FTENTIMES a cryptogram may be so short that—depending, of course, on the relative complexity of the cipher — its solution becomes a difficult matter, if not altogether an impossibility.
In such cases decipherment can often be materially simplified if a number of cryptograms in the same key are available. With one exception, noted below, all the methods so far discussed in this department have depended upon the analysis of a single cryptogram.
In some instances single cryptogram methods may be used with a number of messages, the added effectiveness being due to the increased bulk of material. On the other hand, some of these multiple message methods are peculiarly adapted to a number of cryptograms, not being applicable to the resolution of a single example.
A certain insight into multiple cryptogram methods has already been afforded readers of FLYNN'S WEEKLY in the issue of July 3, where a method was given applicable to the solution of a number of transposition cryptograms in the same key.
In this article for the first time we will actually consider the solution of a number of cryptograms. The cipher selected for this purpose is one of the numerous variants of the famous Vigenère alphabetic square, being that given by John Wilkins—afterward Bishop of Chester—on pages 72 to 76, inclusive, of his " Mercury, or the Secret and Swift Messenger," an early work on cryptography published in London in 1641.
This form of the cipher uses the same type of alphabet as its famous original, and is identical in its results, but holds one advantage, at least, over it, in that instead of requiring a ready-made table of the whole number of alphabets, it employs a special table, formed of just those alphabets selected by the key word.
For example, if the key word TRY be agreed upon, the table will consist of three alphabets, one beginning with each letter of the key. The alphabets used by Wilkins consist of but twenty-four letters, J and V being omitted. For in the English alphabet of that time the letters I and J were used interchangeably, as were also U and V. Here, however, the full twenty-six letter alphabet is employed.
(Message 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
T 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
R 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
Y 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
(Cipher alphabets)
Now, to encipher any message, as the short example given at (b), write a letter of the key above each letter of the message, taking both in their order, and repeating the key as the length of the message may require, as shown at (a):
(a) Key: TRYT RY TR YTRY (b) Message: MEET ME AT ONCE (c) Cipher: FVCM DC TK MGTC (d) Regrouped: FVCMD CTKMG TC
The key letter above each text letter,iow indicates the alphabet in which it is to be enciphered. For example, the first letter of the message, M, is to be enciphered in the T alphabet, its substitute in that alphabet being F, which is accordingly placed below M in line (c).
Similarly, the second letter, E, of the message becomes V in the R alphabet. The third letter, also an E, becomes C in the Y alphabet; and so on. The cryptogram for MEET ME AT ONCE, with the key TRY, is thus FVCM DC TK MGTC, as shown at (c).
As described by Wilkins, the normal word divisions are observed in the cryptogram. In the present day, however, the customary procedure would be to regroup the letters, preferably by fives, as shown at (d).
In passing, it must be mentioned that Wilkins also suggests the use of mixed alphabets in this cipher instead of the straight A-to-Z arrangement, and the change of key letter with each word or line instead of with each letter. The resolution of mixed alphabets will he taken up later.
But both the other devices could easily he solved by " running down the alphabet."
Suppose, for example, that the key letter he changed with each word, thus:
(a) Key: TTTT RR YY TTTT (b) Message: MEET ME AT ONCE (c) Cipher: FXXM DV YR HGVX (d) Regrouped: FXXMD VYRHG VX
To solve this, it is only necessary to write the alphabet—all twenty-six letters if required—after each cipher letter, taking care to preserve the columnar arrangement, the cryptogram itself constituting the first column. The letters forming any word of the message will then appear in a single column, under the key letter by which it was enciphered.
(Key)
Z Y X W V U T S R Q P ...
F G H I J K L M N O P Q ...
X Y Z A B C D E F G H I ...
X V Z A B C D E F G H I ...
M N O P Q R S T U V W X ...
D E F G H I J K L M ...
V W X Y Z A B C D E ...
Y Z A B C D E ...
R S T U V W X ...
H I J K L M N O P ...
G H I J K L M N O ...
V W X Y Z A B C D ...
X Y Z A B C D E F ...
Of course, if a whole line of the cryptogram is enciphered in the same alphabet, or if normal word divisions are observed, decipherment by the above method is still easier.
Now that the reader is acquainted with the system, it is well to produce the cryptograms he is expected to decipher. To increase the interest, these cryptograms have been made the captured correspondence of a supposed hand of kidnapers.
