AD substitution ciphers never evolved beyond the stage exemplified by Edgar Allan Poe in "The Gold Bug," the troubles of the decipherer would have been few, indeed.
For ciphers of this kind use but a single alphabet, having one equivalent for each letter. And any cryptogram of sufficient length in such a system can certainly be solved, regardless of its apparent complexity.
To offset the insecurity of simple substitution ciphers, as these simplest of single alphabet systems are commonly termed, numerous other methods of cryptographic writing have been devised, among which are the so-called multiple alphabet ciphers.
A single alphabet system employs but one cipher alphabet. This alphabet may be made up of letters, numbers, or signs: and its structure may run anywhere from a methodized arrangement that will permit all or part of the alphabet to be determined almost at a glance, to a purely arbitrary form in which no character will afford in itself a clew to the identity of any of the others.
A multiple alphabet cipher, on the other hand, employs more than one alphabet. As in the single alphabet cipher these alphabets may consist of letters, numbers, or signs in any arrangement. (The number of alphabets, and the manner of their use, depends, of course, upon the type of cipher.
Early ciphers of the multiple alphabet class make use of a short fixed series of simple literal methodized alphabets. The celebrated Vigenère chiffre carré, and its variant, the Gronsfeld cipher, both of which have been treated in this series of articles, may be cited as classical examples.
The methods of solving multiple alphabet ciphers described in connection with the above mentioned systems are based on correct assumptions or previous knowledge (a) of the form of the alphabets, and (b) of one or more words, or at least a sequence of letters, in the message itself.
However, as indispensable as are these methods, they cannot be applied to the solution of every type of multiple alphabet cipher. For in some cases the decipherer may not know, or may be unable to correctly guess, any word or part of the message; and again many of these systems are so devised that it would be impossible for him to have any previous knowledge of the exact form of the alphabets.
To better cope with such ciphers would thus seem to demand methods of solution which do not require any information about the alphabets, the wording of the text, or even the language in which the message may be written.
The first notable achievement along these lines seems to have been the work of F. W. Kasiski, a Prussian major, who published the result of his investigations at Berlin in 1863 in his epoch-making book, "Die Geheimschriften und die Dechiffrirkunst."
By the Kasiski method the period—or number of letters enciphered at one application of a series of alphabets—of certain types of multiple alphabet ciphers can be determined mathematically.
The discovery of this principle resulted from Kasiski's observations of repeated sequences of cipher characters—recurrent groups—in single and multiple alphabet ciphers.
In single alphabet ciphers Kasiski found that recurrent groups were frequent, but at irregular intervals, depending wholly upon the wording of the message. But in multiple alphabet ciphers—of the types being considered—he found that while recurrent groups were not so frequent, they were, more often than not, at intervals which were multiples of the period.
The Kasiski principle may be briefly stated thus: In any multiple alphabet cipher using a fixed series of alphabets over a period of fixed length, recurrent groups in most instances result from enciphering similar sequences of text letters in identical series of cipher alphabets; and the intervals between recurrent groups actually so end phered are always multiples of the period.
By this principle it is possible to determine the period of any multiple alphabet cipher of the class mentioned, whether the alphabets consist of letters, numbers, or signs; and it is quite unnecessary to know beforehand the order of characters in any of the alphabets, to guess at the wording of the cryptogram, or to have any acquaintance with the language in which the message may be written.
The application of the principle, which is simplicity itself, will here be demonstrated upon a cryptogram in the Saint Cyr cipher, a system derived from the Vigenere chiffre carré, and, in fact, identical with it in results, only differing in mode of operation.
The Saint Cyr cipher is so named from having been taught at the famous military school located since 1808 at Saint Cyr-L'Ecole, a town of northern France.
This cipher, an exposition of which is given in the Cours d'art militaire of 1880-1881, employs an apparatus somewhat resembling an ordinary slide rule.
Prepared for our own twenty-six letter alphabet, the fixed alphabet consists of the 26 letters in their regular order from A to Z; and the movable alphabet, partly shown in the illustration, consists of the alphabet repeated, save for the final z, which is unnecessary, making 51 letters in all.
