Simple Substitution — Fundamentals
Simple substitution is ordinarily defined as a cipher in which each
letter of the alphabet has one fixed substitute, and each
cryptogram-symbol represents one fixed original. When this cipher is
used for puzzle purposes, as we find it in our newspapers and popular
magazines, the substitutes (which are invariably letters of the
alphabet) may be chosen at random, and the cryptograms must follow
certain arbitrary rulings which are designed to make them “fair”:
Word-divisions and punctuation must follow religiously those of the
original text; a certain minimum of length must be provided; no
letter may act as its own substitute; foreign words are not
permissible; and so on. Aside from the observance of such rules,
however, no holds are barred; the constructor of such a cryptogram,
totally unconcerned with the meaning of his plaintext (except that it
must have one), sometimes gives his chief attention to distorting the
normal language characteristics in an effort to baffle the analyst,
and often will carefully search his dictionary for words like
_yclept_, _crwth_, _syzygy_, _pterodactyl_, _ichthyomancy_, not
infrequently producing a plaintext which is almost as incomprehensible
as its corresponding cryptogram. Our study here will be confined to
the simple substitution cipher as applied to normal English text.
When a substitution key (a pair of alphabets) is being used for
cipher purposes, the letters which make up the cipher alphabet cannot
be chosen at random; the key must be of such a nature that any one of
the several correspondents, desiring to make use of it, will have it
at his disposal. Word-divisions are usually concealed, or,
occasionally, falsified. Punctuation, if used at all, must don the
apparel worn by the rest of the text; no limitations can be placed on
length, and no word whatever can be barred, where the intention is
that of conveying actual messages; and it is not at all uncommon to
find that one or more letters are serving as their own substitutes.
In discussing keys, we will make some arbitrary rulings of our own,
but only in the interests of clarity. We will assume, for all cases,
that the two necessary alphabets are always written horizontally, as
several are shown in Fig. 59; that wherever the two complete alphabets
appear, the upper of the pair is always the one in which plaintext
letters must be found, so that the lower one is always the cipher
alphabet. Thus, whenever the two alphabets are written out in full,
the substitute for any given plaintext letter will be the letter
standing immediately below it; and the original of any cipher letter
will be the letter standing just above it. Wherever it seems advisable
to show a distinction, the cipher letters will be expressed as
capitals and the plaintext letters will appear in lower case.
Among the oldest cipher alphabets ever used for practical purposes
are those of the type called “Caesar,” one such alphabet having been
used by Julius Caesar, and another by Octavius. As may be seen at (a)
of Fig. 59, this type of cipher alphabet is no more than a simple
_shifting_ of the normal alphabet to a new point of beginning. Using
this particular example, the word “Caesar” will be enciphered as
_F D H V D U_; or, if the word _R Y H U_ is found in a cryptogram, it
deciphers as “over.”
At (b) of the same figure, we have a pair of _inverse_ normal
alphabets. Here, it is not necessary to specify that one of the pair
is a plaintext alphabet and the other a cipher alphabet; whenever a
plaintext alphabet is merely reversed and allowed to serve as its own
cipher alphabet, the encipherment becomes _reciprocal_; that is,
whenever _Z_ is the substitute for _A_, then _A_ will also be the
substitute for _Z_, and so for other letters. Thus, we need not write
down more than half of the key shown at (b); and, in any other case
of reciprocal alphabets, only enough of it to make sure that we have
all 26 of the letters; after that, we may find them where we please,
both for encipherment and for decipherment. Simple reciprocal
alphabets are also ancient. The one just mentioned, and also the one
shown at (c), are both said to have been used in parts of the Bible.
The two inverse alphabets of (b) may, of course, be _shifted_ with
reference to each other; that is, one or the other may be caused to
begin at any desired letter, just as is done with the ordinary
alphabet in deriving one of the “Caesars.” It is also possible, as
indicated at (d), to divide the normal alphabet into its two halves,
and shift one of the halves; in this case the encipherment would be
reciprocal whether or not the shifted portion runs in reverse order.
At (e) and (f), we have mixed (or interverted) alphabets which,
though crude, are more in line with modern practice than those which
precede them, since both of these are based on the key-word CULPEPER.
Figure 59
Some Simple Substitution Keys
(a)
A shifted, or "Caeser," alphabet:
Plaintext: a b c d e f g h i j k l m n o p q r s t u v w x y z
CIPHER: D E F G H I J K L M N O P Q R S T U V W X Y Z A B C
(b)
A pair of inverse alphabets:
A B C D E F G H I J K L N N O P Q R S T U V W X Y Z
Z Y X W V U T S R Q P O N M L K J I H G F E D C B A
Other examples of the RECIPROCAL alphabet:
(c) A B C D E F G H I J K L M (e) C U L P E R A B D F G H I
N O P Q R S T U V W X Y Z Z Y X W V T S Q O N M K J
(d) A B C D E F G H I J K L M (f) C U L P E R A B D F G H I
T S R Q P O N Z Y X W V U J K M N O Q S T V W X Y Z
The usual plan for deriving cipher alphabets from key-words is as
follows: First, all repeated occurrences of any same letter, such as
the second _P_ and the second _E_ of the word CULPEPER, are discarded.
The unrepeated letters of the key-word, as _C U L P E R_, are placed
at the beginning of the cipher alphabet, and the rest of the 26
letters are made to follow these, usually in their normal alphabetical
order. If an adequate key-word be chosen, for instance the word
UNCOPYRIGHTABLE, a well-mixed alphabet results; but, in order to have
a cipher alphabet which is truly incoherent, and hard for the
decryptor to reconstruct, we may write this already-mixed alphabet
into block form and subject it to a transposition of some kind.
Several examples of this may be examined in Fig. 60. In example (a),
the repeated letters of the key-word have merely been discarded,
while example (b) retains these two positions in order to produce
more and shorter columns, with three different lengths. In both cases,
the columns of the block have been taken out by descending verticals
to form cipher alphabets (a) and (b), but the transposition may
follow any desired route or other process. Example (c) suggests
further uses for key-words. Still another process (not shown)
consists in writing the key-numbers above a block, exactly as in
example (c), and allowing them to govern the _lengths of rows_. In
the writing-in of the alphabet, normal or mixed, the first row of
letters is made to end under key-number 1, the second row under
key-number 2, and so on, so that the completed block contains rows of
different lengths; it may then be taken off by columns, or otherwise.
Numerous other devices exist, but it should be plain from the
foregoing that we have an unlimited field in which to derive
well-scrambled cipher alphabets, so that there is no need whatever
for forming one at random and later being unable to set it up again.
