HE ancient story of how Achilles got shot in the foot is familiar to every one.
Briefly retold, it seems that Achilles's mother, desiring to make her son invulnerable, dipped him when a child into the river Styx. Hi s entire body was thus supposedly made proof against hurt, except, unfortunately, that part of his heel by which she had held him, and which had therefore remained untouched by the water.
It would also seem that Apollo had been peeking through the bushes at the time, for years afterward he directed the arrow of Paris toward the vulnerable spot in Achilles's heel, thus causing his death.
What was true of Achilles is also true of secret writing. For there is apparently hardly any cipher that is entirely secure.
In framing a cipher it commonly happens that the inventor only evades one weakness to incur another, and even more deadly one. And it is by aiming our missiles at these Achilles's heels that ciphers become the easiest prey.
So it is with the Fleissner grille, fully described in FLYNN'S for December 5.
But before proceeding to the method of slaying this Achilles of the world of ciphers, some remarks about the cipher itself will be illuminating.
First, let us determine how many possible arrangements of the openings are possible with a grille of a given size, for instance, one of a 36 letter capacity such as was used in the last article.
A 36 letter grille operates on a square of six rows and six columns. Herewith is such a square, which, for purposes of reference, has been numbered consecutively from 1 up to 36:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
Now, on account of the manner in which the Fleissner grille is rotated in enciphering, each opening will control four numbers of this square. For example, an opening in the grille occupying the position of figure 1 would also come over 6. 36, and 31, in its successive positions.
From this it is obvious that whatever number be selected for the location of the first opening or aperture of a 36 letter grille there will remain 36 minus 4, or 32 numbers still eligible for the location of the second opening.
One of these now being selected there will remain 32 minus 4, or 28 possible locations for the third opening, and so on, until the unused numbers have been reduced to four, any one of which may he used for the ninth and last opening.
The number of different 36 letter grilles possible of construction is thus equal to the product of 4 x 8 x 12 x 16 x 20 x 24 x 28 X 32 X 36, which reaches the staggering total of 95,126,814,720.
In a 64 letter grille the number of possible arrangements piles up in excess of one hundred sextillions, or a 1 with twenty-three ciphers annexed.
The combinations possible in larger grilles attain still dizzier heights. Nevertheless, though this would seem quite sufficient, the straight Fleissner grille may be modified otherwise than by merely changing the locations of its openings.
For instance, Verne complicated his message by writing it backward before enciphering it.
And in some accounts, the paper being written on is rotated instead of the grille. This produces an altogether different cipher, but one twice as easy of solution, since it will be found, after a study of the method described below, to afford twice as many points of comparison. Further, by this method only one-fourth of the characters are written right side up, increasing the possibility of error in transcription.
Another variation consists of first writing the message into the square in any desired manner, as by rows—ordinary or reversed, columns, diagonals, or spirals. Placing the grille upon the square of letters so written, the letters may be read through it in its successive positions, thus giving the enciphered form of the message.
Finally, the shape of the grille itself may be modified almost at will. It may be a square of either an odd or even number of lines and columns, made to operate in either two or four positions.
Or it may be of triangular form; or rectangular; or a hexagon made to work in either two, three, or six positions; and so on. And any of these may be used, if not with equal advantage, at least with equal ease.
These variations of the original grille may be solved either by a modification of the special method herewith for the even-square four-position grille, or by general methods applicable to transposition ciphers. All of which will provide material for later articles.
Let us now confine ourselves, however, to a consideration of this special method only.
Suppose that there is at hand a cryptogram believed to have been enciphered with an unmodified Fleissner grille. And further, for the purposes of this demonstration, let us use the identical cryptogram enciphered in FLYNN'S for December 5.
In other words the above mentioned article took the reader through the complete process of enciphering, from the plain message, and the making of the grille, up to the finished cryptogram.
Now it is proposed merely to reverse this procedure, working backward from the cryptogram to the original message, and incidentally discovering the form of the grille.
Here is the cryptogram:
HASLA LTTYY IAOSS TIUTR SGEHE NENFA AILDT RLDET RORIT SUREY SIOTE FONRS GETEE OWEIM LVGTE HAENR EYRIX CFNER DOZOR EAFPH ETHNU HND
Upon counting, this is found to consist of 108 letters, which information is of immediate value. For when a message has been enciphered in a square or other geometrical form, it is a simple arithmetical process to determine the dimensions of the forms capable of enciphering a message of known length, as well as the number of times such forms must have been applied.
