From FLYNN's September 4, 1926

# SOLVING CIPHER SECRETS

Edited by M. E. Ohaver
A PROFITABLE LESSON ON THE SOLUTION OF A CRYPTOGRAM
IN AN UNKNOWN CIPHER SYSTEM-ALSO READER CIPHERS

O solve a cryptogram in a known cipher system, it is only necessary to apply methods peculiar to that cipher. But suppose the system is unknown. How, then, would it be possible to determine the method of solution?

That the fans are much concerned with this question would seem to be indicated by the volume of mail from readers who state that they have successfully used the different methods described in these columns for various ciphers, but who wonder if there is any way of finding what method to use when the cipher is unknown.

Fortunately, in many cases a cipher will leave an indelible impress on a cryptogram, allowing the system to be identified, or, at any rate, to be recognized within limits, by certain more or less easily recognizable characteristics.

Sometimes these peculiarities are distinguishable at sight. To illustrate this, consider the Nihilist numerical cipher, the numbers of which are within the limits 22 and 110.

To determine a cipher system in this way is somewhat like identifying a man on the street by the color of his eyes or hair; by a missing right index finger; or by a mannerism of gait or gesture.

On the other hand, the peculiarities of a cipher may be so unapparent as to require the application of delicate cryptographic tests to discover their presence.

If a comparison is again allowable, this would be like identifying the man by his Bertillon measurements, or by his fingerprints.

To demonstrate the practicability of these tests, we have applied some of them in this article to a cryptogram that was submitted to this department without solution or explanation.

This cryptogram was chosen from many similar ones for several reasons. In the first place, it illustrates all the points brought up by the various tests. Again, it happens to be in a standard system that we wanted to present to our readers, anyway. And, finally, the fact that the inditer was absolutely certain his specimen could not be deciphered—an opinion he no longer holds—adds zest to the problem.

The cipher was submitted through another reader of FLYNN'S WEEKLY, who accompanied it with the following letter.

DEAR SIR:

I inclose a message written in cipher. This was made up by a man who has used the same for private messages.

He claims his cipher cannot be solved. For you, and your department, I accepted the challenge, and am sending on the message.

SAM'L J. MCNARY.

Cincinnati, Ohio.

Things begin to look interesting already. Suppose we have a look at the cryptogram Itself?

```o l j m e p p r q v h o i j
m z p h x z u w v b h n a u o -
l v u o h p h a b k s k l e
t l u l v b f b w o p w t p
h o u v r y u c x b b a t d
z b q p y a a t j d e y i a p
f k k k o k r g c u t q o a k
p y i r j p w o f b k o h w
t p d g j d z.—```

The several tests about to be given involve the number of limes various cipher characters are used. Accordingly, a table of their frequencies is herewith appended:

```A 8    H 7    O 10     V S
B 8    I 3    P 11     W S
C 2    J 5    Q 3      X 2
D 4    K 8    R 4      Y 4
E 3    L 5    S I      Z 4
F 3    M 2    T 5      ———
G 2    N I    U 7      122 ```

Had this cryptogram been one of numbers or signs, we could have at once assiuned that it was of the substitution variety. Since it is literal, however, it can be one of either the substitution, transposition, or null class, not to mention combinations of these.

If our specimen is a transposition cipher, it will react positively to the vowel-consonant group test, given by Parker Hitt in his "Manual for the Solution of Military Ciphers," a work formerly published by the Army Service Schools Press, Leavenworth, Kansas , but now, unfortunately, out of print.

This test is based on the fact that in average English text the total frequencies of the vowels AEIOU, and the consonants LNRST and JKQXZ, will ordinarily not vary more than 5% one way or the other from 40%, 30%, and 2%, respectively, of the total number of letters. The figures have been obtained by countless experiments.

