General Methods — Multiple Anagramming, Etc.
In the past few chapters, we have been looking at all of the general
methods for decryptment of transpositions. We have seen the use of
_factoring_, which determines, for the geometric cipher, what
key-lengths are possible, and, for the irregular one, what
key-lengths are not. _Vowel-distribution_ has enabled us, in some
cases, to determine the length of major units, or has assisted in the
restoration of minor units to their original intact groups.
_Anagramming_ has been seen throughout: the matching of letters and
columns with or without the application of language statistics.
So far, we have been materially assisted by advance knowledge as to
what the cipher is. Where the type is unknown, and cannot be promptly
identified, and assuming, of course, that the decryptor has no
probable words, transpositions, taken as a whole, present confusing
problems in the very multiplicity of their possibilities. General
Givierge, in his _Cours de cryptographie_, remarks of this case that
novices, as a rule, display a tendency to recoil from the cryptogram
as if uncertain “which end to pick it up by.” He adds that the best
advice he can give is to pick it up _somewhere_ and do _something_,
rather than be satisfied to sit all day long and admire the
cryptogram!
As to how a type may sometimes be identified, the difference between
the regular and irregular types is ordinarily suggested by the number
of letters contained in the cryptograms. Irregular types, intended
for practical purposes, are nearly always seen in complete
five-letter groups, where the geometric cipher usually results in a
broken group at the end of its cryptogram. This, of course, is never
mandatory upon the encipherer; it merely happens because the only
persons making use of such ciphers are those who do not realize the
advisability of doing otherwise.
Among the irregular types, a columnar formation can usually be
spotted by the “bunching” of vowels at intervals throughout the
cryptogram. Then, too, we are still to see those cases in which the
exact type of the cipher may not become apparent until after solution
is well started.
It is usually well, when a new system is encountered, to analyze it
and find out what the transposition finally does to the letters. This
can be done by preparing actual cryptograms in which the plaintext
letters are serially numbered; or, if the question of
vowel-distribution is not involved, by using the serial numbers
without the letters, as suggested in a previous chapter. Many
ciphers, of course, will not require even this amount of analysis,
even though their type, accurately speaking, is irregular. For
example, the one shown as Fig. 48, whether or not its rectangle is to
be completed, is merely another _route_, so that once having seen it,
we might try to follow this route again. But the student who cares to
give this cipher his careful consideration must notice that its
longer cryptograms would be full of reversed plaintext segments; that
these would grow longer and longer with a constant rate of increase,
and would always alternate with incoherent segments which, in their
turn, would grow shorter and shorter; also that these incoherent
segments, if set up as columns, would show plaintext.
The complete-unit cipher, generally speaking, can hardly present any
real complexities. Consider, for instance, the following variation on
a Nihilist encipherment, which was proposed by Geo. C. Lamb, the
author of Chapter X: The key-length, to begin with, must be divisible
by 3, but this is not used for writing-in. The plaintext is written
into its block, not in straight order, but following a _route_ which
begins in the upper left corner and goes forward for the first three
letters, drops down to the second line and runs backward for the next
three letters, drops to the third line to run forward for another
three, and so on back and forth until the first three columns have
been filled with trigrams written alternately forward and backward.
It then moves over to the second three columns, beginning this time
at the bottom and “snaking” upward to the top. For the third three
columns it moves downward again, and so on until the square block has
been filled. After this very devious primary transposition, the unit
is taken off by means of the key, on the Nihilist principle of
transposing both columns and rows with the same key.
Figure 48
Cipher Requiring Little Analysis
1 2 3 4 5...
T│ H│ W│ S│ E│
──┘ │ │ │ │
S I│ O│ E│ .│
─────┘ │ │ │
D L U│ E│ .│
────────┘ │ │
B O T M│ .│
───────────┘ │
← . . .│
──────────────┘
Plaintext: THIS WOULD SEEM TO BE...
Cryptogram: T H W S E S I O E....
We believe that the resulting cryptogram could prove puzzling to any
cryptanalyst who has met the cipher for the first time. It is true
that he has, in the original square, a large number of intact minor
units, provided he can restore them. But these units are very tiny,
and the several of them which stand on any one row are not continuous
among themselves; thus his vowel-distribution, while approximately
normal, would probably not satisfy his expectations. If, however,
having failed to find a more satisfactory block arrangement, he
attempts to match columns (it being remembered that he is accustomed
to reading in all sorts of directions in order to discover plaintext
fragments), he will most certainly discover the trigrams and trace
their route. Afterward, however, having met and analyzed the cipher,
it would probably occur to him to look for exactly this complexity
whenever he discovers that he is dealing with a square whose
key-length is divisible by 3. We have mentioned before the assistance
which may be had from the mere knowledge that a certain method exists.
Complete-unit ciphers, of course, may be troublesome, but their
complexities are necessarily confined to one small area. An irregular
cipher, on the other hand, usually involves the entire text, and its
complexities may be real. In this class we occasionally find ciphers
in which a single cryptogram is impossible to break; and we find
others in which the eventual solution of one cryptogram will not
instantaneously provide the key to another enciphered exactly like
it. Such ciphers are well worth analyzing, for surely, somewhere,
they have their weaknesses; and most certainly any two cryptograms
enciphered exactly alike should be decipherable with the same key.