Tables for this purpose may be constructed if desired. And these, if not an absolute necessity, will at least be found to be of great convenience.
At any rate, knowing in this instance that an even square has been used, it is evident that the message has been enciphered with a 36 letter grille, used three times.
In all cases it will not be possible, of course, to fix these facts definitely. For a message of 196 letters, for instance, might have been written either with a 36 letter grille used 6 times, or with a 196 letter grille used once. In this event, at least for the present, each possibility would have to be worked out separately.
But in the present example the cryptogram may be rewritten into three squares of thirty-six letters each. This restores the cryptogram to the same form as when written by the grille, thus:
H A S L A L L D E T R O G T E H A E T T Y Y I A R I T S U R N R E Y R I O S S T I U E Y S I O T X C F N E R T R S G E H E F O N R S D O Z O R E E N E N F A G E T E E O A F P H E T A I L D T R W E I M L V H N U H N D
A common method of solving the Fleissner grille by working directly from these squares is given in a number of books on cryptography, among which may be mentioned. Andre Langie's " De la Cryptographie," a French publication. But that given here is much more rapid and convenient.
Solutions of transposition ciphers usually involve a consideration of what letters in a given cryptogram could or could not have been in sequence in the original message to be sent.
The present method not only does this, but also considers those letters, otherwise usable or not in sequence, which on account of the peculiarities of the grille could not possibly be so used.
From the manner in which the Fleissner grille is rotated through four positions, it is evident that each opening will occupy four different places. Below you will find nine columns of numbers formed from the numbered square already given of a 36 letter grille, all the numbers in any one column being those located by the same opening.
1 2 3 7 8 9 13 14 15 6 12 18 5 11 17 4 10 16 36 35 34 30 29 28 24 23 22 31 25 19 32 26 20 33 27 21
From this it will be seen that any letter found at the place designated by any given number cannot be followed by any letter located by other numbers in the same column in that same position of the grille; that is, unless the grille be rotated to a new position.
This fact is used by preparing a number of slips, one for each opening in the grille. Each of these slips, nine in this case, bears the numerical index for one of these openings, and also the letters from the several squares of the transcribed cryptogram corresponding to these numbers,
These slips, preferably of heavy paper, may be prepared by typewriter, or by hand. But to insure accuracy they should all be made at one writing, and cut apart afterward.
The numerical index should first be written out in full, repeating the first three rows for reasons that will soon be obvious. As to the placing of the letters, a few words about the arrangement on one slip will do for all.
Thus, take the one headed by the index 1-6-36-31. The letters H, L, and G, occupy the location 1 in the three squares of the transcribed cryptogram, and are accordingly placed on the slip first. Below these are written L, O, and E, found at 6 in the three squares. Next 36 locates R, V, and D; and 31 locates A, W, and H; all of which are placed on the slip in the same order as their key numbers, as shown in the accompanying illustration.