The movable alphabet can be adjusted by sliding to 26 different positions, forming 26 different cipher alphabets, each of which is designated by its first letter as a key letter.
The illustration shows the F alphabet in position, the strip having been adjusted so that the first F of the movable alphabet is below the A of the fixed alphabet. In this position any letter in the fixed, or message, alphabet is represented in cipher by the letter directly below it in the movable, or cipher, alphabet.
┌─────────────────────────────────────────────────────────┐
│ (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 │
┌───────┤ ├───────────────────────────────────────────────────┤ ├─────────┐
│ A B C │ │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│ │H I J K ╱
└───────┤ ├───────────────────────────────────────────────────┤ ├───────┘
│ (cipher alphabet) │
└─────────────────────────────────────────────────────────┘
The series of alphabets used in any particular instance is determined by the letters of a prearranged key-word. The original instructions for this cipher call for a keyword of from three to five letters. But a key of any length can, of course, be used.
The system will here be demonstrated by using the key FRAY with the message: Prepare to advance against the enemy at once before they are reached by reenforcements.
Each letter of the message can be enciphered at an individual setting of the instrument, if desired. In this case the letters of the key are written above the letters of the message, each letter of which is then enciphered in the alphabet indicated by its key letter, thus:
Key: FRAYFRA YF RAYFRAY ... Text: PREPARE TO ADVANCE ... Cipher: UIENFIE RT RDTFECC ...
But a method less liable to error, and more to be recommended for any cipher of this type, is to transcribe the message in lines whose length is equal to, or a multiple of, the length of the key. By this arrangement the letters that are to be expressed in the same cipher alphabets are brought into the same columns, allowing them to be enciphered at one operation.
FRAY FRAY FRAY FRAY FRAY 4 5 12 16 20 PREP ARET OADV ANCE AGAI UIEN FIER TRDT FECC FXAG 24 28 32 36 40 NSTT KEEN EMYA TONC EBEF SJTR MVEL JDYY YFNA JSED 44 48 52 56 60 ORET HEYA RERE ACHE DBYR TIER MVYY WVRC FTHC ISYP 64 68 72 EENF ORCE MENT S JVND TICC RVNR X
By this method all the letters of the present message in the columns headed by the key letters F would be enciphered, as shown above, in the F alphabet shown in the illustration of the Saint Cyr apparatus; P being thus expressed in cipher by U, N by S, O by T, and so on.
The F columns completed, the slide would now be adjusted for the P alphabet, which would be similarly used for all letters in the R columns. The same procedure is followed for the remaining columns. It will be observed that in the A alphabet each text letter is expressed by itself in cipher. The completed cryptogram, transcribed in the usual groups of five letters, is subjoined.
5 10 15 20
UIENF IERTR DTFEC CFXAG
25 30 35 40
SJTRM VELJD YYYFN AJSED
45 50 55 60
TIERM VYYWV RCFTH CISYP
65 70
JVNDT ICCRV NRX
This cryptogram may be deciphered with the key by merely reversing the process just described. First transcribe it in lines of a length equal to, or a multiple of, that of the key, placing the proper key letter at the top of each of the several columns thus formed.
All columns headed by the same key letter can now be deciphered at one adjustment of the instrument, the equivalent for any letter in any given cipher alphabet being found directly above it in the fixed alphabet.
In applying the Kasiski principle to any cryptogram known to be, or suspected of being, in a multiple alphabet cipher, it is first necessary to list the recurrent groups and their respective intervals.
To facilitate this it is convenient to number the characters of a cryptogram so that the location of any group can be quickly determined. The numbers 5, 10, 15, 20, et cetera, in the present cryptogram as grouped above by fives are for this purpose, the location of any group being indicated by the serial number of its first letter.
The recurrent groups themselves are readily found by inspection. If a cryptogram is lengthy, a tabulation of all the groups may be unnecessary. And in such a case it is usually preferable to find all groups throughout a cryptogram that begin with one or more—as required—of the most used characters, than to confine the search to all of the recurrent groups in a particular section of the cryptogram.