In these cryptograms, the key letter has been changed with each text letter; also, excepting that a twenty-six letter alphabet has been used, and normal word divisions have not been observed, the cipher is otherwise exactly like that described by Wilkins. Here are our cryptograms, six of them, numbered for reference.
5 10 15 20 25 30 35
(1) JOPTE CGENS NTFDF PPGZD THBTM WXCCD JXPU.
(2) OSYIV CHXIV NUQFZ XPOFP TFUCI SGTPH M.
(3) LOETS MUTYE KHGII WKTFN GPNLW.
(4) YSBPX SNPMS HQQMN DVVYR QIHIU OJPTH GTPH.
(5) CLEGG DVSVK MHRUY FAICI PJIKI ELNKM KVVW.
(6) TVYJJ SAHVV AZRVE VFTFT SFRRR KVM.
Now, since this is supposed to be a series of cryptograms in unknown cipher, it cannot be assumed that they are in the same key. Possibly a number of different ciphers have been employed. Again they may be in the same system, hut with different keys.
Consequently, before any two or more of the above cryptograms can he combined for solution, it is necessary to know that they are in identical ciphers.
If the reader desires he can try each cryptogram individually by the transposition test given in the September 4 issue of FLYNN'S WEEKLY. These tests will eliminate the transposition cipher, and allow us to consider the possibility of substitution ciphers.
In this latter class, the substitutes may consist of one, two, three, or more characters. The present cryptograms consist of 34, 31, 25, 34, 35, and 28 letters, respectively. Some of these numbers are not evenly divisible by 2, 3, 4 ... and consequently we can assume—unless substitutes of mixed lengths have been used—that at least some of the cryptograms are of the straight letter-for-letter substitution type.
Messages enciphered in the same key will often have similar predominating characters or groups of characters. For instance, that cryptograms Nos. 5 and 6 both contain a large number of V's might be pointed out as significant.
Predominant groups, however, will receive the bulk of attention here. And to save our readers a few hours of merely routine work, a complete table of all the recurrent groups in all six of the present cryptograms is herewith appended.
(1) (2) (3) (4) (5) (6)
PT 3 20 —— 28 —— ——
SN 10 —— —— 6 —— ——
TF 12 21 18 —— —— 18
FP 15 19 —— —— —— ——
TH 21 —— —— 29 —— ——
XP 32 16 —— —— —— ——
IV —— 4-9 —— —— —— ——
CI —— 24 —— —— 19 ——
GTPH —— 27 —— 31 —— ——
HG —— —— 12 30 —— ——
DV —— —— —— 16 6 ——
VV —— —— —— 17 32-33-34 9
VY —— —— —— 18 —— 2
KM —— —— —— —— 10-29 ——
KV —— —— —— —— 31 26
FT —— —— —— —— —— 17-19
The above differs from the ordinary table of recurrent groups in that it lists the groups repeated in all six cryptograms, and not merely those of each individual cryptogram. Thus, the group PT occurs at the third letter of cryptogram No. 1; at the twentieth letter of No. 2; and at the twenty-eighth letter of No. 4. The reader may easily check them.
Were there enough recurrent groups in each cryptogram, they could he tested by the Kasiski method in the usual manner, See FLYNN'S WEEKLY for August 7, 1926. Here all such groups happen to he accidentals, which are of no value by the above method.
The Kasiski principle, however, is not limited in its application merely to a single cryptogram. It can be used just as well with any number of cryptograms, the recurrent groups of which can be treated exactly as if they occurred in a single specimen. To illustrate this, suppose that we examine the groups found in both No. 1 and No. 2.
Groups (1) (2) Intervals Factors PT 3 20 17 17 TF 12 21 9 3-9 FP 15 19 4 2-4 XP 32 16 16 2-4-8-16
It will he seen that the intervals figured here exactly as if the recurrent groups occurred at their respective numerical places in one and the same cryptogram, instead of two. The largest predominating factor is 4, which suggests a fixed period cipher using four alphabets. By this supposition PT and TF become accidental recurrent groups. At least, we may progress with that assumption.
The supposed natural or periodic groups, FP and XP, however, might have resulted from using different keys of the same length, but with certain characters in common. Just what portions of these keys must here be identical, if they are not entirely so, can be found by transcribing the two cryptograms in groups of four, the supposed period. FP and XP are underlined to facilitate the examination.