Figure 60
Some Methods for Forming a Keyword-Mixed Alphabet
Keyword: CULPEPER
(a) (b)* (c)
C U L P E R C U L P E * * R C U L P E P E R
A B D F G H A B D F G H I J 1 8 4 5 2 6 3 7
I J K M N O K M N O Q S T V A B C D E F G H
Q S T V W X W X Y Z I J K L M N O P
Y Z Q R S T U V W X
*)(An OHAVER Method). Y Z
(a)
Plaintext: a b c d e f g h i j k l m n o p q r s t u v w x y z
CIPHER: C A I Q Y U B J S Z L D K T P F M V E G N W R H O X
(b) Plaintext: a b c d e f g h i j k l m n o p q r s t u v w x y z
CIPHER: C A K W U B M X L D N Y P F O Z E G Q H S I T R J V
(c) Plaintext: a b c d e f g h i j k l m n o p q r s t u v w x y z
CIPHER: A I Q Y E M U G O W C K S D L T F N V H P X B J R Z
For the _encipherment_ of substitution cryptograms, the plaintext is
first written out in full with enough space between its lines to allow
for the later insertion of cryptogram-letters. The correct substitute
for each letter is then written below it, after which, these
substitutes are nearly always marked off into five-letter groups, and
the groups are taken off on another sheet to form the finished
cryptogram. It is sometimes recommended that plaintext and cipher
letters be written in two different colors, so as to avoid any risk
of taking off portions of plaintext along with a cryptogram.
Figure 61
"Running Down the Alphabet"
Cryptogram: Y B P R O B Q L...
Z C Q S P C R M...
A D R T Q D S N...
Plaintext: B E S U R E T O...
For _decipherment_, the plan is the same, except that the cryptogram
is written first, and the two alphabets of the key exchange their
functions. Often, when the cipher alphabet in use is so incoherent
that its letters are not quickly found, the decipherer will prepare
for himself a special _decipherment key_, in which he places the
letters of his cipher alphabet in straight alphabetical order, and
allows the plaintext alphabet to grow mixed.
In taking up the _decryptment_ of simple substitution, we may dispose
summarily of the Caesar alphabets by pointing to Fig. 61. If we
suspect that one of these has been used, we may verify the suspicion
by taking some ten-or-fifteen-letter segment of the cryptogram, and,
with each of its letters as a beginning, extend the ten or fifteen
alphabets, a few letters at a time, until we come to the line which
is purely plaintext. This process is popularly known as “running down
the alphabet,” and whenever it results in a row of plaintext, we may
quickly determine the amount of “shift,” set up the cipher alphabet,
and start deciphering.
The same thing is true of a pair of _inverse normal alphabets_ which
have merely been _shifted with reference to each other_. But in this
case, the cryptogram (or that segment of it which is being
investigated), _must first be enciphered in the same kind of
alphabet_. To explain this, suppose that our cryptogram fragment is
_B Y K I L Y J O_. If we encipher this with the pair of inverse
alphabets which was shown at (b) of Fig. 59, we obtain a new
cryptogram fragment _Y B P R O B Q L_. This new fragment is now a
“Caesar,” and we may “run it down the alphabet” until we find its
plaintext. This particular fragment was done with a pair of inverse
normal alphabets in which the lower one began at _C_, instead of at
_Z_. Most decryptors, in dealing with any kind of substitution, will
make these two tests before trying anything else. When the guess
proves correct, a great deal of paper work can be saved.
Concerning decryptment in the case of the less simple alphabets, the
true vulnerability of simple substitution can be seen when the word
“battalion,” enciphered in alphabet (f) of our Fig. 59, becomes
_T S B B S M Z E P_. Since each letter of the alphabet may have only
one substitute, the pattern of -_atta_- shows up clearly in its
enciphered version -_SBBS_-. The decryptor knows instantly what kind
of pattern it represents, since the letters _S_ and _B_ can have only
one original each. The frequency with which these two letters have
been used in his cryptogram will tell him approximately what their
two originals ought to be, and, by making a few trials, he loses
little time in arriving at a solution. As a matter of fact, a simple
monoliteral substitution, given fewer than a hundred letters of text
and no information whatever as to source or subject-matter, can be
decrypted purely through the frequencies and other characteristics of
its letters; and if, in addition, the original word-divisions have
been preserved, we have the lengths and patterns of these words, plus
the knowledge that individual letters have their favorite positions
in words.
* * *
_The “Crypt” with word-divisions_. — Not infrequently, the cryptogram
which retains its word-divisions can be read at sight, without putting
pencil to paper, and this regardless of how short it may be. Again,
even though based on normal text, it will prove more troublesome; and
thus, in dealing with this type of simple substitution, we attack each
individual example according to what appears at first glance to be its
greatest weakness. The cryptogram shown in Fig. 62, for instance,
would be attacked through its many _short words_, probably the
simplest of the available methods. The words in question are those
numbered 3 (_RD_), 4 (_MD_), 9 (_QYR_), 11 (_RKV_), 13 (_DF_), and 15
(_DN_). Among the two-letter words, it is noticeable that every one of
these includes a letter _D_, used indiscriminately as the initial or
final letter. We do not need to know much of cryptanalysis to guess
that this letter represents the _o_ found in such words as _to_, _no_,
_do_, _go_, _of_, _on_, _or_. A comparison of the two three-letter
words shows that these, also, have a common letter, _R_, which ends
one of these words and begins the other. Of all words in English, the
commonest is _the_. If _RKV_ be assumed as _the_, then _RD_, already
thought to contain _o_, will check as _to_, another extremely common
word.
Thus we are able to begin work by _tentatively assuming_ that the
four cryptogram letters _R_, _K_, _V_, and _D_, are the substitutes,
respectively, for plaintext letters _t_, _h_, _e_, and _o_. These
assumptions are tested by actually making the necessary substitutions
directly on the cryptogram, as seen at (a) of Fig. 62. And we may be
sure that they are correct when we see the 12th word clearly outlined
as _other_. This word gives a new substitution: cipher letter _T_
evidently represents _r_, occurring in three different words; the
actual making of this substitution will cause the 8th word to show a
very common ending: -_tter_.
If we now consider the other three-letter word, the 9th of the
cryptogram, we see that _QYR_ cannot represent any one of the common
words _not_, _got_, _out_, _yet_, since the substitutes for _o_ and
_e_ have already been determined. It may, however, represent the
common word _but_, especially if we care to investigate the frequency
in the cryptogram of its first letter, _Q_. This letter has been used
only once; and its assumed original, _b_, is normally of very low
frequency, and, in addition, is known to have a fondness for initial
positions. The assumption of this word as _but_ gives us the
substitute for _u_, which appears to be _Y_.
Figure 62
Making Substitutions
(a) 1 2 3 4 5 6 7
F D R J N U H V X X U R D M D S K V S O P J R K Z D Y F Z J X
o t e t o o h e t h o
8 9 10 11 12 13
G S R R V T Q Y R W D A R W D F V R K V D R K V T D F
t t e t o t o e t h e o t h e o
14 15 16 17
S Z Z D Y F R D N N V O V T S X S A W V Z R.
o t o e e e t
(b) ...D F S Z Z D Y F R D N... ...Z D Y F Z J X...
o n a c c o u n t o f c o u n c . .