The cipher shown in Fig. 49 is of the double-columnar type known in
this country as the “United States Army” double transposition, and
has, in fact, been authorized for use, under suitable conditions, in
the military service of more than one country. As may be seen from
the figure, this cipher is, in all respects, the columnar
transposition of the preceding chapter accomplished twice in
succession on the same text (decipherment being, as usual, the
reversal of the encipherment process). The same rules apply here, as
in the single columnar transposition, to the use of nulls, and to the
advisability of avoiding the key-length which is a multiple of 5. It
goes without saying that the block should never, under any
circumstances, be allowed to work out as a square; this, in substance,
would be the block unit of the Nihilist cipher. While the figure
shows a primary cryptogram, taken off from the upper block, this, in
practice, is never actually done. The columns of the upper block are
always transferred direct to the rows of the lower one, and only the
columns of the lower block are taken off as an actual cryptogram. In
preparing this cryptogram, both blocks should be laid out at the same
time; otherwise, there is danger that the operator may apply the first
transposition and forget the second, thus sending out a simple
columnar transposition which carries the key to all of his other
cryptograms. This cipher, as may be seen, has its points. Yet it will
have been noticed that its use for military purposes was not
authorized without restrictions.
Figure 49
The "United States Army" Double Transposition
1st Encipherment
P A R A D I S E
6 1 7 2 3 5 8 4
R E G R E T C H Primary Cryptogram
A N G E I N S Y
S T E M S X X X (Not usually
X taken off)
2d Encipherment ENT, REM, EIS, HYX,
TNX, RASX, GGE, CSX.
P A R A D I S E
6 1 7 2 3 5 8 4
E N T R E M E I
S H Y X T N X R
A S X G G E C S Final Cryptogram:
X
N H S R X, G E T G I, R S M N E, E S A X T, Y X E X C.
The special hazards of military correspondence have already been
mentioned: the huge volume of interceptable cryptograms; the
ever-present knowledge as to probable subject-matter and
more-than-probable words, including numbers and dates; the personal
habits of individual operators; above all, the fact that much of the
enciphering is necessarily done by operators who are not, in the
first place, trained for their work, and who, very often, must
perform this work rapidly under conditions which are far from
conducive to clear thinking. These, however, are chiefly the hazards
of the firing line. Back of the lines, where hazards are reduced,
there may be a chance that a cryptogram will not be intercepted at
all. It becomes possible, for many purposes, to make use of a cipher
in which a single cryptogram, though probably read in the end, will
resist the decryptor for the necessary length of time, several hours
or several days. The double columnar transposition can be very
resistant, especially when the key is long and the columns short, and
can be made even more complicated by carrying it through still a
third block, perhaps using a different key with each new block.
Why, then, would it not be possible to use such a cipher for general
communication? To this, there are two answers. For transposition
cipher, taken as a whole, has two very serious drawbacks.
First, a transposition, in order to be a good one, must be a
transposition of the whole text, and not a series of short individual
transpositions. Thus, it becomes possible that an error, either in
the encipherment or in the transmission, will not be confined to one
small area, but will garble the whole message. In this way, we have
not only the delay during which the legitimate decipherer is
attempting to decrypt his own message, but, should he fail, the
danger which lies in having it repeated. The decryptor who has been
provided with both the correct and the incorrect version of a same
cryptogram, is often able to figure out both the system and the key.
The other drawback is the danger which lies in the fact of so very
many cryptograms. These, originating at many different sources, and
all enciphered with the same key, will invariably include many of
_identically the same length_. The nature of transposition cipher
makes it inevitable that when any two texts of exactly the same
length are enciphered with the same key, they will follow exactly the
same route. The first letter in both messages will be transferred to
exactly the same serial position in both cryptograms; the second
letter in both will be transferred to another same serial position,
and so on. If we are able to match correctly any two or three letters
in one of the cryptograms, the two or three corresponding letters of
the other cryptogram will also be correctly matched and will serve as
a check. This being the case, any two or more cryptograms which are
found to have the same length can be written one below another so as
to place corresponding letters in the form of columns, and the
problem is reduced to one of _geometric_ columnar transposition.
With ciphers of the complete-unit type, the same thing can be done
having several of the major units. We have, say, a single cryptogram
accomplished with a Fleissner grille, and taken off by spirals. It
may be that nulls were added in the final group, or at the beginning,
or the final unit may have been left incomplete (by blanking out the
unwanted portion of the final grille-block). In spite of these
possibilities, the unit-length, known to be a square based on an even
number, can be determined — _or assumed_ — and the placing of the
several units one below another provides columns made up of
corresponding letters. It is even possible, at times, to apply this
process, with suitable modifications, to several cryptograms whose
length is only approximately the same. It has been done, for instance,
with cryptograms from Sacco’s indefinite grille, mentioned in Chapter
III (General Sacco himself has explained the modifications). Such a
process is ordinarily referred to as multiple _anagramming_, and we
have already seen, in the case of the grille, how it may be modified
so as to take full advantage of any inherent weaknesses when the
cipher is known.
For discussion of the general case, suppose that we have intercepted
a number of cryptograms (seen, by their letter-frequencies, to be
transpositions), and that among these we have been able to find five
in which the length is 25 letters. Since all of these have been
coming from the same two stations, and within a comparatively short
period of time, it seems reasonable to suppose that at least a portion
of them have been enciphered with the same key, and, upon this
assumption, we have written the five cryptograms one below another so
as to set up the 25 columns shown in Fig. 50. We wish now to
rearrange the 25 columns in such a way as to bring out plaintext on
every row, or, failing that, on some of the rows. Once the set-up has
been prepared, we may arrive at our goal by any road that suits our
fancy. The majority of solvers will simply cut the columns apart and
start matching strips at random; and this, probably, is a good enough
method, especially when columns are so short. The writer, personally,
prefers to leave the set-up intact, at any rate until solution is
well started, trying out in pencil the various possible
column-combinations, and circling out accepted columns from the
set-up in the same way in which segments were circled out of
cryptograms in the preceding chapter.