1234 1234 1234 1234 1234 1234 1234 1234 12
No. 1 JOPT ECGE NSNT FDFP PGZD THBT MWXC CDJX PU
No. 2 OSYI VCHX IVNU QFZX POFP TFUC ISGT PHM
By this arrangement the group FP will be found to occur at the third and fourth letters of the period; and XP at the fourth and first. Consequently, unless these groups are also purely accidental, it may be assumed, tentatively at any rate, that both these cryptograms are in four alphabet ciphers, whose first, third, and fourth alphabets, at least, are identical.
Were these cryptograms longer, or with more groups in common, the results by this method might he more convincing. Nevertheless, sufficient have been shown—especially since these cryptograms are from the same source, the kidnapers, you know—to make it highly probable that both cryptograms have the same key.
Just as the presence of identical recurrent groups at regular intervals in a number of cryptograms can thus he taken as evidence of a common key, so the absence of such groups may he considered as indicating different keys.
Thus, No. 1 and No. 3 have only one group, TF, in common. This, occurring at the twelfth letter of No. 1 and the eighteenth letter of No. 2, gives an interval of 6, suggesting a period of 2, 3, or 6.
We already have stronger evidence, however, that No. 1 has a period of 4. No. 3 would thus seem to he in a different key than No. 1. What the length of its key is can be discovered by comparing it by the method already shown with other cryptograms of the series.
Having thus explained how it is possible to find whether or not two or more cryptograms of this kind are in the same key, it is left for the reader to determine for himself how many keys have been employed in the present instance, and what cryptograms have been enciphered in each.
These points determined, such cryptograms as are in the same key can he combined for solution. For, as a general rule, the greater the amount of material in any cipher, the less difficult is it to solve.
For example, cryptogram No. 1 when its thirty-four Characters are divided among its four alphabets, has only eight or nine characters in each alphabet. And No. 2 has only seven or eight characters per alphabet. To resolve even a simple alphabet with so few characters is sometimes a difficult matter.
If the similar alphabets of these cryptograms—and any others in the same key — are combined, however, larger frequency tables of the several alphabets will he available for analysis.
To illustrate, the frequency table for alphabet No. 1 of cryptograms Nos. 1 and 2 would here consist of the first characters in every group of four; these being the letters J, E, N, F, and so on, of No. 1, and O, V, I, Q, and so on, of No. 2. Tables for the other alphabets would be similarly formed.
The several alphabets so isolated can he resolved by any desired method: as, for instance, by assigning the value E, T, A ... to one of the most used characters, as described in FLYNN'S WEEKLY for August 7, 1926; or by detecting the amount of displacement, or shifting, of a known cipher alphabet, as shown in the issue of October 2.
The actual work of sorting the present six cryptograms according to their keys, and of solving the different alphabets, should afford the reader an hour or so of fascinating entertainment.
And don't forget, either, that these cryptograms, deciphered, will reveal the story of the kidnapers. Who will he the first to discover their plot?
Send in your solutions; and look for the translations in next Solving Cipher Secrets.
There are some points about ciphers from our readers that we must take this opportunity to mention.
First of all, do not he disappointed if the cipher you submit is not used at once. Many excellent ciphers are being held until the time when they can he presented to the best advantage. Some ciphers will be printed along with special articles dealing with similar systems.
Another matter of importance is that your ciphers or inquiries, to receive attention, must always he accompanied with your correct name and address. If you prefer, your name will not be printed in the magazine. But unsigned, or anonymous, communications will not be considered.
In this connection a number of interesting unsigned ciphers have been received. One of these was based on the wigwag alphabet. Another, from Southington, Connecticut, used false word divisions. These, and others like them, we are sure, would interest our readers. We regret that we cannot publish them.
Finally, we have been in receipt of a number of insistent requests that we provide an adequate means of placing those interested in cryptography in contact with each other.
After a careful consideration of all the ideas advanced as to how this could best be done, we believe that the most feasible plan, for the present at least, would he to list in these columns the names and addresses of those who desire to correspond on the subject of cryptography.
How does this idea strike you? If you would like to have your name on such a list, write us at once to that effect. Whether or not this plan is put into operation will depend upon the enthusiasm with Which it is received by our readers.
Now that these affairs are all cleared away, we can place some readers' ciphers before you. And good ones they are, too!