The present cryptogram is so short, however, that an exhaustive search will probably be necessary. Accordingly, beginning with the first pair of characters, Ul, carefully examine the entire cryptogram for repetitions of these same letters. None will be found.
Proceed similarly with the second pair of letters, IE. Two other such groups will be discovered at the 6th and 42nd letters of the cryptogram.
As each recurrent group is found, examine it to see if it consists of more than two characters. The recurrent group at 6 and 42, for example, is thus of three letters, IER, instead of but two. Just a moment's scrutiny will make this clear.
Next search for EN in the same way; and then for NF, FI, IE, and so on, until every pair of letters in the material at hand has either been exhausted, or sufficient information has been uncovered to render further examination unnecessary.
The intervals between these recurrent groups are found by counting the characters between them. Thus TR occurs at the 9th and 23rd letters; the interval is therefore 23 minus 9, or 14.
The period of the cipher is now calculated from these intervals, it being, as a rule, the greatest common divisor of the largest number of intervals. Frequently this can be done mentally. In fact, in the present case a consideration of the following three intervals is sufficient for the purpose.
IE 4=2×2 IE 40=2×2×2×5 IER 36=2×2×3×3
All of these intervals are evenly divisible by both 2 and 4; but 4 is more probable as the period, since it is the larger number.
Sometimes, however, several periods may seem equally probable from a superficial inspection. A complete tabulation of intervals and their factors, similar to that subjoined, will in such cases ordinarily prove valuable.
The following table lists all the recurrent groups and their intervals of the present cryptogram. The factors of these intervals up to any desired number, in this case 15, follow their respective intervals ' in the proper columns; and the total frequency of each factor is given in the bottom line as shown below:
—————————————————————————————————————————————————————————————————————————————— Recurrent Group Interval Factors Group Locations 2 3 4 5 6 7 8 9 10 11 12 13 14 15-etc. —————————————————————————————————————————————————————————————————————————————— IE 6 - 2 = 4; 2 - 4 - - - - - - - - - - - IE 42 - 2 = 40; 2 - 4 5 - - 8 - 10 - - - - - IER 42 - 6 = 36; 2 3 4 - 6 - - 9 - - 12 - - - *TR 23 - 9 = 14; 2 - - - - 7 - - - - - - 14 - *DT 40 - 11 = 29; - - - - - - - - - - - - - - *DT 64 - 11 = 53; - - - - - - - - - - - - - - DTI 64 - 40 = 24; 2 3 4 - 6 - 8 - - - 12 - - - etc. CC 67 - 15 = 52; 2 - 4 - - - - - - - - 13 - - CF 52 - 16 = 36; 2 3 4 - 6 - - 9 - - 12 - - - RMV 44 - 24 = 20; 2 - 4 5 - - - - 10 - - - - - YY 47 - 31 = 16; 2 - 4 - - - 8 - - - - - - - *YY 47 - 32 = 15; - 3 - 5 - - - - - - - - - 15 VN 70 - 62 = 8; 2 - 4 - - - 8 - - - - - - - —————————————————————————————————————————————————————————————————————————————— 10 4 9 3 3 1 4 2 2 0 3 1 1 1-etc. ——————————————————————————————————————————————————————————————————————————————
The period is now determined from these totals by the rule just given. There are two predominating factors here, 2 and 4, which occur 10 and 9 times respectively. In such cases, the largest factor that is also a multiple of some or all of the others—as 4 is of 2 here—may generally be taken as the period. When the period is a prime number it will usually be the only predominating factor.
Another aid in determining the period is that factors which are multiples of the period occur in diminishing frequencies. Thus in the present table 8 and 12—which are multiples of 4—occur respectively 4 and 3 times.
Intervals in a cipher of this kind may be either periodic or aperiodic.
Periodic intervals are those produced by recurrent groups which represent identical sequences of text letters enciphered in identical sequences of alphabets.
This class of intervals ordinarily occasions no trouble except, perhaps, when a cipher employs a series of alphabets in which a certain succession of alphabets is repeated. For example, the repeated TI in the key-word INSTITUTION used with the Saint Cyr cipher might cause some trouble. In such instances the longer recurrent groups will usually aid in determining the relationship of such apparently contradictory intervals.