13 14 15 7
In addition to the points mentioned, it is not unusual to find that
short words, by their very positions with reference to some longer
word, will identify a whole sequence, as might happen with the
sequence shown at (b) of the same figure. Good examples of this are:
_as well as_, _as soon as_, _in order to_, and so on. In this
particular case of (b), we began with only the identified _o_, and
immediately were able to identify _t_; this alone should serve for
spotting the whole sequence _on account of_, taking into consideration
the doubled _c_. Notice what the identification of the word _account_
will do toward identifying the 7th word.
Among methods which do not seem indicated in the given example, there
is a very fertile field for research in the examination of _terminal
sequences_. When two or more of the affixes -_tion_, -_ing_, _in_-,
and _con_- are present in the same text, as they practically always
are, they will serve to identify one another, and may, in addition,
be cross-compared with many of the short words, as in, _on_, _no_,
_not_, _into_, _upon_, _can_. The prefix _sub_- may serve to identify
the word _but_. There is a whole group -_ment_, -_ence_, -_ance_,
-_ency_, -_ancy_; another group _pre_-, _re_-, -_er_, _de_-, -_ed_,
etc.; or a good comparison in _be_-, -_able_, -_ible_, etc.
Still a third road to solution, especially popular with those who
solve the “aristocrats,” is found in _pattern words_, that is, words
having one or more letters repeated. The puzzler, examining a
dictionary, prepares lists for his permanent use, one list for each
“pattern”; such a list, for instance, would contain PATTERN, FALLING
and all other words in which the third and fourth letters are the
same and all others different, another would contain all words having
the pattern STATE, DEFER, ROBOT, still another all words of the
pattern BANANA, ROCOCO, and so on. The solver, having thus armed
himself in advance, begins work by searching his cryptogram for words
having repeated cipher letters, and attempts to identify these from
the proper lists. He may provide himself, also, with non-pattern
lists, on which words have given lengths but contain no repeated
letters; and with “transposal lists” containing pairs of words (as
NIGHT and THING) which use the same letters but not in the same order.
It is true that such lists are troublesome to prepare, but they are
extremely effective; they will break the most resistant of the
“aristocrats” or the shortest example of legitimate cipher.
No matter how resistant the cryptogram, all that is really needed is
an _entry_, the identification of one word, or of three or four
letters. The experienced solver knows well that persistence will find
this entry, and trusts largely to instinct and perseverance; the
beginner, however, may feel at a loss for a “system,” and, if so,
may, perhaps, be able to find suggestions for one in the next few
paragraphs.
Figure 63
A Favorite Form of Frequency Count
Combined With CONTACT Data
A D S 2/4
R W
B
C
D F R M Z W W V T Z R 10/11
R M S Y A F R F Y N
E
F * Y D D Y 5/6
D Z V S R
G X 1/2
S
(Etc.)
Concerning the numbers: A has a
frequency of 2, and a variety-count
of 4. D has a frequency of 10, and
a variety-count of only 11. (Yet
D, with so little variety of contact
is a vowel!)
First of all, in any substitution problem, there should be a counting
of the letters in the cryptogram in order to find out their
frequencies. This is called a _frequency count_, and is usually
accomplished as follows: The decryptor first lays out the normal
alphabet — either horizontally or vertically. He then begins with the
first letter of his cryptogram, taking letters one by one just as he
finds them, and for each time that he finds a letter in his
cryptogram, he places a tally mark beside that same letter as found
in his prepared alphabet. The result of such a count, taken on the
foregoing cryptogram, will be shown further on, when the same
cryptogram appears again without its word-divisions.
If the problem seems likely to prove really difficult, there should
also be a _contact count_; that is, a list showing every letter,
together with the two which have flanked it right and left each time
it was used. Such a count is partly shown in Fig. 63. This, like the
frequency count, may be prepared either vertically or horizontally;
and, just as in making ready for the frequency count, an alphabet may
be laid out in advance ready to receive the contact letters, taken
from the cryptogram as they happen to be found. Specifically: The
letter _F_ comes first in the cryptogram; it has no left-hand contact,
but is contacted on the right by _D_. We find the _F_ of the prepared
alphabet, and place beside it its contacts: *-_D_. The second letter
of the cryptogram is _D_, flanked by _F_ and _R_. We find the _D_ of
the prepared alphabet, and place beside it its contacts: _F_-_R_; and
so on to the end of the cryptogram. Some solvers do not prepare an
alphabet in advance, but simply put down the main letters as they
happen to come across them in the cryptogram. It should be added,
too, that the few contacts included in Fig. 63 were taken from the
_undivided_ cryptogram. When word-divisions exist, and are known to
be the correct ones, a great many solvers do not include any contacts
which involve two different words. Here, for instance, the second
appearance of _D_ is shown with contacts _R_-_M_. These solvers,
knowing that this _D_ stands at the end of a word, will leave the
_M_-contact blank: _R_-*
It will be noticed from the figure that the contact-count is, in
itself, a frequency count; it shows that _A_ has been used twice
(frequency 2), that _B_ and _C_ have not been used at all, that _D_
has a frequency of 10, and so on. We may also make it a
_variety-count_, by noting down beside each letter the number of
_different_ letters present among its contacts. Ordinarily, the
vowels have more variety in their contacts than do the consonants,
and take part in more reversals. The uses of contact data will be
examined more closely later on.
Now, giving our attention to English frequencies: No matter what
frequency table we examine, we always find that the letter _E_ tops
the list, with a frequency of over 12%. Except in telegraphic text,
the letter _T_ always has the second frequency, near 10%. After that,
the frequency tables will disagree as to whether _A_ or _O_ should
have the third frequency, or whether _I_ should come before _N_, or
_S_ before _R_; but always the same nine letters, _E T A O N I R S H_,
will constitute the _high-frequency group_ of letters. These
particular letters will make up about 70% of any English text, and it
is almost impossible to prepare one, no matter how short, without
using them in about that proportion, though in the shorter texts, _L_
and _D_ will sometimes creep up into the high-frequency class, taking
the place of _H_. Following the high-frequency group, we find a group
of letters which are always of _moderate frequency_; and a third group
made up of _low-frequency_ letters. Since the frequency tables
themselves are not duplicates throughout, we could not expect, even
having a 10,000-letter cryptogram, to make substitutions by simply
following the frequency table and be absolutely sure of coming out
with the correct solution, though we might very nearly do so, and
might, to some extent, succeed in doing this with a cryptogram of
2,000 letters. The “aristocrats,” however, are arbitrarily confined
to lengths which run between 75 and 100 letters. Even without
manipulation, a text of this length will not always show _E_ as a
frequent letter, and may, for some reason, show _Z_ or _X_ with a
fairly high frequency.
However, the “class distinctions” among the letters are always, to
some extent, dependable. High-frequency letters, moderate-frequency
letters, and low-frequency letters, all tend to be very exclusive.
They will exchange frequencies with letters of their own class, but
all three classes are disinclined to welcome outsiders. The vowels,
also, as we have seen, have their fraternity; if the frequency of _E_
is lowered, some other vowel, even _U_ and _Y_, will insist upon
making up the difference, rather than yield this privilege to a
consonant.