Figure 50
A series of five cryptograms prepared as columns:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
C D D N C A A R T H L O I K A O E R T L S N A N O
D A I T E L O C W A I U X D N T Y M I N M O E Y O
B T O A T T U T O C F L I Y K X N E I O S B F Y Y
T A R O T O R E I L N A O H R I O N M D S R J Y S
W E K L N C H T S T S I E G E I H O O P D T N A O
For those who like this method, we repeat a suggestion which has
already been made: Many columns are usually present in such a set-up
which contain _more than one_ of the “clue-letters,” as here, for
instance, column 14 is practically made up of them. Such a column
makes a good point of beginning, since we may search the set-up, not
for some single letter, but for a pattern made up of several. For
column 14, specifically, we might examine the top row of letters,
pausing whenever we come to one of those letters frequently preceding
_K_, and examining the rest of its column to find out what letter
would have to precede _H_ on the fourth row. We may fail with the
first such column, but not with all.
Another particularly good method, and one which might work in the
present case in spite of the very brief columns, is that of finding
the particular column which contains the first letters of all the
messages. Well over half of the initials used in the language will be
found in the group _T A O S W C I H B D_, and with a frequency in
somewhat that order. Any column made up entirely of these particular
letters may be the one which begins the messages; and when this can
be found, it pays to remember that a vowel is practically always
present among the first three letters of each message.
As to finding the end-segment, it seems that this would be of little
value except in those cases where final groups are not completed.
However, the letter _E_ has a great fondness for final positions,
with terminals restricted largely to the group _E S T D N R Y O_; and
it is also true that many encipherers make a habit of completing their
final groups with such letters as _X_ and _Q_.
Aside from the general case, each individual case carries clues of its
own, and the finding of these must depend upon the detective ability
(or experience) of the decryptor. Here, for instance, we find that the
letter _K_ has appeared three times in only 125 letters of text. This
letter, normally, has one of the lowest frequencies in the language,
and often is not found at all in 125 letters of text. Finding it
three times, then, rather suggests the presence of some one word, a
word so important to the subject-matter that it has been used in
three different messages.
When considering the letter _K_, the first combination which comes to
mind is a digram _CK_ preceded by a vowel; and the letter _C_, also,
is not a letter which we expect to find in confusing numbers. When an
examination of the set-up shows that, for each of the _K_’s, there is
a _C_ present on the same row, we are inclined to accept the
hypothesis of a repeated word. In practice, we should pick out the
three columns containing _K_, place beside each one a column which
will set the digram _CK_ together, and _build on all three
combinations simultaneously_ to the point at which the supposed word
appears or is proved non-existent. Following out only one of these,
let us consider column 14, where _K_ is on the top row. On this row
we find that _C_ has appeared twice. Both of the _C_’s are tried with
_K_, as shown in Fig. 51; we find that both combinations will provide
acceptable digrams, but there is little doubt as to which we would
select. Combination 1-14 is merely acceptable, while combination 5-14
provides a very accurate description of the column which would fit
best on its left. There should be a vowel on the top row, to precede
_CK_, and another on the bottom row, to precede _NG_. After that,
perhaps another vowel should be found on the fourth row, to precede
_TH_, or perhaps, in this case, an _S_, since the list of frequent
trigrams includes a sequence _STH_; and, finally, something suitable
to precede _TY_, which appears to be a syllable, but may belong to
two different words. The five columns which will meet these
requirements have been added in Fig. 52. In this figure, two
combinations may be discarded, because of trigrams _KTY_ and _YTY_.
The others appear acceptable. At this point, however, the sequence
_XTY_ of combination 16-5-14 begins to draw attention because of its
very few possibilities (SIXTY, NEXT YEAR, etc.), making it likely
that one of these will quickly select or discard the entire
combination. For building SIXTY, row 3 of the set-up contains two
_I_’s and one _S_. The two _I_’s, columns 13 and 19, when inspected
visually, are found to bring out, on the top row, the two sequences
_I O C K_ and _T O C K_, while the _S_, column 21, brings out, on the
top row, another _S_, which would extend these, respectively, to read
_S I O C K_ and _S T O C K_, the latter surely the more acceptable.
The results of these additions, with subsequent development, can be
examined in Fig. 53. The completion of the word SIXTY has brought out
also: STOCK, _MITED_, SMITH, DOING. The presence of the word STOCK
suggests extending the sequence _MITED_ to read LIMITED, and the
addition of two more columns on the left brings out another CK,
suggesting another appearance of the word STOCK. The chances are that
we have already been building on this other word STOCK, but if not,
we may build it now to the point shown in the figure, where the top
row suggests RAILROAD STOCK, the third row, FIFTY TO SIXTY, and the
second may or may not suggest MEXICO. Thus we are well on our way to
solution, and have not once had recourse to a long prepared list of
probable words: _division_, _regiment_, _battalion_, _attack_,
_advance_, _report_, _forward_, _artillery_, _ammunition_,
_communication_, _enemy_, _signal_, _retreat_, _troops_, and so on.