In No. 7 photographic fans will recognize the formula of a well known developer. Innocent enough, apparently, it has yet been bent to the purposes of cryptic communication. This is different from anything we have yet printed. Read Dr. Miller's letter, and try to find the meaning of the cipher:
DEAR SIR:
Although your department is most interesting, it has occurred to me that you have never given the female cipher fans anything particularly adapted to their intuitions.
Here is a cryptic message which was smuggled out of prison by a woman to let her friends know what to send her in aiding her to escape.
Let's see what the ladies can make of it!
MALCOLM DEAN MILLER, M.D.
Akron, Ohio.
CIPHER No. 7 (Malcolm Dean Miller, M.D.):
Metol ........................... 9 grains
Hydroquinone .................... 38 grains
Sodium sulphite, dry ............ 605 grains
Sodium carbonate, dry ........... 800 grains
Water ........................... 20 ounces
"Imogene"
The next cipher, though easy, is, nevertheless, not without interest. Having guessed at a word of the message, try to discover the plan of the alphabet. It is to a famous statement of a celebrated author that Mr. Duree (Los Angeles, California) refers in his message.
Our correspondent says this cipher is sometimes used by bootleggers hack in the effete East.
CIPHER No. 8 (Murnon Duree):
36 48 44 18 14 52 36 26 30 4 46 24 52 40 18 44 44 8 36 14 38 44 46 40 52 18 52 30 30 52 26 22 24 44 42 24 18 14 38 44 38 12 28 52 26 28 36 26 46 36 16 16 12 18 44 30 4 36 26 40 44 26 36 24 12 16
Mr. Goldman, Cleveland, Ohio, originator of No. 9, say's that his system can be learned in an hour's time. He has attempted to make an undecipherable system. Will it get by the enterprising readers of FLYNN'S WEEKLY?
CIPHER No. 9 (B. Goldman):
EJ GEBUF XEPIQLEFIC GEBIQEC SQUZIJMEH SEP NEBILEF VO BE M VEMITEPIKUBAKIF DEPICEF, AVIS EJ TEFF SEGIBES ZEPIV GEBUF OVIS PEMIF PUFEQ PEM NEF BEMIC EJ XEJIKK GEBUF SEP SEQUZ BEHIBEJIM.
The solutions to all the ciphers in this issue will he given in next Solving Cipher Secrets. Don't fail to see it. In the meantime, try your skill, and send us your solutions.
A complete explanation, with special method of solution, of Mr. C. A. Castle's Radio Cipher, which was No. 3 in the October 2 issue of FLYNN'S WEEKLY, will be given in the next installment of this department.
No method of solving this type of cipher has yet been published in these columns. In fact, to discover how his cipher could he solved was one of the reasons that prompted Mr. Castle to offer the seventy five-dollar radio set.
Now we really anticipate some solutions to Mr. Castle's cipher. And if the expected list of solvers actually materializes it will be printed in an early issue, naming the fortunate winner. Look for it.
Here are the solutions to the remaining ciphers of the October 2 issue:
Cipher No. 1. Key: L—B. Message: We expect to hold up the messenger Wednesday noon. Be ready to act as advised.
Cipher No. 2. Key: O—Z. Message: We leave to-night for San Francisco. Meet us at Jim's place, and bring the money with you.
No. 4 (R. M. Packard) was an ingenious autokey cipher, using the straight 1-to-26, A-to-Z alphabet. Mr. Packard's own explanation of his system is appended:
This is a variation of the Gronsfeld cipher. using letters for key and cipher, and extending your Gronsfeld table to the full alphabet, but differing from it by one letter in every place, and giving results equivalent to adding the numerical values of the letters of the key to those of the letters of the message, the numerical value of each letter being its order in the alphabet.
The whole cipher is the key. The first six letters are nulls as far as the message is concerned, but they are the first six letters of the key. They are the key to the next six letters of the cipher, which in turn are the key to the following six. The message may be deciphered by using a table, or by writing the cipher under itself, six places to the right, subtracting the numerical values of the key from those of the letters of the cipher (adding 26 where necessary), and changing the resulting differences into letters of the message. To illustrate:
F R J P A C———K N O H Z F———T D W ...
6 18 10 16 1 3 11 14 15 8 26 6 20 4 23 ...
6 18 10 16 1 3 11 14 15 ...