Aperiodic groups are merely accidental, representing different sequences of text letters enciphered in different series of alphabets. The four groups, TR, DT, DT, and YY, indicated by asterisks (*) in the table are of this kind.
The peculiar difference between these two kinds of recurrent groups is that the former vary with the number of alphabets, and the latter with the identity of these alphabets.
The present cryptogram, for example, enciphered with any four-letter key-word whatever would give the same nine-periodic recurrent groups. The characters in the groups would differ, of course, but their locations would be exactly the same whatever the key-word
On the other hand, each change of keyword would produce a different series of aperiodic groups. As an extreme example of this the key-word FORT would give no aperiodic groups whatever with the present cryptogram.
Recurrent groups of either kind vary in their length. As a general proposition, the longer a recurrent group, the greater is the probability of its being periodic. The groups lER and RMV in this case are thus more liable to be periodic than those of but two letters. However, long aperiodic recurrent groups are by no means rare in this sort of cipher.
So much for the Kasiski method. By its means the period of a cipher can usually be limited to a single probability. But when several periods seem equally probable, each possibility must be followed out until the true one is reached.
In the present case, we have determined that the period is four, or, in other words, that a series of four alphabets has been used. These alphabets, it is true, are of simple formation. But exactly similar results could have been obtained had they been of more complex structure.
In this connection, many ingenious methods have been devised for resolving different kinds of alphabets. The present article, however, is concerned chiefly with determining the number of alphabets, leaving the matter of their resolution for articles to follow.
Nevertheless, a few words about the handling of the present kind of alphabet should not be amiss. An y alphabet of this kind, whether used in a single or multiple alphabet cipher, can be determined by identifying a single character; as, for example. the substitute for E, the most frequently used letter.
The accompanying frequency tables for the four alphabets of the present cipher are made from the subjoined arrangement of the cryptogram in groups of four letters. Frequency table for alphabet No. i is formed by counting the letters U, S, T, J, F, M, et cetera, of the columns numbered 1. And those for alphabets Nos. 2, 3, and 4, are similarly made from the columns headed by their respective numbers as the reader will readily see.
| (l) | (2) | (3) | (4) | |||
|---|---|---|---|---|---|---|
| A | A | A Ⅰ | A Ⅰ | |||
| B | B | B | B | |||
| C | C | C ⅠⅠ | C ⅠⅠⅠⅠ | |||
| D | D Ⅰ | D Ⅰ | D ⅠⅠ | |||
| E | E Ⅰ | E ⅠⅠⅠⅠⅠ | E | |||
| F ⅠⅠⅠ | F ⅠⅠ | F | F | |||
| G | G | G | G Ⅰ | |||
| H | H | H Ⅰ | H | |||
| I Ⅰ | I ⅠⅠⅠⅠ | I | I | |||
| J ⅠⅠⅠ | J Ⅰ | J | J | |||
| K | K | K | K | |||
| L | L | L | L Ⅰ | |||
| M ⅠⅠ | M | M | M | |||
| N | N | N ⅠⅠⅠ | N Ⅰ | |||
| O | O | O | O | |||
| P | P | P | P Ⅰ | |||
| Q | Q | Q | Q | |||
| R Ⅰ | R Ⅰ | R Ⅰ | R ⅠⅠⅠⅠ | |||
| S Ⅰ | S ⅠⅠ | S | S | |||
| T ⅠⅠⅠ | T Ⅰ | T Ⅰ | T Ⅰ | |||
| U Ⅰ | U | U | U | |||
| V | V ⅠⅠⅠⅠⅠ | V | V | |||
| W Ⅰ | W | W | W | |||
| X ⅠⅠ | X | X | X | |||
| Y Ⅰ | Y | Y ⅠⅠⅠ | Y ⅠⅠ | |||
| Z | Z | Z | Z |
In alphabet No. 1 there are three predominating characters, F, J, and T, each occurring three times, any of which can be E, or some other frequently used letter. And in alphabet No. 4 both C and R occur four times each.