The high-frequency group, as mentioned, includes the nine letters
_E T A O N I R S H_. Even in this exclusive circle, there are cliques
— not ironclad, but clearly noticeable:
_Class I_. The letters _T O S_ appear frequently _both as initial
letters and as final letters_ in their own words, with terminal _O_
confined largely to short words. All three of these are very freely
doubled.
_Class II_. The letters _A I H_ appear frequently as _initial
letters_, but far less frequently as finals, especially _A I_. Not
one of these is readily doubled.
Class III_. The letters _E N R_ appear frequently as _final letters_,
but far less frequently as initials. The letter _E_ is very freely
doubled; the other two not so often.
The following further observation might be made: When one of these
letters changes its class, the least likely exchange is one occurring
between classes II and III.
* * *
Now let us return to the foregoing cryptogram and consider the
application of this information. A frequency count taken on this
cryptogram will show that when its letters are rearranged according
to their frequencies, they divide automatically into three rather
clearly-defined groups, much like those of the normal frequency table.
There are eight letters which outrank the rest, and these, named in
the order of decreasing frequencies, are: _R_, _D_, _V_, _S_, _F_,
_Z_, _K_, _X_. Presumably, then, most of these are substitutes for
letters of the class _E T A O N I R S H_.
If an examination now be made of the terminal letters in the
cryptogram, it will be found that, of the eight considered, the
letters _R D F_ have appeared at least once in both positions. These
we may label class (a), as being good material for the originals _t_,
_o_, _s_. It is found that the letters _S Z_ have appeared at least
once as initials, but not at all as finals. These we may label class
(b), that is, good material for the originals _a_, _i_, _h_, except
for a point which will be mentioned in a moment. The remaining three
letters, _V K X_ are found at least once as finals, but not at all as
initials; these we will call class (c), good material for the
originals _e_, _n_, _r_. Thus, we are enabled to begin our work by
noting down the following possibilities:
(a) _R D F_ might represent (I) — _T O S_. (Compare the facts: _t_, _o_, _n_).
(b) _S Z_ might represent (II) — _A I H_. (Compare the facts: _a_, _c_).
(c) _V K X_ might represent (III) — _E N R_. (Compare the facts: _e_, _h_, _l_).
While such a classification is probably never 100% accurate, the
writer has still to find a cryptogram (unless among the very badly
manipulated “aristocrats”) in which at least part of the assumptions
are not correct. We are dealing, however, with the _very short
cryptogram_, in which a single occurrence of a letter in a given
position can be regarded as of some importance.
Ordinarily, the most frequent letter of (c) will represent _e_, as it
does here. This letter is famous as a final letter, and any printed
page will show it at the end of 17 or 18 words in every hundred.
There is not so clear a distinction between _T_ and _S_ of class I.
The most vulnerable of the groups, however, is (b). Of the three
letters which may be represented here, two are vowels, concerning
which we are to hear more, and not one is readily doubled. When _Z_,
tentatively included in this group, is found to have been doubled
near the beginning of a word, it is seen to be wrongly classified.
This method, as mentioned, is intended merely as a suggested means
for effecting an entry. The correct identification of only four
letters, as we have seen, will make enormous inroads into the
contents of a cryptogram.
Other points which will at times prove helpful are as follows: In
words of three and five letters, the central one is nearly always a
vowel, taking it for granted that the words _the_ and _and_ will
never be present in any difficult cryptogram. In the longer words,
the favorite positions of the vowels are the two positions which
follow the initial letter and the two positions which precede the
final letter. The favorite position of _I_, in fact, is well known as
the third-to-last. About half the words used in any written text are
of the type called _negative_, or _empty_; that is, the pronouns and
auxiliary verbs, and particularly the various kinds of connectives
_without which_ _no sentence can be put together_. If your cryptogram
is an “aristocrat,” you will probably find that most of your
prepositions begin with _A_: _amongst_, _amidst_, _adown_, etc. Every
sentence contains a verb, and these are more or less limited in their
possible terminations. Any letter used only two or three times, and
always followed by the same letter, is good material for _Q_. With
what has been said, the student should have no trouble in dealing
with the first fifteen “aristocrats” which follow the next chapter.
As to the remaining thirty-five of Mr. Lamb’s collection, we need say
only this: It is impossible to avoid every characteristic of the
English language and still write English.
* * *
_The General Case_. — Now let us examine carefully Fig. 64, where the
foregoing cryptogram is repeated without its word-separations, and is
followed by its frequency and contact data. The various devices
indicated in this figure are all of a more or less optional nature.
Concerning the preparation of the cryptogram itself, the chief
requirement is that it be done in ink, or typewritten, on paper which
will suffer a great deal of erasure. The placing of its frequency
figure above each letter is highly recommended, but not vital. Many
solvers will underscore all possible repeated sequences, and will
indicate in some other manner all reversals of digrams; others will
underscore only the repeated trigrams and longer sequences; and still
others do not underscore at all, being content to have all of these
repetitions and reversals listed before them in the contact data.
Figure 64
5 10 11 3 3 2 1 9 4 4 2 11 10 1 10 6 4 9 6 2 1 3 10 4
F D R J N U H V X X U R D M D S K V S O P J R K
5 10 3 5 5 3 4 1 6 11 11 9 3 1 3 11 3 10 2 11 3 10 5 9
Z D Y F Z J X G S R R V T Q Y R W D A R W D F V
11 4 9 10 11 4 9 3 10 5 6 5 5 10 3 5 11 10 3 3 9 2 9 3
R K V D R K V T D F S Z Z D Y F R D N N V O V T
6 4 6 2 3 9 5 11
S X S A W V Z R
Ordinary Frequency Count:
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
2 10 5 1 1 3 4 1 3 2 1 1 11 6 3 2 9 3 4 3 5
Contact-Information:
(High-frequency symbols)
R D V S F Z K X
D.J F.R H.X D.K ..D K.D S.V V.X
U.D R.M K.S V.O Y.Z F.J R.Z X.U
J.K M.S R.T G.R D.V S.Z R.V* J.G
S.R Z.Y* F.R F.Z D.S Z.D R.V* S.S
R.V W.A K.D T.X Y.R V.R
Y.W W.F K.T X.A
A.W V.R N.O
V.K T.F O.T (Low-frequency symbols)
D.K Z.Y* W.Z
F.D R.N G H M P Q
Z.. X.S U.V D.D O.J T.Y
(Moderate-frequency symbols)
J N T W Y A O U
R.N J.U V.Q R.D* D.F* D.R S.P N.H
P.R D.N V.D R.D* Q.R S.W V.V X.R
Z.X N.V V.S A.V D.F*
As to the preparation of the contact data, most of the expert
decryptors seem to prefer the vertical arrangement of Fig. 63 to the
one shown here. But, in simple substitution, a full listing, made for
all letters, is not necessary in dealing with the average cryptogram.