Figure 51
1-14 5-14
C K C K
D D E D
B Y T Y
T H T H
W G N G
Figure 52
12-5-14 13-5-14 15-5-14 16-5-14 25-5-14
O C K I C K A C K O C K O C K
U E D X E D N E D T E D O E D
L T Y I T Y K T Y X T Y Y T Y
A T H O T H R T H I T H S T H
I N G E N G E N G I N G O N G
Figure 53
11 8 25 6 3 21 19 16 5 14
L R O A D S T O C K
I C O L I M I T E D
F T Y T O S I X T Y
N E S O R S M I T H
S T O C K D O I N G
Naturally, there are times when the matching of the columns, for one
reason or another, proves troublesome. We are thrown off by errors,
by the presence of nulls, initials, abbreviations, etc., or by the
encipherer’s use of cover-up devices, such as the writing of _YH_
instead of _TH_. Or we find that the handling of many paper strips,
caused by message length, is awkward and confusing. But if, in the
eyes of the decryptor, there is any good reason for finding out the
contents of such messages, he can always succeed, even with only two
letters per column.
So far, nothing has been said about helping ourselves to the serial
numbers of the columns, which, during the rearrangement of letters,
are automatically forming in a certain sequence across the top of the
set-up. Regardless of the cipher, it can do no harm to examine these,
and find out what information, if any, they are able to give. In some
cases, they will provide us with both the system and its key,
enabling us to throw away the strips and start deciphering. Suppose,
for instance, we have correctly matched sixteen columns, and find
their numbers in the following order:
31-10-24-37-17-3-32-11-25-38-18-4-33-12-26-39. A careful examination
shows that the numbers are running in sets of six. After the first
six are passed, the next six have repeated them with an increase of
1, and another six appear to be forming up which will repeat them
with an increase of 2. We may verify this by finding the columns
which have numbers 19-5-34-13, etc., and, if the set-up continues to
show plaintext, we know that we are dealing with a simple columnar
transposition. Notice that if the above series were marked into
segments of six numbers each, and the segments placed one below
another, we should have _six columns_, each one made up of numbers
which are consecutive. Thus, we may sometimes learn from a series of
numbers: (1) the system, which is straight columnar transposition;
(2) the key-length, which is 6; and (3) the key itself, which, taking
the six numbers according to size, is 5-2-4-6-3-1, possibly with the
wrong numbers coming first, though it happens that in this case they
do not. This is our old friend SCOTIA, used on forty numbers, in case
the student cares to verify it.
The trail of the columns is not so plain where a second transposition
has done something to the first. But it is still present; the most
complex of ciphers has method of some kind, provided we can find it.
Consider, for instance, the series of numbers,
11-8-25-6-3-21-19-16-5-14, which has been forming in Fig. 53.
Examination here shows pairs of consecutive numbers, 11-8, 6-3, and
19-16, all having the same numerical difference of 3; that is, the
plan of our present encipherment, whatever it is, has, on three
separate occasions, caused some plaintext digram to appear in the
cryptogram reversed, and with its letters three positions apart.
Irrespective of the type of transposition, this constant numerical
difference of 3 might be found again; perhaps we can set some two
columns together correctly simply by _reproducing this numerical
difference_ in the two column-numbers. A glance ahead at the next
figure will show that we actually could, by setting together columns
12-9 or columns 20-17. Where we cannot discover a repeated numerical
difference, perhaps we can discover a progressing difference, or some
other signs of regularity.
Now, returning to the particular case, let us pass on to Fig. 54, in
which the matching of the 25 columns has finally been completed, and
make a careful comparison between the two numerical series 12-9-10-15
and 20-17-18-23. What can these represent but the _fragments of four
columns_, belonging to a _first encipherment block_, which have been
laid down along the _rows_ of a _second encipherment block_, and taken
out in slices? And since the lineal distance apart of any pair of
numbers, as 12 and 20, is seen from the figure to be six positions,
it would be possible, by writing the series of numbers in lines of
six numbers each, to place each pair of corresponding numbers in a
same column. The trail, usually, is not so wide, but there is little
doubt here that we have been dealing with a case of double columnar
transposition in which the key-length of the original block was 6. We
shall come back to this in a moment.
Suppose, now, we give our attention to the various series of numbers
which appear in Fig. 54, and make sure that we understand what they
are. The numbers running across the tops of the columns were,
originally, the _serial numbers of cryptogram letters_ (or columns).
When we restored these letters to their plaintext order, we
disarranged their serial numbers, causing these to come out in the
order 1-7-24-22-12-9, etc. This series, then, is made up of
_cryptogram serial numbers_. But it is also a _key_, since it shows
us exactly the order in which we might _take off a plaintext_ in
order to form a cryptogram. It is a key of the Myszkowsky type,
according to which every letter in the text has its individual
key-number, as we saw in Fig. 46 (imagine that encipherment
accomplished twice in succession). We do not desire, however, to take
off plaintext. And, to use this same key on a cryptogram, we should
have to use it in the _writing-in_ manner; that is, first lay out the
series of key-numbers, and then, taking the cryptogram letters in
their 1-2-3 order, place them, one by one, below their key-numbers.
