Case 1.—Geometrical ciphers. This case includes all ciphers in which a certain number of the characters are chosen so that they will form a square or rectangle of predetermined dimensions; and then these characters are arranged according to a geometrical design.

Taking the message:

A B C D E F G H I J K L M N O P Q R S T U V W X

of twenty-four letters and assuming a rectangle of six letters horizontally, and four letters vertically, we may have:

(a) Simple Horizontal:

(b) Simple Vertical:

(c) Alternate Horizontal:

(d) Alternate Vertical:

(e) Simple Diagonal:

(f) Alternate Diagonal:

(g) Spiral, clockwise:

(h) Spiral, counter clockwise:

It is simply a matter of inspection to read a message in a cipher of this type, once the dimensions of the rectangles have been determined. We place the whole or a portion of the message in such rectangles and read horizontally, vertically and diagonally forward and backward. Parts of words will at once be apparent and the whole message is soon deciphered. Two examples will show the process.

Message

ILVGIOIAEITSRNMANHMNG

This message contains eight vowels or 38% out of twenty-one letters, and the letters LNRST occur 7 times or 33%, the letters XQJKZ not appearing. It is therefore a transposition cipher. Twenty-one letters immediately suggest seven columns of three letters each or three columns of seven letters each. Trying the former we have:

and reading down each column in succession (Case 1-b) reveals the message to be “I am leaving this morning.”

Message

There are 120 letters in this message with 57 vowels or 47% vowels, and the letters LNRST occur 31 times or 26% of the whole.

Non-occurrence of K and W and vowel proportion leads us to the assumption that it is a transposition cipher of a Spanish text. The factors of 120 are 5 × 3 × 2 × 2 × 2. We may then have one rectangle of 4 × 30 or one of 5 × 24 or two of 5 × 12, or three of 5 × 8, or four of 5 × 6, or five of 3 × 8, or ten of 3 × 4, or twenty of 3 × 2. The message being in a rectangle of 4 × 30, we can inspect it as it stands and this is clearly not the arrangement if it be a geometrical transposition cipher at all. It is best however to try the largest possible rectangles first so we will put it in the form 5 × 24, thus:

Here an inspection shows this to be Case 1-f, alternate diagonal, and the text to be “ME SITUO SOBRE PARRAL PORQUE ME PRESENCIA FUE REVELADA POR U”; here the sense breaks but note that U is the twelfth letter of the line and continue as if the rectangle were 5 × 12 and we have “NA PAREJA QU.” Now inspect the second rectangle of 5 × 12 in the same way and the sense continues “E SE ME ACERCO Y HUBO QUE RECHAZAR POR EL FUEGO ALLI ESRERO ORDENES FINISX”.

The practical way of examining a cipher of this type is to have several men prepare rectangles of different dimensions, using the letters of the cipher in the order received. The rectangles can be inspected very rapidly when once prepared. Note that the dimensions of any rectangle will rarely be such as to contain more than fifty letters, on account of the necessity of filling up a rectangle with nulls if the number of letters of the message is just a little greater than a multiple of the rectangle. Also large rectangles give, for all but the diagonal method, whole words in a line or column and these are easily noted.

The following ciphers come under Case 1:

Case 1-i.—The rail fence cipher, useful as an operators’ cipher but permits of no variation and is therefore read almost as easily as straight text when the method is known. The message:

HOSTILE CAVALRY HAS RETIRED

is written:

and is sent:

OTLCV LYART RDHSI EAARH SEIEX

Case 1-j.

Message

To solve this cipher, read down the columns in this order 8, 1, 15, 2, 14, 3, 13, 4, 12, etc. A variation is to arrange the cipher so the columns are read upwards. Another is to arrange the ciphers so the columns are read alternately upward and downward. The factors of the number of letters in this case give the shape of the rectangle as usual.

It will be seen that there are a great number of possible transposition ciphers that come under Case 1 but practically all of them are useless from a military standpoint because they do not depend on a key which can be readily and frequently changed. However such ciphers constantly crop up in cipher examination, being used for special communication between parties who consider the regular military ciphers too complicated. Thus some of these expedients have been used.

Reversed Writing.—(Special case of Case 1-a).

LEAVING TONIGHT is enciphered THGINOT GNIVAEL or it may be reversed by words, thus GNIVAEL THGINOT or by groups of five letters, thus IVAEL NOTGN XTHGI.