Usually, it will serve the purpose to make a frequency count first,
and then prepare a listing of contacts which includes only chosen
letters, those of very high frequency and those of very low frequency;
with many cryptograms, no listing at all need be prepared. The contact
data, however, are valuable. Each pair of contact-letters actually
indicates a trigram. Examining, for instance, the listing under _R_:
The first expression, _D.J_, represents a trigram _DRJ_ in which the
central letter was omitted in order to conserve time and space. When
we find, lower down in the same listing, another letter _D_, we see
in this a repeated digram _DR_. Considering the right-hand side of
the same listing: When we find _K_ used three times, we see this as a
digram _RK_ used three times. _By finding its duplication, under K_
(left side), we are able to see that two of these repetitions are
continued as parts of a repeated trigram _RKV_. In the list of
contacts for _D_, we find a repeated trigram _ZDY_, which may be
traced, under _Y_, as part of a longer repeated sequence, _ZDYF_. It
is usually best to underscore these longer repeated sequences on the
cryptogram; often, they can be identified from the list of frequent
trigrams. But repeated digrams, as a rule, are so numerous as to be
in the way when noted on the cryptogram itself. With digrams, only
those which are repeated oftenest need be underscored; they can
nearly always be identified directly from the list of frequent
digrams. The solver, then, prepares his cryptogram and sequence data
to suit himself, varying his method according to the difficulty of
the given example. With this done, his usual method of solution
follows the process popularly known as “vowel-spotting.”
* * *
_The Vowel-Solution Method_. — Using this process, the first step is
that of separating the vowels from the consonants; the second is that
of assigning identities to the selected vowels, and afterward to the
most recognizable of the consonants.
For assistance in applying this method, suppose we extract certain
information from the digram chart and have this concretely before us
in a series of numbered “pointers”:
1. The vowels _A E I O_ are normally found in the high-frequency
section of the frequency count; the vowel _U_ in the section of
moderate frequencies, and the vowel _Y_ in the low-frequency section.
2. Letters contacting low-frequency letters are usually vowels.
3. Letters showing a wide variety in their contact-letters are
usually vowels.
4. In repeated digrams, one letter is usually a vowel.
5. In reversed digrams, one letter is usually a vowel.
6. Doubled consonants are usually flanked by vowels, and vice versa.
7. It is unusual to find more than five consonants in succession.
8. Vowels do not often contact one another. If the letter of highest
frequency can be assumed as _E_, any other high-frequency letter
which never touches _E_ at all is practically sure to be another
vowel, and one which contacts it very often cannot be a vowel. (This
will apply equally to other vowels, wrongly assumed as _E_.)
With a text of reasonable length, say 150 letters, it is sometimes
possible to determine with certainty just which of the
cryptogram-letters represent the six vowels; with shorter cryptograms,
we can usually find four; sometimes only three. But once the
separation has been made, individual vowels can usually be established
as follows:
The most frequent one is ordinarily _E_. The one which never touches
it is most likely to be _O_. Both of these are very freely doubled,
and for that reason are often confused with each other, but seldom
with any other vowel. They rarely touch each other.
The vowel which follows _E_ and almost never precedes it, is _A_.
The vowel which reverses with it is _I_.
The same two observations will apply to the vowel _O_; but a
distinction occurs when the vowel _U_ can be found; this vowel
precedes _E_ and follows _O_.
The only vowel-vowel digrams of any real frequency are _OU_, _EA_,
_IO_.
Three vowels found in succession may represent _IOU_, _EOU_, _UOU_,
_EAU_.
As to identification of the consonants: Those letters still remaining
in the high-frequency section of the frequency count will usually
include _T N R S H_. Of these, the most easily identified is _H_,
which precedes all vowels and seldom follows one; it may be identified
often as part of repeated sequences _TH_, _HE_, _HA_.
Next to _H_, the most recognizable of the consonants, aside from
frequency, is probably _R_, which reverses freely and indiscriminately
with all vowels, and has a strong affinity for other high-frequency
letters.
The consonant _T_ can usually be identified by its frequency, by its
tendency to precede vowels rather than follow them, and by its almost
inevitable combination with _H_ on more than one occasion. It is also
notably difficult to distinguish from the vowels.
The letter _N_ has characteristics which are to some extent the
opposite of those mentioned for _H_; it prefers to follow vowels and
precede consonants, and, to a lesser extent, the same is true of _S_,
according to some charts. However, _N_, _S_, and _T_ are all readily
reversible with vowels, and are sometimes hard to tell apart.
The only frequent reversals of two consonants are _ST_-_TS_ and
_RT_-_TR_.
The doubles _TT_ and _SS_ are among the most frequent in the language.
Having this information, together with what we know of frequent
digrams and frequent trigrams and very common short words, we are
well armed against the longer cryptograms. Those which are shorter
will give more trouble; but it takes a very short cryptogram indeed
to be really resistant.
Our foregoing cryptogram contains only 80 letters.
Figure 65
(Cryptogram Frequencies:)
R D V S F Z K X
11 10 9 6 5 5 4 4
E T A O N I R S H
(Normal Grouping)
To apply “pointers” in this case, let us begin by considering the
individual frequencies of the letters _E T A O N I R S H_. Their
frequencies per 100, according to our own chart, are about as follows:
_E_, 12; _T_, 10; _A_, 8; _O_, 8; _N_, 7; _I_, 7; _R_, 6; _S_, 7; _H_,
5. Thus, when frequency alone is considered, _E_ and _T_ have a
tendency to draw away from the others and form a private
high-frequency group of their own. The distinction among the others
is not so clear, and not always the same in all tables; we can only
say of these that _A_ and _O_ will always outrank the rest, and will
be closely followed by one of the others, usually _N_, and that _H_
will always rank last.
Thus, the high-frequency group itself tends to sub-divide more or
less clearly into three minor groupings: _E T_ — _A O N_ — _I R S H_.
Of these, the first minor group shows one vowel, the second shows two,
and the third shows one; the vowels _U_ and _Y_ are not present.
Now if the eight leading letters of our cryptogram, already listed as
_R D V S F Z K X_, be examined in this respect, it is found that
these, also, have a tendency toward separation into groups of
differing frequency, which more or less correspond to the normal
groupings, as indicated roughly in Fig. 65.
Normally, we expect the highest of these subdivisions to contain one
vowel and one consonant, specifically _E_ and _T_. When we find that
the corresponding subdivision of the cryptogram contains three
letters, the supposition is that one of the vowels, _O_ or _A_, has
moved up into this section; in that case, it has taken part of the
frequency of _E_, making it not at all unlikely that the most
frequent letter of the cryptogram will not represent _E_, and will
not, in fact, represent a vowel. And if, as we believe, there are two
vowels in the highest section, then we are not likely to find more
than one in the central subdivision, especially when we note that it
contains only three letters. This would leave the fourth vowel to be
found in the third subdivision.
Thus, we have applied pointer No. 1. For the application of pointer
No. 2, we turn to the contact data. Comparing first the three letters
_R D V_, and making a careful inspection of all cryptogram letters
whose frequency is 3 or lower, we find that, of our three letters,
the letter _R_ has 7 contacts with low-frequency letters, the letter
_D_ has 9, and the letter _V_ has 8. Thus, the letter _R_, though
having a higher frequency than the other two, has fewer low-frequency
contacts than either, and so begins to draw away and assume the
aspect of a consonant.
