as we may now divide the message into blocks of five letters and note that ZSZ (= YOU) form the 3d, 4th and 5th letters of a group. The corresponding key letters, BEF, are then the 3d, 4th and 5th letters of the key which must be CHBEF.

This special solution for Case 7 depends so largely on the intuition of the operator in choice of a word that it is not, in general, advisable to use it unless the message is very short and the regular methods of analysis have been tried unsuccessfully. It is, however, a wonderfully short cut in difficult cases where the other methods fail.

[1] The method used is not the most satisfactory one for several reasons and a better method is that of writing the message in multiples of the key and enciphering the columns as already described. [↑]