But once the plaintext has been restored, the _plaintext letters_
(or columns) _may also have serial numbers_, and these new serial
numbers, in the figure, have been added at the bottoms of the
columns. Should we now restore these columns to the order in which we
found them, that is, to their cryptogram order, each column taking
with it its new serial number, we should find, running across the
bottom of the set-up, another mixed series of numbers in the order
1-10-20-9-24, etc., which is a different order from that of the
cryptogram numbers, and this new series is made up of _plaintext
serial numbers_. This is the other key, having the same relationship
to the first as that explained in connection with the short Nihilist
key. Applied to the plaintext, it would have to be used in the
_writing-in_ manner; used on the cryptogram, it serves for
_taking-off_. Thus we are able to recover from our reconstructed
plaintext two long keys, either one of which will serve to decipher
additional cryptograms, _but only on condition that these new
cryptograms contain exactly 25 letters_.
Figure 54
The Columns of Figure 50, After Solution by Multiple Anagramming:
1 7 24 22 12 9 10 15 4 2 20 17 18 23 13 11 8 25 6 3 21 19 16 5 14
C A N N O T H A N D L E R A I L R O A D S T O C K
D O Y O U W A N T A N Y M E X I C O L I M I T E D
B U Y B L O C K A T O N E F I F T Y T O S I X T Y
T R Y R A I L R O A D O N J O N E S O R S M I T H
W H A T I S T E L E P H O N E S T O C K D O I N G
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
(Plaintext serial numbers, added at bottoms of columns)
(Appearance of the plaintext serial numbers, if the above columns should
be restored to their cryptogram order)
1 10 20 9 24 19 2 17 6 7 16 5 15 25 8 23 12 13 22 11 21 4 14 3 18
If, then, we hope to decipher cryptograms of other lengths, which
originally were enciphered with exactly the same key as our present
five, it is still necessary that we take one or the other of these
long Myszkowsky-type keys and reduce it to the short columnar form.
The theory on which this is done should not be at all difficult to
understand if it be kept in mind that both of our long keys are
actually the serial numbers of letters, and that each individual
serial number accompanied its letter throughout the encipherment
process. This will explain any references which are made to FIRST and
SECOND encipherment blocks, with their respective columns and rows.
Whichever of the long keys we decide to reduce, our first objective,
always, is that of determining the _length_ of the shorter key; after
that we restore its _order_.
The first process, summed up in Fig. 55, was originally published,
so far as the writer knows, by M. E. Ohaver, and makes use of the
cryptogram numbers which were the first series obtained. The
discovery of the shorter key-length is made by searching the set-up
for some numerical difference (between any two numbers whatever)
which is repeated by corresponding pairs of numbers at some regular
interval. For convenience in making the search, Ohaver suggests that
the mixed cryptogram numbers be written, with uniform spacing, on two
strips of paper, in one case repeated. One strip can then be moved
along beside the other so as to place pairs of numbers in actual
contact. It is immaterial what numerical difference is used; the
difference 1 pointed out in the figure seemed a little more visible
than others. This difference 1 has been noted between the numbers 9
and 10, and the next difference 1 has been found _six positions away_
between the numbers 17 and 18, but is not found again between the
numbers 25 and 6, which stand at the next interval of six positions.
This may be a clue, but it is not what we had hoped to find. The clue
is strengthened, however, by the observation that a difference of 5
occurs just at the right of the original difference 1, and is also
repeated at the lineal interval 6.
Figure 55
Finding the Original Short Key from the CRYPTOGRAM Serial Numbers - M.E.OHAVER
Finding the key-length:
1 7 24 22 12 9 10 15 4 2 20 17 18 23 13 11 8 25 6 3 21 19 16 5 14.
1 7 24 22 12 9 10 15 4 2 20 17 18 23 13 11 8 25 6 3 21 19 16 5 14 1 7
x . . . . . x (Repeat series)
A difference of 1 occurs again at the interval 6. The two
series 9-17 and 10-18 are fragments of columns from the first
encipherment block. The key-length necessary for placing
either pair in a same column is 6.
Replacing cryptogram numbers in first encipherment block:
(As PLAINTEXT)... 1 7 24 22 12 9
10 15 4 2 20 17
18 23 13 11 8 25
6 3 21 19 16 5
14
COLUMNS of the FIRST encipherment block are converted to ROWS of the SECOND:
(a) (b) (c)
1 10 18 6 14 1 10 18 6 14 22 1 - 3 - 5 - 2 - 4 - 6
22 2 11 19/ 7 15 23 3 2 11 19 7 15 23
12 20 8 16 3 12 20 8 16 24 1 10 6
24 4 13 21/ 9 17 25 5 4 13 21 9 17 25 2 . 7
5 3 8
4 9
5
At (a) the columns of the first block are (C O S M O S)
arranged so as to make the cryptogram numbers At (c) the order is
run consecutively in each of the new columns. shown in which the columns
At (b) this block has been adjusted, so as of (b) would be taken off.
to form six columns. This order is the KEY.
To find a good clear example, using the strips as they stand, let us
go back toward the left, and look for a difference 2. We find it
first between the numbers 24 and 22; exactly six positions away, we
find it again between the numbers 4 and 2; another six positions, and
we find it between the numbers 13 and 11; still another six positions,
and we find it for the fourth time between the numbers 21 and 19. Thus
we have two series of numbers, 24-4-13-21 and 22-2-11-19, which run
parallel to each other with their numbers always separated by
interval 6. Sequences of this kind came from the _columns of a first
encipherment block_, and can all be placed back in these columns by
re-writing the mixed cryptogram numbers in lines of _six numbers
each_. Sometimes we find such columns broken to bits, as would be the
case should we continue moving the strip until we have completely
exhausted the possibilities for difference 1; and we never find them
complete, since these columns of the first encipherment block were
taken out in irregular order and written continuously upon the rows
of a _second encipherment block_, and after that were sliced through
in the taking out of columns from the second block. We found traces
of them once before, where a difference of 8 was found throughout
four consecutive pairs of numbers 12-20, 9-17, 10-18, 15-23, always
at an interval of 6 positions.