The application of pointers Nos. 3, 4, and 5, provides no satisfactory
distinction. But in pointer No. 8, we find a very clear distinction:
_D_ and _V_ have touched each other only once, while _R_ has contacted
both with a total of six contacts — a great many for a cryptogram of
this length.
We decide, then, that _R_ is a consonant, and that _D_ and _V_ are
vowels.
Considering the central subdivision, where we expect to find one
vowel: Application of pointer No. 2 shows that _S_ has four of the
low-frequency contacts, while _F_ has two and _Z_ has only one.
Further examination of _S_ by pointer No. 3 shows that it has an
unusual variety in its contact-letters. Thus, _S_ would appear to be
the vowel here.
As to the third section, there is so little difference in frequency
between these letters and some others not included in the
high-frequency class, that any distinction found would not be
convincing.
The individual cryptogram, however, has happened to contain the
sequences _VXXU_, _SRRV_, _SZZD_, _DNNV_. Application of pointer No.
6 confirms our previous selection of _D_, _V_, _S_, as vowels, and
suggests that the letter _U_ might also represent a vowel. Since the
frequency of this letter is only 2, we cannot feel so confident in
drawing conclusions about it; however, a glance at the contact data
shows that it has touched four different letters, which is 100%
variety, that one of these four letters is an accepted consonant, and
that none of the other three, so far, is an accepted vowel (pointers
3 and 8). The chances are that this letter _U_, with its low
frequency, represents _y_ in some such formation as _ally_, _ully_,
_etty_, etc.
With four vowels tentatively isolated, we are now in a position to
apply pointer No. 7, and this we may do by returning to the cryptogram
and marking for attention each appearance of each supposed vowel. This
is usually done by circling each one with a pencil mark. In Fig. 66,
a small letter “v” has served the same purpose, and a few serial
numbers have been added for convenience of reference. Now let us
examine Fig. 66.
At (a), watching the small “v’s,” we find a fairly uniform
distribution of vowels except for three long segments beginning,
respectively, at the 20th, 27th, and 37th letters. For convenience,
these have been copied out at (b). The two of these which are longer,
and therefore most likely to contain at least one of the missing
vowels, are both found to have included _Z_ and _J_. Of these two
letters, _Z_ is one which was previously discarded (from the central
section of the high-frequency group) during our preliminary
investigation. Examining it again, to make sure, we find it now as a
double between two supposed vowels, and having two additional contacts
with supposed vowels (pointers 6 and 8). But _J_, we find, has never
contacted any supposed vowel; it reverses with a supposed consonant,
and shows as much variety as could be expected of a letter appearing
only three times.
Figure 66
(a)
v ? v v v v v v v v ? 25
F D R J N U H V X X U R D M D S K V S O P J R K Z
v ? v v v v v 50
D Y F Z J X G S R R V T Q Y R W D A R W D F V R K
v v v v v v v v v v v 75
V D R K V T D F S Z Z D Y F R D N N V O V T S X S
v 80
A W V Z R
(b) 20-25 27-32 37-41
O P J R X Z Y F Z J X G T Q Y R W
? t ? t
(c)
F D R J N U H V X X U R D M D S K V S O P J R K Z
e t i y o y t e e a h o a i t h
D Y F Z J X G S R R V T Q Y R W D A R W D F V R K
e i a t t o t e t e o t h
V D R K V T D F S Z Z D Y F R D N N V O V T S X S
o e t h o e a e t e o o a a
A W V Z R
o t
(d)
Preliminary assumptions: y t e . e a h o a . t h o e t h o .
CORRECTIONS: y t O . O a h E a . t h E O t h E .
...to go ahead... ...the other...
(e)
F D R J N U H V X X U R D M D S K V S O P J R K Z
o t i y e y t o o a h e a i t h
N F G D W
Notify *e**y to go ahead with.......
The acceptance of _J_ provides five of the vowels, with frequencies
of 10, 9, 6, 2, and 3 — a total of 30 out of an expected 32. In a
longer cryptogram, we should probably look for the sixth vowel among
those letters having approximately the correct frequency for making
up the expected 40%. As to the present case, we should have no trouble
selecting it from the five-letter segment at (b); but this would cause
us to spot also the short word in which it is used, and our immediate
concern is that of spotting vowels only through their known
characteristics as vowels. We will assume, then, that the last vowel
cannot be found.
The next step demands that we assign to the most frequent of the
supposed vowels the value _e_, which happens to be a wrong assumption.
Concerning this, it may be well to repeat here something which has
already been said: In dealing with the simplest of cryptograms, there
is often a short detour into trial and error. Also, the average
decryptor, accustomed to the work, and fully aware of what he may
expect from only 80 letters of text, will usually pause at this point
and make some further observations before filling in any of his
substitutions. However, there is value even in the making of wrong
substitutions; the actual placing of supposed plaintext values in
their supposed positions puts the plaintext possibilities before us
_in visual form_, causing us to note easily those very points for
which the experienced decryptor examines in advance.
Figure 67
1. F D R J N U H V X X U R D M D S K V S O P J R K Z D Y F Z J
X G S R R V T Q Y R W D A R W D F V R K V D R K V T D F S Z
Z D Y F R D N N V O V T S X S A W V Z R.
(80 letters).
2. H V X X U T V W D T R A Z D Y F Z J X T V S O U R D S Z R N
S E D T S Q X U L K S E V O T D W W V O D R K V T G S R R V
T Q Y R A Y M M V A R P V A K D Y X O H V V W K S G G V T J
F M S R R K J A R K T D Y M K T J Z K S T O A L R K J F H R
K V U G S U M T S F R R K V A Y Q A J O U R K S R U D Y A W
D H V D N.
(155 letters. - Total for both cryptograms: 235).
At (c), then, we have made our substitutions. We have assumed that
the most frequent vowel, _D_, is representing _e_. Having noted the
v-v digrams _DS_, _VD_, _VS_, we have selected _S_, rather than _V_,
as the substitute for _a_, preferring a digram _oa_ (_DS_) to a
digram _ao_ (_VD_). This leaves the vowel of second frequency, _V_,
to represent _o_. This will cause the third of the v-v digrams (_VS_)
to represent _oe_, not frequent, but better than the digram _ao_
previously mentioned. _J_, then, probably represents _i_, and _U_ may
represent _y_.
As to consonants, we have assigned the value _t_ to the most frequent
one, _R_, and there has been no difficulty in identifying _h_ in the
letter _K_, which three times has followed _R_. But our present
cryptogram is too short to provide any clear distinction among letters
which might represent _n_, _r_, _s_. With the seven substitutions
made, as shown at (c), notice how quickly it becomes possible to spot
the incongruity of sequences _tho_, more than once, in a short text
which contains not a single occurrence of _he_ or _ha_. Notice again,
at (d), how quickly the mere exchanging of the values _e_ and _o_
will bring out word-suggestions.