A common method of applying the test is to first count the vowels directly from the cryptogram, not taking the consonant counts unless the vowel count falls within the prescribed 35%-45% limits. For illustrative purposes, however, the counts for al l the groups are given herewith in this instance.

```A  8    L  5    J  5
E  3    N  1    K  B
I  3    R  4    Q  3
O 10    S  1    X  2
U  7    T  5    Z  4
31      16      22
(25.4%) (13.1%) (18.0%)```

A difference of more than 5% in any group from the 40%-30%-2% averages could be taken as evidence that the cipher is not of the transposition class. Here all three groups are outside their respective limits, rendering such a conclusion even more probable.

Having thus disposed, apparently, of the transposition possibility, we will now proceed to discover if the cipher is of the substitution class; and, if so, whether the characters are fixed in their values as in the simple substitution cipher, or variable as in multiple alphabet and other varieties of substitution ciphers.

In the simple substitution cipher, where a given character always represents the same letter, quite frequently the number of different characters in a cryptogram will be less than twenty-six, since one or more letters of the alphabet are often unused even in long messages.

A peculiarity, however, of ciphers employing characters of variable values, is that almost always all of the characters will be present even in short cryptograms. The present cipher would thus seem to be one of this kind, using, as it does, all twenty-six letters, presumably the whole number of characters employed by the cipher.

Another characteristic of the simple substitution cipher is that repeated words will at each recurrence be represented by the same cipher characters. The present cryptogram, as shown, contains a number of two-letter recurrent groups, and one of three letters, but none of any greater length, which would be likely if the cipher were of the simple substitution type.

Another aid in recognizing the variable substitute cipher is that ordinarily it affords no characters of either extremely high or low frequencies, corresponding respectively to the substitutes for E, T, A, O, N, et cetera, and J, K, Q, X, Z, et cetera, of the simple substitution cipher; the tendency being, on the other hand, for all characters to approach an average frequency of (100% ÷ 26 letters = 3.85%) approximately 4% for each character.

This being so, we are able to offer the following test, based on the fact that the combined frequencies of the five most used letters, ETAON, comprise approximately 45% of all letters in average English text. In the simple substitution cipher the five most used characters will either represent the above five letters, or other letters of practically the same frequencies, whose total will thus approximate 45% of all the characters in the cryptogram.

In variable substitute ciphers, however, where a given character can represent several different letters, and a given letter can have several substitutes, the combined frequencies of the five most used characters will fall below the 45% average, approaching (5 letters × 3.85% = 19.25%) approximately 20% as a limit.

The following comparative table shows the five, most used letters, ETAON, with frequencies taken from the table of 10,000 in FLYNN'S WEEKLY for January 23, 1926, and the five most used characters, POABK, of the present cryptogram.

```E  1251      P  11
T   950      O  10
A   806      A   8
O   800      B   8
N   712      K   8
4519         45
(45%)     (36.8%) ```

The total of 45 characters is 36.8% of 122, the whole number of characters in the cryptogram. The nearer this total approaches 20% in any given cryptogram, the more probable does it become that the cipher is not of the simple substitution type.

The difference of 8% in this case is not as large as might be, but, taken with what follows, it is still sufficient to eliminate simple substitution and null ciphers.

The above test may also be extended to the five least used characters, if care is taken to assign a frequency of zero to any characters not used in a given cryptogram. The combined frequency in the variable substitute cipher will in this case be more than 2%, approaching 20% as a limit. In applying these tests due allowance must lie made where substitutes for the word-space, punctuation marks, figures, and so on, may have been used.

Having eliminated the simple substitution cipher we will next investigate the possibilities of a variable substitute system.

At this point it is necesary to mention that such ciphers are legion. Some of them, for example the Vigenère chiffre carré, the Gronsfeld, and Saint Cyr ciphers, use a fixed series of alphabets, determined by a short key.

In others, the fixed series of alphabets is avoided by using a continuous and non-repeating key; or, as in autokey ciphers, by allowing the letters of the message itself to determine the alphabets.

Again the cipher may be based on digraphs, as is the Playfair cipher, for example, in which each letter can have five substitutes, and each substitute can represent any one of five letters, depending on the letter with which it is paired.

However, this multiplicity of classes and types can hardly be more than mentioned here. For the present we must content ourselves with following up the main stream to only one of its many branches, reserving the others for later exploration.

One method of finding if our cipher uses a fixed series of alphabets is to apply the Kasiski test for recurrent groups, described, in detail in FLYNN'S WEEKLY for August 7.