The key-length, then, is 6, and the cryptogram numbers (in their
plaintext order) if written into a block of that width, will
reproduce the first encipherment block. From this, we wish to carry
the numbers, column by column, into their second encipherment block,
from which they may then be taken out, again by columns, in such a
way as to bring them back to their cryptogram order 1-2-3. If this
is to happen, the numbers must run consecutively in the new columns,
and the number 1 must be on the top line. We select, then, from the
restored plaintext block, the column which contains the number 1,
then the column containing the number 2, and so on, writing these
columns horizontally on the rows of the new block, in such an order
as to make the numbers consecutive in every column. This may or may
not require the adjustments indicated in the figure at (a) and (b).
When block (b) is completely adjusted, the order in which it would be
necessary to take its columns so as to produce the cryptogram numbers
in their original 1-2-3 sequence, is the order of the original short
key. Our key-word COSMOS, incidentally, could have been better chosen.
In Ohaver’s process, we have taken the _cryptogram numbers_ and
_enciphered_ them. By the process of General Givierge, summed up in
Fig. 56, we do the opposite: we take the _plaintext numbers_, in
their cryptogram order, and _decipher_ them, so as to bring them back
to their correct plaintext order 1-2-3. For learning the key-length,
General Givierge endeavors to find that number which, when added or
subtracted throughout the series of numbers, will most often cause
one of its segments to repeat another. The portions which repeat are
the columns, or partial columns, not from a first encipherment block,
but from a _second_, since the process here is to follow out a
decipherment. In the figure, the left-hand block (not strictly
necessary) represents the plaintext, written as a cryptogram, and the
one on the right represents it in what is known to have been its
first encipherment block. To develop the second block: either take
columns from the right-hand block and lay them on the rows of the
central one in such an order that its columns can be taken out to
form the cryptogram; or, write the cryptogram arrangement into the
columns of the central block in such an order that its _rows_ will
show the columns of the plaintext block on the right. The order in
which columns must be taken from the right-hand block to form the
central one (or that in which columns must be taken from the central
block to reproduce the cryptogram arrangement) is the order of the
original short key. The condensed presentation here is also drawn
from the writings of M. E. Ohaver. General Givierge, who seems first
to have published the method, was chiefly concerned with exposing the
possibilities of _analysis_, as applied to numbers generally, and
explains to us the reason of the increase 6 which betrays the
key-length in the plaintext series of numbers. The width of the
original block being 6, each number is larger by 6 than the one just
above it, making every one of the columns an arithmetical progression
in which the constant difference is 6. These columns, still retaining
their regular increase of 6, are laid down on the rows of a second
block, and, for at least a portion of their length, some two or more
of them always continue parallel, with progressions of 6 running side
by side. Thus the taking out of columns from the second block will,
at times, select _one each_ from two or more different progressions
of 6, and the new columns, throughout some portion of their length,
will differ from one another by exactly 6, the original key-length.
Figure 56
Finding the Original Short Key from the PLAINTEXT Serial tumbers - GIVIERGE
To find the key-length: Try adding (or subtracting) possible
key-lengths (4, 5, 6, 7, etc.) to the whole series until some one
of these added numbers causes portions of the series to repeat.
1 10 20 9 24 19 2 17 6 7 16 5 15 25 8 23 12 13 22 11 21 4 14 3 18
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
7 16 26 15 30 25 8 23 12 13 22 11 21 31 14 29 18 19 28 17 27 10 20 9 24
The portions which repeat when the correct key-length, 6, is added,
are columns, or part-columns, from the SECOND encipherment block.
Plaintext Serial Numbers S E C O N D F I R S T
In CRYPTOGRAM Order: Encipherment Block Enoipherment Block
/ 1 10 20 9 1 7 13 19 25 4 1 2 3 4 5 6
24/19 2 17 10 16 22 2 8 14 7 8 9 10 11 12
6/ 7 16 5 20 5 11 17 23 3 13 14 15 16 17 18
15/25 8 23 9 15 21 6 12 18 19 20 21 22 23 24
12/13 22 11 24 25
21/ 4 14 3 18
The ROWS of the CRYPTOGRAM BLOCK, (approximately of column-length), must be
written back into the COLUMNS of the SECOND ENCIPHERMENT BLOCK in such an
order that the ROWS of this SECOND encipherment block could have been taken
off as a primary cryptogram from the COLUMNS of the FIRST ENCIPHERMENT BLOCK,
extreme right, known to be the original order of the numbers.
The original short KEY can then be found by observing (in the central block)
the order in which columns have been taken from the right-hand block. That
is, find the small numbers which were on the top row; these are standing in
the order 1, 4, 2, 5, 3, 6 (a writing-in key), and the columns which are
headed by these receive key-numbers in the order 1-3-5-2-4-6.