At (e), the first line of the cryptogram is repeated, as it would
appear after the making of this exchange. The beginning of the
message can almost be read: The first word appears to be _notify_,
furnishing two new substitutes. Three more can be furnished in the
suggested sequence _to go ahead with_. And here, the word _with_
would be tried in any case, because it is a common word, and because
the frequency of the letter _P_ is suggestive of _w_. Arrived at this
point, we begin to notice patterns: _postpone_, _council_, _account_,
_matter_, and so on; so that the rest of the solution is largely a
matter of filling in framework. In the given example, it would also
be noticed that _F_ and _N_ have resulted from reciprocal
encipherment; this may not be the case with other letters, but it
presents a possibility which is always well-worth investigating.
Figure 68
Digram Count for the Longer Cryptograms
(First-Letters)
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
A 1 1 1 1 2 1 3 1 A 11
B B
C C
D 1 1 1 1 1 3 3 1 2 4 3 D 21
E 2 E 2
F 2 2 1 3 F 8 *
S G 1 1 1 1 1 G 5
e H 1 1 1 1 H 4 *
c I I
o J 1 2 1 1 2 2 J 9
n K 1 1 1 10 1 1 1 K 16
d L 1 1 L 2
{. M 1 1 1 1 2 M 6
L N 2 1 1 1 N 5 *
e O 1 2 1 3 1 O 8
t P 1 1 P 2
t Q 1 2 1 Q 4
e R 3 3 2 1 1 1 4 4 1 3 1 2 2 R 28 *
r S 2 1 3 4 1 1 3 2 1 S 18
s T 2 2 1 1 1 1 6 1 T 15
U 1 2 1 1 1 3 U 9
V 1 1 1 4 6 1 1 1 1 2 2 1 2 V 24
W 2 1 2 2 1 W 8
X 2 1 1 2 2 1 X 9
Y 2 6 2 Y 10
Z 1 2 1 1 2 1 1 Z 9
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
9 5 4 27
Most Frequent Digrams
RK, 10 KV, 6 WD, 4 SR, 4
VT, 6 DY, 6 RR, 4 KS, 4
HV, 4
* * *
_The Digram-Solution Method_. — This method, representing another of
our many debts to M. E. Ohaver, may be used either in conjunction with
the vowel method, or independently, as the fundamental method of
attack. For a satisfactory demonstration, however, we need more
material, and Fig. 67 shows our cryptogram again, together with a
suspected reply. Thus we have a length of 235 letters, so that the
preparation of contact-notations, which we found sufficient in the
preceding case, becomes here an irksome task.
For these longer cryptograms, it is usually best to put all of our
data into the form of a _digram-count_, as indicated in Fig. 68. This
is most easily done as follows: Using a sheet of cross-section paper,
mark off the limits of a 26 x 26 square; write the normal alphabet
across the top, so that each of its letters will govern a column; and
write it again along one side, so that each letter will govern a row.
For added convenience, these two alphabets may be repeated, as they
are shown in the figure. Now, remembering that each letter in the
text is the first letter of a digram (except the two which are
finals), our two texts, with their total of 235 letters, are to
provide a count on 233 digrams. Taking letters one by one, just as
they come in the cryptograms, find each letter in the upper alphabet;
find, in the side alphabet, the letter which immediately follows it
in the cryptogram, and count this digram by placing a tally-mark in
the cell at which the column and row governed by these two letters
are found to intersect. In the figure, the tally-marks have been
replaced with numbers showing their totals. It will be noted that the
process described is identically the method which would have been
used by Meaker in preparing the digram chart; and, just as in the
case of the digram chart, the counting of the digrams has
automatically counted the single letters. To obtain their frequencies,
we may total either the columns or the rows, taking the larger figure
in those few discrepancies caused by initial or final letters. With
the chart understood, the digram-method of solution can be shown in a
nutshell.
An inspection of this chart enables us to find quickly that the
leading digrams are those listed: _RK_, _VT_, _KV_, _DY_, etc. These,
almost certainly, are the substitutes for digrams ranking high on the
normal list, and many others, having a frequency of 3, are very likely
indeed to be substitutes for digrams from that same high-frequency
class. Our text, of course, is still short, even with 235 letters,
and we do not invariably find, in texts of this length, that the
ranking digram (in this case _RK_, frequency 10) is the substitute
for _th_, though the chances are, at all times, that it is. And
should it prove here that _RK_ does not represent _th_, then we may
be quite sure that _th_ is represented in one of the digrams _VT_,
_KV_, _DY_, having the next frequency, 6. With the single exception
of _RR_, each digram of the nine which are listed below the chart can
be checked against three other digrams: Its own reversal; the doubling
of its first letter; and the doubling of its second letter. In
addition, it may be checked through the individual frequencies of its
two component letters. These points of comparison, made for each of
the nine leading digrams, have been tabulated in Fig. 69, so that the
discussion may be easily followed.
Examining _RK_, assumed to represent _th_: Its reversal, _KR_, has
not appeared on the chart, which is satisfactory for a digram of no
greater frequency than its supposed original, _ht_. The doubling of
its first letter, _RR_, has appeared four times, which is satisfactory
for _tt_, one of the leading doubles of our language. The doubling of
its second letter, _KK_, has not appeared, which is eminently
satisfactory for a digram as rare as _hh_. Its first letter, _R_, has
a frequency of 28, the highest in the cryptogram, which is not at all
unusual in the case of _t_; and its second letter, _K_, has a
frequency of 16, a little high for _h_, but not unsatisfactory. Thus,
we find nothing, so far, to contradict the supposition that the
digram _RK_ is the substitute for _th_. But if _K_ represents _h_, it
should be possible to find digrams beginning with _K_ which will
check equally well as the substitutes for _ke_ and _ka_. We do, in
fact, find _KV_ and _KS_. But which is which? Examination of Fig. 69
shows that one of these, _KS_, has a reversal, _SK_, frequency 1; but
this is not informative, since it would be equally expected of _eh_
or _ah_. Further examination shows that _V_ has been doubled, which
is far more characteristic of _e_ than of _a_. Also, the individual
frequency of _V_, 24, is the second highest in the cryptogram, and
more likely to be that of _e_ than that of _a_. Thus we may assume
that _KV_ represents _he_ and that _KS_ represents _ha_. This
automatically identifies the digram _SR_ as _at_. As to _VT_, this,
apparently, involves the only reversal of any prominence in the
cryptogram. Its first letter has already been identified as _e_, and
the outstanding reversal of the language is _er_-_re_. This is not so
certain as in the preceding cases, but the frequency of _T_ is
satisfactory as that of _r_.
Thus we have identified the letters _t_, _h_, _e_, _a_, _r_, which is
as far as the tabulation has been carried. Having the substitute for
_h_, we may now bring in the vowel-solution method through examination
of digrams _KD_, _KJ_, _KT_, _KZ_; or continue with the
digram-solution method by looking over the field for some of the other
_h_-digrams: _sh_, _ch_, _wh_, _ph_, _gh_, and so on. The first of
these should be easily identified by the frequency of _s_, and, in
addition to the regular three check-digrams, we might check this
against a possible _st_, another of our leading English digrams. With
the process explained, we need not go further; the substitution of
letters _t_, _h_, _e_, _a_, _r_, _s_, will surely break any simple
substitution cryptogram. Possibly, enough has not been said as to the
use of the trigram list, the consideration of common affixes, common
short words, and so on; but these are all points which the student
can best develop for himself.