———————————————— ————————
Message: Every cipher formed on this plan carries its own key and is its own key. There is
nothing to remember except the general principle and the numerical order of the letters of the
alphabet.
No. 5 (Paul Napier), like Nos. 1 and 2, used the digraph table, without, however, including the dash or word space. Accordingly, his alphabets used but twenty-six characters, the right-hand column and the bottom row of the table being disregarded. Mr. Napier's message is based on a statement in Bullivant's hook, mentioned in the preceding article. Its solution is presented herewith.
Key: K—S. Message: This cipher is based on a system of digraphs. It was used by a well known European country. As far as I know, it is still used.
In Mr. Levine's, No. 6, we have a remarkably simple and efficacious method of combining two messages in the same cryptogram. This cipher is based on the following two alphabets:
A B C D E F G H I J K L M 1 2 3 4 5 6 7 8 9 10 11 12 13 27 28 29 30 31 32 33 34 35 36 37 38 39 N O P Q R S T U V W X Y Z 14 15 16 17 18 19 20 21 22 23 24 25 26 40 41 42 43 44 45 46 47 48 49 50 51 52
To illustrate the method of encipherment, take the first letters of the two present messages, C (29) of the first message, COME HERE, and S (19) of the second message, STAY AWAY. The substitute for these two letters is 24 5, one of which numbers (24) is half the sum of 29 and 19, and the other (5) the difference between this 24 and either 29 or 19. Mr. Levine expresses this relation algebraically, thus:
x + y = 29
x — y = 19
2x = 48
x = 24
y = 5
In deciphering, the numbers must be taken in pairs. To get the first message, COME HERE, add the numbers of each pair. The sums will indicate the letters in the 27-to-52 alphabet. The second message, STAY AWAY, is deciphered by taking the differences between the numbers of each pair, these indicating letters in the i-to-2 6 alphabet.
Cryptogram: 24 5 30¼ 10¼ 20 19 28 3 ... Sums: 29 41 39 31 Message No. 1: C O M E ... Differences: 19 20 1 23 Message No. 2: S T A Y ...
A system of this kind offers the advantage of sending a real and a supposed message in the same cryptogram. Should the cryptogram be intercepted, suspicion might be diverted by explaining the supposed message. The real message might in this way escape detection. Incidentally, fractions could be avoided in this cipher by using only the even numbers from 2 to 104. Ingenious cipher fans will find a thousand and one occasions in which a cryptogram of this sort may be useful. Prying eyes are likely to accept the supposed message as the ultimate one and neglect further attempts to read it. Without having achieved an indecipherable cipher, its user may have accomplished similar ends.
No. 7 was in the simple substitution alphabet given in the next column, having been formed on the key word, CRYPT, in accordance with the following method:
In preparing an alphabet of this kind, first write down the selected key word. Then below it, in lines of the same length, place the remaining letters of the alphabet, forming a number of columns equal to the number of letters in the particular key word.
Now, take the columns so formed downward, and from left to right, as shown in the subjoined cipher alphabet, where each text letter is represented in cipher by the letter directly below it:
C R Y P T
A B D E F
G H I J K
L M N O Q
S U V W X
Z
Text: A B C D E F G H I J K L M
Cipher: C A G L S Z R B H M U Y D
Text: N O P Q R S T U V W X Y Z
Cipher: I N V P E J O W T F K Q X
Using this alphabet, our crypt becomes: Wicked iceman pleads guilty; admits having stolen costly nickel-plated bucket while honest owners busily played casino near by.
The word crypt is here adapted from puzzledom, where it is applied to the kind of cipher just given, and which we know as a normally spaced, literal, simple substitution cipher. Most crypts also employ an unusual wording of the message to make decipherment more difficult.
In our own example, for instance, you will note that no short words, which are usually easy to identify, have been employed. Further, no word uses the same letter twice. Words of any and all lengths can be used in the same crypt. We have used all six-letter words for purely fanciful reasons. Our alphabet was based on a key word. Any other kind of literal alphabet is permissible in a crypt.
A total of twenty-seven solutions make up our list of August 7 solvers. The most complete set of solutions was sent in by Mr. Winsor, who walked off with all but No. 3. The arrangement indicates the order in which solutions were submitted, and has no other signification.
The September 4 solvers' list, if compiled in time, will be printed in next Solving Cipher Secrets.