Vertical Writing.—(Special case of Case 1-b). Same message is enciphered,

Case 2.—This case includes all transposition ciphers in which lines and columns of the text are rearranged according to some key word or key number. There are many varieties of this case but their solution usually is arrived at through the methods suggested for Case 1, that is, arrangement into appropriate rectangles and examination of lines and columns for words or syllables. Rearrangement of columns or lines follows until the solution is completed.

Case 2-a.

Message

There are 108 letters in this message and examination shows it to be a transposition cipher, English text. The number of letters, 108, immediately suggests a rectangle of 12 × 9 or 9 × 12 letters. Put into this form we have:

The vowel count of the lines shows the first arrangement to be the more likely. We will now number the columns and try pairing off certain ones which in no line would give impossible combinations of letters.

These combinations appear among others:

The word FIGHT stares at us from the first line; let us arrange the columns thus:

We have the words FIGHTI(NG), VICIN(ITY), RENEWE(D), ANDVIL(LA), RDINGT(O), RECE(IVED). With this to go on, we must choose column 11 as the next one and then in order, columns 8, 10, 7, 12, 9. But note that the order 11, 8, 10, 7, 12, 9, is the same as the order 5, 2, 4, 1, 6, 3. The message was written in twelve columns and the columns have been transposed in that order. We may, although it is entirely unnecessary, speculate on the key word used. It was probably

meaning that the 4th column of the plain text was transferred in enciphering so it became our 1st, the 2d column remained the 2d; the 6th column became our 3d, etc.

Actually, this cipher was solved because the word VILLA was suspected and all the necessary letters were found in line six of the arrangement in twelve columns. The order 1, 6, 3, 11, 8 was tried and gave this result.

The remainder of the solution followed the lines already laid down and, naturally, offered no difficulties, in view of the large number of connected syllables available.

Case 2-b.

Message

This is a transposition cipher, English text, and contains 105 letters. The factors of 105 are 5 × 3 × 7 so that we must investigate the following rectangles; 5 × 21, 15 × 7, three of 5 × 7, five of 3 × 7 and seven of 5 × 3.

This is also excellent, so we will try three blocks 5 × 7 and see if rearrangement of horizontal lines will give results reading the columns vertically.

Among other combinations are:

The addition of line 6 above line 3 and line 4 below line 7 will complete this cipher. The successive columns should be read downward.

Case 2-c. In this case, both lines and columns are rearranged by means of a key word or key words. The method of solution is the same as Case 2-a and 2-b except that the lines must be rearranged after the columns have been correctly arranged, or in some cases, vice versa. This cipher is not infrequently met with because it seems to offer safety by use of two key words and by the great but only apparent complexity of the method.

Message

This is a transposition cipher, English text and the number of letters, 70, leads us to try rectangles of 10 × 7 and 7 × 10.

The first form looks the more likely from the vowel count. We proceed to number the columns and lines and try rearrangement of columns so as to obtain possible letter combinations from every line.

Among other combinations we have these:

A very casual inspection of the lines shows that they should be rearranged in order 6, 1, 2, 7, 3, 5, 4, as follows:

Although of no particular importance, it may be stated that the column key in this case was GRAND and the line key was CENTRAL, both used as in enciphering Case 2-a.

Case 3. Route ciphers. In this case, whole words of the message are transposed according to some of the methods of Case 1 or 2 or their equivalents. The route cipher is little used at present. Its development and use during the Civil War was caused by the inability of the telegraphers of that day to handle regular cipher matter correctly and rapidly. It was, even in those days, frankly only a delaying cipher and, to be of any value, had to be filled with meaningless words to conceal the message proper. An example from the Signal Book will suffice to show the general character of route ciphers. To one familiar with monoliteral transposition ciphers, even the best of route ciphers offers but little difficulty.

“To encipher the message ‘MOVE DAYLIGHT. ENEMY APPROACHING FROM NORTH. PRISONERS SAY STRENGTH ONE HUNDRED THOUSAND. MEET HIM AS PLANNED.’ arrange as follows:

Here the route is down the first column, up the fourth, down the second and up the third.”

This cipher was often complicated by the introduction of nulls for every fifth word. Thus the above message might be sent:

The words in italics are nulls and not a part of the message and the receiver eliminates them before arranging his message in columns to get the sense of it.

As an additional complication, it was customary for each correspondent to have a dictionary or code in which the names of all prominent generals and places and many of the prominent verbs,—as to march, to sail, to encamp, to attack, to retreat,—were represented by other words.

A route cipher using the code words of the War Department code might have some advantages over the method of enciphering code messages as prescribed in that Code.

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.