Figure 69
Digram Doubled Letter Letter Frequency Supposed
Identity
Original Reversed 1st 2d 1st 2d
R K 10 K R... R R 4 K K... R 28 K 16 t h
V T 6 T V 2 V V 1 T T... V 24 T 15 e r
K V 6 V K... K K... V V 1 K 16 V 24 h e
D Y 6 Y D... D D... Y Y... D 2l Y 10 ?
W D 4 D W 1 W W 1 D D... W 8 D 2l ?
S R 4 R S... S S... R R 4 S 18 R 28 a t
K S 4 S K 1 K K... S S... K 16 S 18 h a
R R 4 .... .... .... R 28 t t
H V 4 V H... H H... V V 1 H 5 V 24 ? (-e)
Another point, however, must not be overlooked: _the long repeated
sequences_ _HVXXU_, _ZDYFZJX_, _DRKVT_, _GSRRVT_. Repeated sequences
of these lengths will usually come from _repeated whole words_, making
it possible, to some extent, to attack the cryptogram by word-division
methods. It is, in fact, the repetition of sequences, these and many
others, which, in the beginning, has led us to assume that both
cryptograms are using the same key. As to the recovery of this key, we
need not wait until solution is complete. Even in simple substitution,
it is well, during the identification of substitutes, to have before
us a sort of skeleton key, in which the plaintext alphabet has been
written out in normal order, so that the substitutes, as fast as
their identities are discovered, can be placed below their originals.
Thus, having identified as many as twelve letters in our present
cryptogram, this skeleton key, or framework, might begin to assume
the appearance which is indicated in the upper tabulation of Fig. 70.
Here, we are able to note a reciprocal encipherment between _A_ and
_S_, _F_ and _N_, _R_ and _T_, and _U_ and _Y_, suggesting that the
whole encipherment may have been reciprocal; if so, we have the
identities of four additional substitutes: _O_, _I_, _H_, _E_,
representing _d_, _j_, _k_, _v_, respectively. If they are present
in the cryptogram, these four substitutions may be tried; but with
or without their presence in the cryptogram, they can be added to the
skeleton key, as in the lower tabulation of the figure. Notice that
when this has been done, the cipher alphabet is beginning to show
alphabetical sequences (reversed). We find _H I J K_, and, just
before this, _D F_, which is an alphabetical sequence if the letter
_E_ has been taken out for use in a key-word. Between _DF_ and _HIJK_
of the cipher alphabet, we need only _G_ to fill out the sequence;
therefore either _l_ or _m_ must belong to the key-word; comparing
this with what is found at the other end of the sequence, we find
that either _L_ or _M_ would be the substitute for _g_. Between _NO_,
we find _V_, evidently misplaced; and, following _O_ and preceding
_S_, we find two positions which may be occupied by two of the
letters _PQR_, of which _R_ has already been placed (under _t_). That
is, where the encipherer has used a key-word-mixed alphabet without
troubling to carry it through a transposition process of any kind, we
are often able to build it up again, and make it help us in the
solution. This is especially true if he has used reciprocal
encipherment; with the substitutes which may actually be found in our
foregoing cryptograms, a little rearrangement is all that is needed
in order to discover exactly what the original key was. When the
cipher alphabet has been carried through a transposition block, it is
not so easy to recover during the actual process of solution;
afterward, however, it is not usually difficult to treat it by one of
the transposition processes, just as if it were a transposition
cryptogram of 26 letters. In the examples which follow, the
key-word-mixed alphabets were used as they stood, though we believe
that none of the encipherment was reciprocal. In one case, however,
the plaintext and cipher alphabets were both mixed, according to
different key-words, so that the recovery of this key may prove
troublesome.
Figure 70
Supposing 12 substitutes to have been identified:
Plaintext alphabet: a b c d e f g h i j k l m n o p q r s t u v w x y z
CIPHER ALPHABET: S V N K J F D T A R Y U
Assuming reciprocal substitution:
Plaintext alphabet: a b c d e f g h i j k l m n o p q r s t u v w x y z
CIPHER ALPHABET: S O V N K J I H F D T A R Y E U
Q?P? * L? G? C?B?* * T?
M?
45. By PICCOLA.
S C Y J T O P N R M J T U E A W S R O R O A E P Q R J C R O A R M P H
Q K J Q S R S J H A X P F K E A Q R M Y S R P Q P M P S E C A H G A W
S R O P E E E S H A Q O P V S H I R O A Q P F A E A H I R O P H N P Q
R J H T F U A M C J M R Y R O M A A W A E E B T Q R W M S R A S R J H
A I M J T K U A E J W P H J R O A M P H N Q A A W O P R Y J T Q A A L.
46. By PICCOLA. (Plaintext and Cipher Alphabets have each a key-word).
J C W E H S N D F S B N J I V T E A G V D H O C Q Q I Q F R P H F K Q
E A R F Q A R F A H F Q E J C B N J N H B E O C B N L N O V H B L F Q
J B N A B L F V H C A J I V B N W N S T B L E A G V A J N S R F W N S
Y R V S S C A E H V A Q F C J E A G J N A W N S O V B V C Q Y D C S P
H E H O C S P E A G B E O N A F R L C A G N E A K C S O N S H A C B E
F A C Q X.
47. By PALOMITA. (No key-word).
B O Y B A N K I L L A P K R I Y A P Y Y U P B L Y E R P B P L G Y G M
H L A B O Y K J A K L P Y L H H J A C R P O R C Q U Y N B H L A B O Y
G N A Z N Y L H B O Y K N A N P R B R W O J C B R C Q D N P K.
48. By PICCOLA. (Of these two, one has normal word divisions; the other has not).
W T E I C H E P P C A E P T J W P O Y D Q P R M E L U E I N D E P Q T C
Q D Q D P C P D H K G E P U O P Q D Q U Q D J I C. I S Y E Q T C P V E M Y R
E W M E K E C Q E S P E L U E I N E ? P D Q H U P Q C G P J T C V !
E O E E I Q M C I, P K J P E S X Q T E Q M C I P K J P D Q D J I D P U P U
C G G Y J R Q T E V E M Y P D H K G E P Q F D I S.
49. By PICCOLA.
P B K L A B E I C D J D B I L Y P K L D O I X L Y I P K V Y A L ?
A G F Y A M I L K L Y I K I D C A G G L D O I X V D J R K L Y I C P B R P B N
X D Q A J I ? Q K J I S P B R K L Y A L A B R M X Q F P L F P E O L D
I B R V Y P E Y O B D V X D Q P C E G I A J F I J C I E L G X P K
S I A B P B N P L K. A J P K L D E J A L A B B D L P K L Y P K B D !