But in alphabet No. 2 the most used character is V, which occurs five times, and thus is a likely substitute for E. Now if this V is E, in a simple shifted alphabet of this kind the fifth letter before V, namely R, must stand for A which is the fifth letter before E. In other words, this is the R alphabet.
By the same line of reasoning alphabet No. 3, in which E is the most used character, is, in all likelihood, most probably the A alphabet.
These two alphabets can now be applied to the cryptogram with the following results:
1234 1234 1234 1234 1234 -RA- -RA- -RA- -RA- -RA- RE RE AD NC GA UIEN FIER TRDT FECC FXAG ST EE MY ON BE SJTR MVEL JDYY YFNA JSED RE FY ER CH BY TIER MVYY WVRC FTHC ISYP EN RC EN JVND TICC RVNR X
The translation may be completed by making various suppositions for the other key letters; or by supplying letters for partly completed words of the message.
The Kasiski principle is one of the most useful tools in the cryptographer's kit. No cipher enthusiast will get very far if he is not fully experienced in its use. It will be referred to time and again in future cipher articles. So now is the time to master it.
Ciphers Nos. 1 and 2 are appended for this purpose. Both of these are in the Saint Cyr system, modified as in this article, for our own twenty-six-letter alphabet. Also we have not limited ourselves to key-words of three, four, or five letters.
Fortunately, the Kasiski principle is easy to apply. And the Saint Cyr alphabet is not difficult to determine.
So, first, hunt for the recurrent groups.
From these determine the number of alphabets.
Discover the most used characters in each of these alphabets.
Call these characters E, and from them find the key-word.
That's all there is to it!
CIPHER No. 1 (Saint Cyr).
ZBRKH RSSYU MFKMU GPRHY RTBRG PLGHQ ZBREB NBYAK UERSR DBNAM GKXGN YVXMH VJYOY FUZNS GHTCG OIAGH QVLBB CFOIA Y.
CIPHER No. 2 (Saint Cyr).
FJWRE ESJCN TGJCY VOELZ NRCXN DEJJI SKHRT IIZDA QXJOI FVESV CRUWN KYBTE YCENU XFUEF KVJFF GTESJ MVVXN EGVPJ TIMNV MTEFE QQTEE VPHNM IQWEQ KONPS YYEEK RXLCU CQFEN RTEXK ORNYI VGRPI WRLPQ QUIEU GRXZO AUSBV MNAAJ CLFWT UFSRV LJGRN EXNTE BHAWZ TVPKN ECVRL JITBD ITWGE GEYRN GKUZZ TL.
CIPHERS FROM OUR READERS
It is an interesting lot of ciphers, indeed, that our readers are offering this time. The first of these, by Mr. Bellamy, has come all the way from Montpelier, France.
Mr. Bellamy has used the Vigenere table in FLYNN'S WEEKLY for last February 20, without, however, employing a key-word. Any one having knowledge of the system can decipher this cryptogram either with the table, or by using the Saint Cyr device described in this article. Normal word divisions have been observed.
CIPHER No. 3 (William Bellamy).
Q sx zrjn fi wrn lfz pf degd vqg soy hdfq qott fqg iyn uxwr vs njp mtz di iiyb ubf ahlz yf pmpb bjd rx ri zl nd ocxn poxu ymda wxwr jnq gff klir nla dgx chpd inq qony qf gpes htwrw gv dnwd qoxi ptz px ri dtd hule tis ki iwybm sptln qtvj xdaj nbkt pv gym kgx lmpb ef pysm kr blnwt uraz.
Mr. Bellamy writes us that he is now more than eighty years old, and has lost interest in most things; but he takes pleasure in saying that FLYNN'S WEEKLY'S cipher department much interests him. We must add that our correspondent is the author of several books of charades, in one of which —"Century of Charades"—he uses an original cipher key to conceal the hidden answers.
In No. 4, submitted by Mr. Baldwin, Calgary, Alberta, our readers will have a chance to see how skillful they are in separating the sheep from the goats.
Only certain letters of this cryptogram, as indicated by a secret numerical key, are significant. The rest are nulls. Given the key, this cipher can be read at sight. What can you do without the key?