* * *
We have seen, then, the general case in which the “enemy” decryptor,
having several cryptograms of the same length, enciphered with the
same key, is able to use a purely mechanical method in order to
restore the plaintext, and afterward, by observing traces of a known
cipher, to extract their key. For the solution of single cryptograms
enciphered in complicated systems, the writer knows of no other method
than straight anagramming, in which the single letters, accompanied
by their serial numbers, are written on individual cardboard squares
(or imagined to be so), and the attempt made to match them up.
Attention has already been called to some possibilities which may lie
in the serial numbers whenever the sequences or probable words are
thought to be correctly matched. But with absolutely nothing known or
suspected as to source or subject matter, and with nothing
discoverable from serial numbers or possible routes (and taking it
for granted that any accumulation of letters represented in about the
normal frequency-proportions can be made to yield dozens of different
solutions), it would hardly seem that the decryptor, even should he
find the correct solution, would have a means of distinguishing it
from any other.
Figure 57
A Single Cryptogram in Double Columnar Transposition:
L H D L A O D D H L H E E U I X D F P I U T A E R O I T Q A E T E R L
N I E N A U D K L I E E H Y N M S J L C N H P B O A D G R N.
The Solution, Enciphered by a Method Mentioned in Chapter III:
M T Q P I N A I E N E I T H R G E K D U U D L L I R I H F R T E C L O L N J
L A S H A A U Y D O E E L N E N D H P D H D E A B O.
For the student who may care to struggle with a case of single
anagramming, we have appended a problem in Fig. 57, together with a
means for finding out the solution and perhaps even the key-word. It
has come from the Philadelphia headquarters of a band of
revolutionists, and our stool-pigeon tells us that the leaders of
this movement are to be called together for consultation during the
coming summer.
* * *
The finding of a _key-word_, after recovery of the numerical key, is
not, of course, necessary to the decipherment of further cryptograms.
However, this recovery will afford us the same convenience which it
gave to the encipherer; that is, a simple mnemonic device for
reproducing the numbers at will. And to recover the actual original
key-word may, at times, provide some insight into the habits or
mental make-up of the person who selected it, and who may select
others like it, or might, conceivably, make use of this same key-word
in some other kind of encipherment. If the key is short, it is
practically always possible to recover more than one word; but with
long keys, we seldom, if ever, recover more than the one word on
which the numbers were actually based. In this connection, however,
it must be remembered that key-words are not necessarily taken from
any one language; thus, their recovery becomes largely a matter of
combined information, intuition, guesses, trials, and determination,
so that an exact method for accomplishing it is hard to give. But,
presuming that key-numbers have been derived in the usual way, those
which are small are, in general, likely to have derived from the
earlier portion of the alphabet, which contains _A_, _E_, _I_. So
long as they increase toward the right, they may continue to represent
a same letter, and when they do, this letter is usually a vowel, When
an increase occurs on the left, the new number has certainly derived
from a new letter, coming later in the alphabet. Whatever the
language, then, it is very easy to determine the two extreme
alphabetical limits outside of which no one of the letters can
possibly be found.
This can be seen at (a) of Fig. 58. The numbers 1, 2, 3, might all
have derived from _A_, but the number 4 cannot have derived from a
letter coming earlier in the alphabet than _B_. Similarly, the
numbers 4, 5, might, by possibility alone, have derived from _B_; the
numbers 6, 7, 8, might all have derived from _C_, the numbers 9, 10,
from _D_, and, finally, the number 11, from no letter earlier than
_E_. When these earliest possible limits have been established for
every key-number, and it is seen that the range is five letters, then
the last five letters of the alphabet, _V_, _W_, _X_, _Y_, _Z_, may
be used to establish the limits at the other end of the alphabet. It
is seen now, that the key-number 6, must have derived from some
letter between _C_ and _X_, inclusive, and similarly with the others.
But when we come to the particular case, it becomes necessary to make
assumptions; for instance, were these numbers derived from a common
English word or from a Russian proper name? The person who selected
it, so far as we know, is accustomed to speaking English, and in all
of his past cryptograms we have been able to recover common English
words rather than proper names. Assuming, then, as at (b) of the same
figure, that we are to recover his usual common English word, we set
down _A_ as a possible letter for the key-numbers 1 and 2. But when
we arrive at the number 3, we see that we cannot assign here a third
_A_, since common English words of this length do not contain a
doubled _A_. The earliest letter possible, then, is _B_, and, upon
noting the consecutive letters _AB_ at this particular point, we
think at once of the common English terminal sequence -_ABLE_.
Figure 58
(a) Limits: (b) Assumption of English word:
6 9 1 4 11 7 10 2 3 8 5 6 9 1 4 11 7 10 2 3 8 5
C D A B E C D A A C B A A B L E
X Y V W Z X Y V V X W (FL (MY A C (NZ (FL (MY A B L E
D
E (New limits)
To find whether this is possible, we make sure that the new letters,
_L E_, alphabetically considered, do not run contrary to their
supposed numbers, 8 5. Then, having accepted these four letters as
entirely possible and likely, we work back to the missing number, 4,
and find, now, that it has new limits; it must have derived from _E_,
_D_, or _C_, and from nothing else, and of these, we are inclined to
discard _E_, which would give a sequence _AE_. We then work back to
other missing numbers, 6 and 7, and find that these, too, have
acquired new limits; they must be found somewhere between _F_ and
_L_, inclusive. All numbers which follow 8 have attained a new limit
in the earlier portion of the alphabet, but not in the latter portion.