Should this test result negatively, some other type of variable substitute would probably be indicated. It is evident, however, from an inspection of the subjoined table of recurrent groups in the present cryptogram, that a series of ten alphabets has been used.

```OL   29− 1 = 28     FB   110-50 = 60
JM   14− 3 = 11     WO   l05-52 = 56
HO   58−11 = 47     PW   107-54 = 53
PH   33−17 = 18     WTP  115-55 = 60
PH   57-17 = 40     AT    78-69 =  9
PH   57-35 = 22     DZ   121-71 = 50
VB   48-23 = 25     PY   102-75 = 27
UO   32-28 =  4     JD   120-80 = 40
LV   47-30 = 17     YI   103-83 = 20
OH  113-33 = 80```

Our cryptogram is accordingly transcribed, as shown, in lines of ten letters, by which arrangement all the letters in any alphabet are thrown in the same column. While we have thus isolated the characters enciphered in each alphabet, we still know absolutely nothing of the structure of these alphabets.

Given sufficient material, such alphabets can be resolved regardless of their complexity. But here we have only a few letters from each alphabet; not enough to solve an unknown mixed alphabet by a general method. An assumption as to the form of the alphabets, and their relationship, is therefore necessary.

Since ciphers of the Vigenère type are most generally known, more than likely the alphabets are of that variety. If so, a solution can readily be effected by guessing at a word of the message.

The most fertile ground for speculation along these lines is the longest recurrent group, WTP, which more than likely signifies one of the most used trigraphs. According to Valerio. these are: THE, AND, THA, HAT, EDT, ENT, FOR, and so on.

Suppose that we assume that WTP = THE.

In the Vigenère cipher this would require the key letters DML. These are unlikely, since they do not form part of a word. But they can be definitely rejected for the reason that they will not decipher any other series of three letters in columns 5-6-7.

The Vigenère square, however, can be used in many ways not prescribed by its originator. Suppose, for example, in searching for a method that will produce a likely sequence of key letters, that WTP and THE be taken from the sides, and the key letters from the body of the square.

This plan will give the key letters PAT, which, upon trial, produce probable sequences in columns 5-6-7 throughout the cryptogram.

Further suppositions may now be made as to additional letters of the key, as well as other letters of words of the message. For example, the first WTP is preceded by OP, and the second by OH. These are probably two-letter words, whose initial letters are identical, as, for instance, BE-BY, IF-IN-IS-IT, or OF-ON-OR.

The words OF and ON, tried respectively with OP and OH in the cipher, both give the key letters CU, which give good sequences in columns 3-4, expanding the key to -CUPAT---.

The rest of the cryptogram can be similarly deciphered. Thus --TILLE--- in line 1 is obviously ARTILLERY. And -EMPLO--- in line 9 is probably some form of the word EMPLOY. In this way the whole key, OCCUPATION, is developed. An interlinear translation of the message is subjoined.

```
1  2  3  4  5    6  7  8  9  10
———————————————————————————————
O  C  C  U  P    A  T  I  O  N

O  L  J  M  E    P  P  R  Q  V   10
A  R  T  I  L    L  E  R  Y  S

H  O  I  J  M    Z  P  H  X  Z   20
H  O  U  L  D    B  E  B  R  O

U  W  V  B  H    N  A  U  O  L   30
U  G  H  T  I    N  T  O  A  C

V  U  O  H  P    H  A  B  K  s   40
T  I  O  N  A    T  T  H  E  V

K  L  E  T  L    U  L  V  B  F   50
E  R  Y  B  E    G  I  N  N  I

B  W  O  O  W    T  P  H  O  U   60
N  G  O  F  T    H  E  B  A  T

V  R  Y  U  C    X  B  B  A  T   70
T  L  E  A  N    D  S  H  O  U

D  Z  B  Q  P    Y  A  A  T  J   80
L  D  B  E  A    C  T  I  V  E

D  E  Y  I  A    P  F  K  K  K   90
L  Y  E  M  P    L  O  Y  E  D

O  K  K  G  C    U  T  g  O  A   100
A  S  L  O  N    G  A  S  A  N

K  P  Y  I  R    J  P  w  O  F   110
E  N  E  M  Y    R  E  M  A  I

B  K  O  H  W    T  P  D  G  J   120
N  S  O  N  T    H  E  F  I  E

D  Z
L  D```

Message: "Artillery should be brought into action at the very beginning of the battle and should be actively employed as long as an enemy remains on the field.''