| 9 | |||||||||||
| 17 | 14 | 7 | 3 | ||||||||
| 13 | 1 | 8 | 28 | 10 | 5 | 18 | |||||
| Key | 1 | 2 | 4 | 6 | 11 | 15 | 20 | 23 | 30 | 34 | |
| 2 | 12 | 24 | 36 | 29 | 16 | 9 | 27 | 32 | 19 | ||
| 3 | 35 | 33 | 31 | 26 | 22 | 17 | 14 | 7 | 3 | ||
| 4 | 25 | 13 | 1 | 8 | 21 | 28 | 10 | 5 | 18 | ||
| 2 | 4 | 6 | 11 | 15 | 23 | 30 | 34 | ||||
| 12 | 24 | 36 | 29 | 16 | |||||||
| 35 | 22 | ||||||||||
| Y | |||||||||||
| I | S | T | S | ||||||||
| O | H | T | N | Y | A | U | |||||
| Sec. 1 | 1 | A | L | L | I | S | R | E | A | D | |
| 2 | A | H | R | F | T | Y | E | I | T | ||
| 3 | T | L | A | N | G | I | S | I | S | ||
| 4 | E | O | H | T | S | N | Y | A | U | ||
| A | L | L | I | S | E | A | D | ||||
| A | H | R | F | T | |||||||
| T | G | ||||||||||
| T | |||||||||||
| O | Y | R | E | ||||||||
| E | L | I | E | S | O | T | |||||
| Sec. 2 | 1 | D | T | O | U | S | F | R | O | M | |
| 2 | R | S | V | E | I | T | T | E | E | ||
| 3 | L | I | W | E | N | O | Y | R | E | ||
| 4 | G | E | L | I | O | E | S | O | T | ||
| D | T | O | U | S | R | O | M | ||||
| R | S | V | E | I | |||||||
| L | N | ||||||||||
| E | |||||||||||
| E | C | N | E | ||||||||
| X | G | R | H | Y | A | R | |||||
| Sec. 3 | 1 | T | H | E | R | F | O | R | T | H | |
| 2 | I | E | D | E | N | E | P | N | D | ||
| 3 | N | U | H | F | O | E | C | N | E | ||
| 4 | A | X | G | R | Z | H | Y | A | R | ||
| T | H | E | R | F | R | T | H | ||||
| I | E | D | E | N | |||||||
| N | O |
The letters having been written on all of the slips in a similar manner, the first three rows of each section of letters are repeated. Each of the completed slips will thus bear seven numbers, and three groups of seven letters each.
In working with the slips, two lines of investigation may be followed. First, slips forming probable combinations of letters, or words, that also produce possible sequences of key numbers, may be tried. And second, possible sequences of key numbers may be experimented with in trying to find likely sequences of letters.
In the first case there are certain sequences of two letters, or digraphs as they are commonly called, that occur more frequently than others in any language. Tables of digraphs can be found in most books on cryptography. And while tables by different authors vary somewhat, they are all of about the same practical value.
The most frequently used digraphs in English, as found in " De la Cryptographie, " by P. Valerio, and arranged in the order of their descending frequencies, are as follows: TH-HE-AN-ER-ON-RE-lN-ED-ND-AT-OF-OR-HA-EN-NT-EA, et cetera.
Now, taking any of these, say TH, select the slips that bear these letters. And placing any two of them side by side, adjust them vertically by sliding so that these two letters come in the same row.
Suppose that, possibly after several attempts, the slips headed by key numbers 2 and 13 are tried together. Properly adjusted, these will bring out TH in the first row of the third section.
Now since all the squares have been enciphered in an exactly similar manner, if this combination of slips is correct, the sequences of letters in the corresponding rows of the first two sections must also be usable. In section 1, line 1, the combination is AL, which is good. In section 2, line 1, it is DT, apparently not so good; yet it must be remembered that D might end a word and T begin the next one.
Further, since at the third position of the grille—when the marked edge was at the bottom—the relative order of the openings was reversed, then line 3 in this pair of slips must form usable sequences reversed. These three sequences, corresponding with 35-33 in the key, are LT, IL, and UN, all of common occurrence.
Next, let us consider the number sequences in the key. Since there are only one-fourth as many openings as spaces in the grille, an average interval of four spaces must separate the former. This interval will be shown by the key numbers on the slips. The above pair of slips gives the numerical sequence 2-4, with a difference of 2. These differences may actually run anywhere from / to 10, or even more, but very large differences may usually be excluded at once.
In solving this cryptogram the present method allows seven points of comparison; the three normal sequences in the rows numbered 1; the three reversed sequences in the rows numbered 3; and the numerical sequence in the first row of the numerical key.
Proceeding in this way, additional slips are added before or after any combination already obtained, and adjusted vertically to all possible arrangements in an effort to develop the sequences already obtained into larger sequences or words. The accompanying illustration shows one correct adjustment of all the slips required to solve this cipher.
The key numbers in line 1 read in ascending order, corresponding with the first line in each section of letters below. The key numbers in line 3 are in descending order, corresponding to lines 3 in reverse order. And the numbers in lines 2 and 4 are in mixed order, and are also the corresponding lines of letters.
It happened in this instance that the sequences were developed in the first lines of the different sections. But this could have been done in any other line, in which case the corresponding line of the numerical key index would then have been the one forming the ascending series.