These are all shown in (b). At this point, any knowledge at all of
English prefixes will suggest what the first two letters are and will
narrow the limits still further. The student, perhaps, has already
guessed the word.
Of the keys which follow, (a) and (b) were derived from English words,
one of which has been used in the present chapter. The remaining four
are derived from proper names, respectively (c) German, (d) Italian,
(e) Spanish, and (f) French.
(a) 1-9-2-4-11-3-7-8-6-10-5. (b) 2-7-8-3-4-1-6-5-9-10.
(c) 2-5-11-3-9-13-6-12-8-1-4-7-10. (d) 9-1-10-6-5-2-8-7-4-3.
(e) 2-11-3-6-7-9-1-5-8-4-10. (f) 5-1-4-6-2-3-9-8-7.
36. By TITOGI.
(a) U O Y M E E T E N A W H T I M C I C T I J I U S O G N H Y F.
(b) Y T M I L L E M L E W U A A J T W O N F O R T A H L H T G I.
(c) R O P U L E A E E B A H F T K O D T S C I L T T M R Y T I H.
(d) U M H T S E U O K S I H W T R A N C I O W A O H T Y O S S Y.
(e) E C E R L T A D A R M R E A O G P O Y M E E A A T N I B S A.
(f) R E U O T K N A E H E H H L Y W D E L E E E E O M N W S L L.
(g) I H L P U H T T G I Y T T A S N E R T E O R Y T A H N J D S.
(h) E S E F K A C A P E E O L S A M E J N S T E O M S L E O T I.
(i) T E N E W O H S K I I N S G T M O O H T A A T H U E U T O B.
(j) H T P R A H L E R E E R E T A T L E E H S T T T E H B N B S.
37. By EFSEE.
(a) I U E G N M O W H X T A N O I P D I L S F P I A R -
(b) F N E E T X I E T O N O T S M G R T R Y V G P A C -
(c) S F U F N I C E Q E S C U N R I L T M Y I O I P T -
(d) B T E E S N B I H I E T L N X O E S N R E I E G T.
38. By SIR ORM. (This has a keyword!)
T A S H L E C P W E T C I H A O T N R A O O H L W D O Y I L E O H R L
E V A T E A O M N L E V N W I W I E I H S M H E T H N W O I O L S V I
I F S S O W A S O T F I L E H N M G O F I E R A L O C G N N.
39. By DAMONOMAD. (And he calls this a "Nihilist" !)
A H H S E S T I H D I S O M E A T H I O O H D I O U T T I K M I E S O
F G S N E R W U G T S G Y I S L A T I T T A A N H O G E N Y L A W E A
L E R T M I W T O E D.
40. By FRA-GRANT. (A military message sent by General Calamity to Major Catastrophe).
T E H A N E M G S L L I W S N E T T A C K Y E I A A E B P S O U R P E
M O C E E T U N R I S T E R S A F O E T O R T D A E R T E F D I N C A
S E R E T T U O P W A R U R E F F O Y A E E D F O R D R C R.
No. 40 can be decrypted by the multiple-anagramming of its units. Afterward,
if you are unable to reconstruct the system, No. 41 will tell you all.
41. By PICCOLA. (Single block - completed unit - with columns transposed. The
key to this transposition may amuse you, provided you can
reconstruct it in letters!)
A O U U P D M C A N I O G T R S A A Y N K N C A B M N A O A T L E C H
Q S D O R E E W W D N C K E E S T S H N I E T E U H K N I F D I T Y F
U X G I V L T A I P H R C S N R R E H S B M E E A R M T A I U T E W O
P I R S M H O O E V R W F N X S D A H I E T S S U F C N N E E S N F S
E O O L T U A E A O F T V L T E E O E C.
42. By TITOGI and PICCOLA. (General information - nothing more).
(a) I H S E W D O X H D H T S E O E H R N E C T O O A G A R S A
N O E A O S O H U W R T C A U R E N T T O M S O C N Y N P G S H A P P
N F S N E R T E H E P M A W S M E G I A E A P O R Y D T A A S S A F M
I H S R C H E C W N E I T A T R X E I S O A C F A T I C E N I R T E U
Y H T E R T S R S E L S T E G P A H R W. (b) S R H J I A X E C A
N E Y P K A N D A T S D L I L A S L N T G E A D Y E B L Y T S C C I D
T C S G A M C E E N W A T I E A E N H L A B D Y A G H C H E G I H O I
L P O N P A S E D N T T W E S Y E F I M L A R E R H N E D I O T E L R
O S I T D S S R I S N I R R F S S P E C T R E I F B G O M R X S E N A
H A R N L. (c) A E G Y B A T Y N S R I D T O O S D N E Y E E E O
G N I U U T W S N L H E I I S C G H H W D R R U W E A H E T K C T W V
O E H H I.
43. By TITOGI. (Keerful, Si! All is not gold that glitters).
C T I H N A I E S O R M F Y E E C T H U W I S L A E D K R L B E R N M
J I T S D A N D O O H T V A T H T E R Y G A U N O T S A P E M O E S U
R I L T E D I E O N E N R C A F I N P O L H O E A G R B X S.
44. By ALII KIONA. (Nou hooda thawt it uvvim?)
E N W N O T N S E N Y U H O I K H N O E W A O T I U S S A L B W S F R
M I E I D I H R W N T F N D S E E O T U E Y B N O T W E W Z E E D I B
A E R Y I P L R N P Z R S M U T A S O I S U S D T D T R N H N O A S A F E Z.