The cipher employed in this instance was devised in 1857 the English admiral. Sir Francis Beaufort, K. C. B. It is commonly known as the Beaufort cipher, and several editions of it have been published.

It was observed by August Kerckhoffs that Beaufort, in using the central square for key letters instead of cipher letters as in the Vigenère, provided an altogether different cipher from the latter, the alphabets being in reverse instead of normal order.

This is illustrated in the subjoined P alphabets of these two ciphers.

```Text:     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
Vigenère: P Q R S T U V W X Y Z A B C D E F G H I J K L M N O
Beaujort: P O N M L K J I H G F E D C B A Z Y X W V U T S R Q```

The cipher is thus identical in results with the United States army cipher disk, illustrated in Webster's New International Dictionary.

Kerckhoffs also observed that the Beaufort alphabets were similar in structure to the reciprocal substitution alphabets of the Porta cipher, an early system yet to be described here. The Beaufort P alphabet, in the Porta arrangement, is as follows:

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

Beaufort facilitates the use of his table, shown herewith, by increasing the number of rows and columns to twenty-seven. All four sides of the square are thus exactly alike, which permits the user to enter any side he pleases, follow the row or column to the key letter, and leave the square at either of the adjacent sides.

```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
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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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```

Having thus proved that the supposedly impossible was possible after all, we sent our correspondent, Mr. McNary, the key word, stating—all this occurred some time ago—that before long a method of solving a similar cipher would be given in FLYNN'S WEEKLY; and making so bold as to predict that his friend, who had prepared the present cryptogram, would not only be convinced that such ciphers could be solved, but also that he would easily be able to solve them himself.

The article referred to was printed in the February 20, 1926, issue of this magazine. And, true to our expectations, a few days later we were in receipt of the solutions to the two Vigenère ciphers in that issue, along with the following letter:

DEAR SIR:

I am the party who sent you through Mr. McNary last September a sample of a cipher which I was certain was absolutely safe, and which I had employed for years with the confidence of a backwoodsman.

And now?

You have taught me a most valuable lesson through your department, and I thank you profusely.

I find it again profitable to consider also the other fellow's opinions.

Yours very truly,

FRED WALTHARD.

Cincinnati, Ohio, Feb. 23, 1926.

In answer to this we may say briefly that we are always glad to be of service to any of our readers.

At this point we must remark that the present analysis has been made complete as it is only to familiarize the reader with a general procedure for a wide variety of unknown ciphers.

To the experienced eye, the predominance of seldom used letters eliminates the transposition cipher at sight.

The lone three-letter recurrent group, with its sixty-letter interval, stands out to the retentive memory at the first reading as Strong evidence of a multiple alphabet cipher.

Discovery of the key letters PAT, by applying THE to WTP, and determination of the period by trying PAT at critical intervals of five and six letters, is but a matter of minutes.

Indeed, it may be stated without exaggeration that a cryptogram like this can be deciphered almost as quickly without the key as with it.

Thus have we outlined, as far as possible in a single short article, a plan of analysis that will enable the reader to determine the type of an unknown cipher, and its method of solution.

And accordingly we are saying absolutely nothing about the following two cryptograms.

The solver only needs to place them in his cryptographic test tubes, use the proper cipher reagents, and observe the resultant reactions.

These will tell the story.

CIPHER No. 1.

```MYAEW  HNOTD  ILEAN  LARIE  IEHMT  FSVKO  EARLA  ETNNE
OSEPH  TEVRO  NNUIT  DSSEA```

CIPHER No. 2.

```What are you doing to execute the instructions sent you to HCDLLVW XMWQIG KM
GOEI DMWI JN VAS DGUGUHDMITD. If success will be more certain you can substitute
EJTFKMPG OPGEEVT KQFARLF TAG HEEPZZU BBWYPHDN OMOMNQQG
by which you may effect O TPQGEXYK above that part HJ OPG KWMCT patrolled by
the ZMGRIK GGJUL CW EWBNDLXL.```

Some novel ideas are offered in the following selection of ciphers submitted by readers of FLYNN'S WEEKLY.

Several of these are based on the International Morse telegraph alphabet. Just -which ones these are we will leave our readers to discover for themselves. However, a copy of the Morse alphabet is appended herewith for the convenience of those not familiar with it.