CIPHER No. 4 (Fred Baldwin).
Gee ant fish at brim bad at a brown man crept or perhaps he owed I will at all cram bun kiss home to remove bugs rub lie off of some fur unset.
This note accompanied No. 5.
DEAR SIR:
Here is a code we used in the Signal Corps while I was in the service. Let's see who can get this one.
GEO. A. LAUB.
Ft. Wayne, Indiana.
CIPHER No. 5 (Geo. A. Laub).
To CAPT. HARDEN,
C. O. Co. E 53, Teleg. Bn.
From Sgt. Shepherd.
Sent by AL Station B.
BORRD NHMSP XSWMB GMXMS MQAMO ULXSW BRGMO PNZRH QZRHQ DMNNJ.
Sig. SHEPHERD.
The above cipher employs a simple substitution alphabet based on a key-word. It demonstrates how a short message can make a simple cipher difficult of solution.
Whether or not you solve the next one, by Joseph Murray, New York City, depends on how you look at it.
CIPHER No. 6 (Joseph Murray).
4-52-33-04-41-24-01-32-03- -04-45-12-04-35-44-43-03-44- -13-32-03-02-15-44-05-01-21- -03-52-13-03-51-35-22-32-04- -32-04-52-32-05-14-05-22-03- -34-41-04-32-0
In the earlier issues of this department it was not customary for ciphers submitted
by correspondents to be followed in the next article by their solutions. The answers to some of these were published subsequently, but twenty-one of them are still unexplained.
In response to a number of requests for some of these solutions, we have decided that the best way to handle the situation is occasionally to reprint one of these ciphers, offering its solution in the following article.
No. 7 is one of these. Originally it appeared in FLYNN'S WEEKLY for August 15, 1925. It is a modified Gronsfeld, in which any key number up to twenty-six is allowable. It can be solved by the method in this issue. Two solutions were submitted at its first printing. How many of you will get it this time?
CIPHER No. 7 (Austin Minette).
ZAQYVWJXQYMIQXVLKWSMPKLBUKG, ZAMMBITMZGYB, CKQZMMTUGPNTKL DKKVK. MPOLIAMPUKEXHBKAQYUWU DAUOMXYQLMGEXIXLIMHENXVZAMS TRUKQZRWLMPKMPOGOYAMCKWZXI HHCZPMXXCTWZKTUKWWL. YZUFIYV QKGBOYQITVJBVZXZKLBOGOXXIJBV MIWOGBOVWTLQJXZNBUGGMDVMRE MTMIAMPUK.
Now, fans, do your best! Try to solve these, and send in your answers. Then look for the solutions to all seven in next Solving Cipher Secrets.
There were nineteen letters in cipher No. 1 in FLYNN'S WEEKLY for July 3. This number being prime, the cryptogram obviously consists of but one transposition cycle.
Given more than one cryptogram of this length in the same key, and they could be combined for solution by multiple anagramming. But with only one message, since its letters practically constitute an arbitrarily transposed series, solution must be effected by the ancient and honorable method of straight anagramming.
That ciphers Nos. 1 and 2 are probably on the same subject can here be turned to account by first solving No. 2, and then looking for words in No. 1 suggested by the text of No. 2. Thus QUARTERS is found in No. 2, and all the letters required for this word are also in No. 1. This assumption will leave the remainder AADEEENRRWY.
ARE seems likely as a verb, leaving the remainder ADEENRWY. If now the solver can see READY in these letters, the remainder will form NEW, completing the sentence NEW QUARTERS ARE READY, or ARE NEW QUARTERS READY; the question form being obviously more probable, since cipher No. 2 is seemingly in answer to No. 1.
No. 1 was enciphered with the key ALWAYS BE ON YOUR GUARD, which gives the numerical key 1-8-17-2-18-14-4- 6-10-9-19-11-15-12-7-16-3-13-5.
Cipher No. 2 used the key phrase STRIKE WHILE THE IRON IS HOT, which gives the numerical key 18-20-16-7-11-1-23-4-8-12-2-21-5-3-9-17-14-13-10-19- 6-15-22. The message was: "Your note received. Dies were finished day before yesterday. Call Wednesday for a supply of halves and quarters."