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

Such of these ciphers as are not based on this alphabet should, unless otherwise mentioned, be readily solved with the aid of the present article.

No. 3 hails from Silverton, Oregon. Look, it over, fans!

CIPHER No. 3 (Rudolph O. Casperson).

```O I G M V O L Q P W G D I M I
K T B W L P V K W P V Z X J B
Z W Z Q W V R T V V K F L R E```

Now take a whack at No. 4, of Toronto, Canada, vintage. Mr. Bell writes that his cipher "is liable to fool quite a number of fans." How about it?

CIPHER No. 4 (W. R. Bell).

```A girl to see to was B stay i am No T i aRe
Me oO A on PYK So oN aLoe KL MEN rOT
sos z WhEn ARE You e zKC went to WoRk
gone is one CoP To THE dEP Ot T ebri n
gBA CKH iSp rIso Ner SEN gumS s oRe.```

No. 5, submitted by a Brooklyn, New York, fan, is also about as good as they come. And if you get it you're good, too!

CIPHER No. 5 (Frank N. Dodd).

```90845  26715  39485  71950  72954
79653  82870  64850  15069  30081
73546  77289  09276  37851  59749
02846  60107  36985  47213```

The next cipher, a clever one from Tompkinsville, New York, can be read at sight if you know the system. Try to discover it.

CIPHER No. 6 (Carlton Beil).

```and gyp open drip an go pyt og gaps in jump
into a apt is not spot as pay t opyn do page
gap in ye pyt ug spin qyp gage pig jyp go t
any sea a set ye pyg jap a jogg.```

No. 7, submitted by Mr. John Q. Boyer, Baltimore, Maryland, a former president of the National Puzzlers' League, and a newcomer to these pages, requires a few words of explanation.

Mr. Boyer has attempted a "double cipher," that is, one having two sets of words for a solution, somewhat similar to one published several years ago in the Waverly Magazine.

Each number of the present cipher signifies two different letters. The legitimate translation, using one set of letters, forms a complete sentence. The parallel translation, using the other set, consists of all-dictionary words, which do not, however, form a sentence.

CIPHER No. 7 (John Q. Boyer).

```4-5   10-5-10   9-1-10-4   2-5-8   6-5-9   1-9
5   3-1-10   3-1-10   9-1-9-1   2-5-4   5-10
8-1-10-4   10-1-1-8   8-5-9-1```

Our readers who are always inquiring about books and articles on cryptography will be glad to learn that Mr. Boyer is the author of an article, in part about ciphers, in the "Key to Puzzledom," the text book of the above mentioned league. This book also contains a special article on the construction and solution of the National Puzzlers' type of cryptogram, examples of which are printed in each issue of The Enigma, the official organ of the organization.

## SOLUTIONS TO PREVIOUS CIPHERS

How did you make out with the Saint Cyr ciphers in FLYNN'S WEEKLY for August 7?

In No. 1 the recurrent group ZBR, at the 1st and 31st letters with an interval of 30, and GHQ, at the 27th and 78th letters with the interval 51, are alone sufficient, since they both have 3 as a common divisor, to indicate three alphabets.

The 91 letters of the cryptogram, divided among these three alphabets, gave about 30 letters for each alphabet, ample to determine the key word, GUN, by the method given, thus unlocking the message: "The enemy losses have been heavy and they have nearly exhausted their supplies of ammunition and provisions."

No. 2, although lacking In recurrent groups of more than two letters, had plenty of the latter, fixing 6 as the period, or number of alphabets. The cryptogram, consisting of 232 letters, thus gave nearly 40 letters for each alphabet, making it fairly easy to get the key word, FRANCE. The text in this instance was a sentence from Edgar Allan Poe:

As we can scarcely imagine a time when there did not exist a necessity, or at least a desire, of transmitting information from one individual to another in such a manner as to elude general comprehension, so we may well suppose the practice of writing in cipher to be of great antiquity.

Now for the rest of the August 7 ciphers. No. 3 (William Bellamy) was put in cipher by using the Vigenère table in the February 20, 1926, issue of FLYNN'S WEEKLY. The Beaufort table in this issue will also serve the purpose.

This cipher is of the autokey variety, based on the Vigenère system. Mr. Bellamy appends his own explanation.

"Any letter of the message," writes Mr. Bellamy, " when its next previous letter is known, will be found in the line which begins with that letter, and in the column headed by the letter to he deciphered. It is necessary that some next previous letter of the message should be known. In this instance it is the letter Q, supposed to be secretly communicated as beginning the message."

The message, wholly made up of short words intentionally, is a bit of advice from one Nihilist to another:

If ever we are put in quad, you may find that you can hear me rap. But we must not talk in code. For if we do, be sure they will hear, and jot down all our taps, and thus in time learn to read them. But if we had kept mum, we might later have been able to use our code in case of great need.

Cipher No. 4 (F. Baldwin) carried the message: " Get him at once or he will cause trouble for us." The cipher was of the null variety, with the significant letters indicated by the numerical key 1-2-3-4-5, thus:

```1 2   3    4      51  2   3 ...
Gee ant fish at brim bad at ...
G E   T    H      IM  A   T ...
```

The next one. No. 5 (Geo. A. Lauh), was based on the following simple substitution alphabet formed on the key word HARDEN, the name of the officer to whom the message was addressed.

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

Here H=L, L=H; A=M, M=A, et cetera, the alphabet being similar to that used in the Porta cipher mentioned in this article. The message conveyed to Captain Harden was: "Troops landing at Waianea marching towards Kolekole pass." The italicized words are Hawaiian geographical terms.

In cipher No. 6 (Joseph Murray), based on the subjoined alphabet, the two figures representing a given letter are separated by a dash in the cryptogram. Thus 4-52-33-04-41—really is 45 (T), 23 (H), 30 (I), 44 (S). The alphabet:

```A 10  E 20  I 30  O 40  U 50
B 11  F 21  J 31  P 41  V 51
C 12  G 22  K 32  Q 42  W 52
D 13  H 23  L 33  R 43  X S3
M 34  S 44  Y 54
N 35  T 45  Z 55```

The key to No. 7 (Austin Minette), a modified Gronsfeld, was 20-7-18. This cipher is similar to the Gronsfeld with the exception that the key numbers are not limited to a single digit, and the count is backward in the alphabet instead of forward. A portion of Mr. Minette's message: "This code is taken from the story, 'The Giant Raft,' by Jules Verne—" is appended for illustration.

```Key:      20-7-18   20-7-18 20-7-...
Message:   T H  I    S C  O  D E ...
Cipher:    Z A  Q    Y V  W  J X ...```

No. 3 (Charles P. Winsor), the free subscription cipher in FLYNN'S WEEKLY for July 3, is based upon the use of the following two numerical alphabets. Mr. Winsor does not claim to have originated this system, having taken it from P. I. E. Valerio, a French writer on cryptography, who proposed it as an economical method of telegraphic communication.

```A  1 027   J  10 170   S  19 513
B  2 054   K  11 207   T  20 540
C  3 081   L  12 324   U  21 567
D  4 108   M  13 351   V  22 594
E  5 135   N  14 378   W  23 621
F  6 162   O  15 403   X  24 648
G  7 189   P  16 432   Y  25 675
H  8 216   Q  17 459   Z  26 702
I  9 243   R  18 486```

Mr. Winsor's message was : "If General Hooker's army remains inactive you can leave two brigades to watch him and withdraw with the three others. But should he not appear to he moving northward, I think you had better withdraw this side of the mountain to-morrow night."

In enciphering, the letters are taken in pairs, as shown at (a). The values of the first letters of these pairs are now substituted from the 1-to-26 alphabet, and those of the second letters from the 027-to-702 alphabet, as shown at (h) and (c).

The two numbers thus representing a given pair of letters are next added together, as in line (d), and finally regrouped by sixes, as at (e), completing the process.

```(a)  IF   GE    NE   RA   LH   OO ...
(b)   9    7    14   18   12   15 ...
(c)  162  135  135  027  216  40s ...
(d)  171  142  149  045  228  420 ...
(e)   171142    149045    228420  ...```

We expect to take up methods of solving ciphers based on digraphs in later issues, and regret that we have not the space to offer any suggestions here. We regret also that exigencies of space necessitate the holding over of our list of May 22 solvers until the next installment of Solving Cipher Secrets.