The solution to the free subscription cipher, No. 3 (Charles P. Winsor), will be given in next Solving Cipher Secrets. This is a good one. Don't fail to see the answer in FLYNN'S WEEKLY for September 4.
In cipher No. 4 (Mrs. Charles J. Mundy) we have an ingenious method of varying a simple substitutional alphabet by means of a key-word or phrase. Mrs. Mundy chose the phrase UNITED STATES OF AMERICA, which gives the series UNITEDSAOFMRC when the repeated letters are omitted.
The method of forming the alphabet, shown below, is described in her message: "This is a cipher with a patriotic key which utilizes the first half of the alphabet, the latter half being simply reversed."
U N I T E D S A O F M R C A B C D E F G H I J K L M Z Y X W V Q P L K J H G B N O P Q R S T U V W X Y Z
Possibly you may have solved No. 5 (Arthur Bellamy), but did you discover the system of transposition? Mr. Bellamy used a 5 X 5 Fleissner grille—see FLYNN'S WEEKLY for December 5, 1925—with the openings disposed as follows:
- - - - ○ A E G T S - - - - - R A T I E ○ - X ○ - O S S L A - ○ - - ○ C V I R I - - - ○ - M P O N H
The grille was rotated in a counterclockwise, instead of clockwise, direction, and the central cell, marked with an x, was filled with a nonsignificant letter. The order given the first twenty-four letters of the message, and the null S, is shown above. Mr. Bellamy's message: " Solving a cipher is a matter of trial and error, discarding one possibility after another until we find the solution."
Cipher No. 6 (W. E. McCracken) is based on the A=1, B= 2 . . . Z=26 alphabet. Each number shows how many alphabetical places its letter is in advance of the preceding letter, taking the alphabet as a continuous cycle, A following Z.
In this forward count, the alphabet may be taken through more than once, adding 26 or a multiple thereof to any desired number. Thus 27 for the second S in POSSIBLE could have been 1, 53, or 79. Numbers of three digits, as 631=BUT, are reserved as arbitrary substitutes for frequently used short words.
The alphabet for the Secret Writing in The Schoolboy Message, No. 7 (A. S. Binnie) is based on the calendar month. The month is decided by the first single figure in the first column, and the year by the last figure of the last column. These were 2 and 26 respectively, thus giving February, 1926, as the key month.
In preparing the key the letters of the alphabet are substituted for the first 26 numbers for the days of the month, and the digits 1 to 7 are used in place of the days of the week. The rows are also numbered from 1 up, as shown:
(FEBRUARY, 1926) 1 2 3 4 5 6 7 1 A B C D E F 2 G H I J K L M 3 N O P Q R S T 4 U V W X Y Z
Any letter is represented in this key by two figures, the first of which indicates the column, and the second the row of the desired letter. Thus 21 means column 2, row 1, ox A. The end of a word can be represented by any number—as 2, 79, 9, 98, et cetera—that does not signify a letter, and also by the end of a column.
The Schoolboy Message: "At six thirty the Pirates will meet at the Den to plan the undoing of John Brown for his ill-treatment of William Johnson, second mate of the Good Ship Argo."
Mr. Binnie submitted this to show the ingenuity of the schoolboy's mind at the age of twelve or thirteen. Very clever, don't you think so?
The following solutions to April 24 ciphers have been received. All answers are listed in the order submitted.
Observe the two answers to No. 3 (J. R. Midford), the free subscription cipher. Mr. Midford writes us that he would have been better pleased with a larger number of solutions, but seeing there were only two he decided to call it a tie and award a free year's subscription to FLYNN'S WEEKLY to both contestants.
FLYNN'S WEEKLY'S cipher fans will no doubt be interested in an article on cryptography in the recently published book, "Real Puzzles," a general work on word puzzles. The article we mention is written by Mr. John Q. Boyer, and deals especially with the type of cipher favored by the National Puzzlers' League, such as are published every Sunday in the New York World and other newspapers throughout the country.