Finally, if a grille be made with the openings arranged according to the numbers in any one of these four lines of key numbers, it will be identical with that used in the previous article for enciphering this message. The four series of numbers merely indicate the four different positions taken by the same grille.
Here is the completely deciphered message, divided for easy reference with the illustration by short dashes into groups of nine letters, and by long dashes into cycles of thirty-six: "ALL IS READ-Y. AT THE FIR-ST SIGNAL T-HAT YOU SEN—D TO US FROM-TRIESTE, EV-ERYONE WIL-L RISE TOGE— THER FOR TH-E INDEPEND-ENCE OF HUN-GARY. XRZAH. "
All of the work of solving this cipher, including the preparation of the slips, should not take more than an hour's time.
On the other hand, if you were to try, one by one, each of the 95,126,814,720 possible grilles of this size, even a lifetime of labor might not enable you to hit upon the one that had been used. Your selection of any one grille would have less chance of success than a random shot at Achilles.
Below you will find two "regiments" marshaled in accordance with Colonel Fleissner's orders.
But considering that you have observed just how the colonel dipped his grille into the river Styx of cryptographic invulnerability, these should occasion you no alarm. Remember Achilles, and direct your aim at their most vital spots.
Here are the ciphers:
CIPHER No. 1 (Fleissner grille).
TRNEB ERHEE GFCDR OIMLI EFLIE FSSMI CSLUE OLSHE IERTZ TAOES STAND IENTC CDRIE ASPST SAHEF SGTHE ELEED QMEXC NEGVS TRGEH ARSOS TAS.
CIPHER No. 2 (Fleissner grille).
ETGSE THAIE SMNWW EAIMG SERSW TSHRT HIILA TFHEI DLERA ESSRI ITNNW WEAIS NGUTC HETIH SPAHE SNTHT EEDUG CRREI INTFE FHLEL AEWDT ORTPO EPRVE ERMTR ISNXI GHADE VUETN HBEUT EUDC.
The solutions of these two ciphers will be published in next Solving Cipher Secrets, together with those of the two Fleissner ciphers in FLYNN'S for December 5.
The solutions to these latter have been withheld from this issue in order that every one, now having the method of solving this cipher, could have another trial at them.
To round out the evening's entertainment, here is a glittering galaxy of five more cryptograms submitted by our readers for the delectation of their fellow fans.
There is something here for every taste. Those who have been asking for hard ones need look no further. And there are some easier ones, too, for those not yet so far advanced in the art of deciphering.
To start the ball rolling, just read this letter:
DEAR SIR :
Just a hasty note. I did decipher Friend Hutchinson' s cipher—in FLYNN'S for October 10—but, honest, it was so easy I decided everybody 'd send it in. Surprised when I saw there was but one customer!
Here' s how—the old army cipher disk gag - make your alphabet so :
A B C D E F G H I J K L M Z Y X W V U T S R Q P O N
There y'are ! Used that in 1917 and 1918 "en la guerre." Also the last two substitutions—September 12—were simple. Solved your No. 1 — "This cryptogram, et cetera"— by what we used to call "running down the alphabet," like this:
X D K C Z M Y E L D A N Z F M E B O A G N F C P B H O G D Q C I P H F R D J Q I F S E K R J G T
Compris? Your No. 5 in the issue of October 10 in the same way. (Solutions of 4 and 5 attached.)
Thought you and your readers might lie interested in that short cut— a good one to try with the first four or five letters of any substitution cipher.
A combination of the cipher disk shown above, with this one—see Cipher No. 7 below—is a wow for impromptu enciphering and deciphering — honest-to-goodness, war time use. (By using only the next letter in the alphabet for each letter of the message it makes a fine sight-reading cipher!)
CAPTAIN W. O. COOPER.
Chicago, Ill.
CIPHER No. 3 (Captain W. O. Cooper).
TAKEN WRITING KEY HAWAII FLYNN'S DECIPHER IDEA BOOK COM- ING CRYPTOGRAM.
Now, for an easy one, try this cipher from William S. Rawsden, Pasadena, California, which he prefaces: " To FLYNN'S with my compliments!"
CIPHER No. 4 (William S. Rawsden).
URRXKZ ZEYMSM LUZQWQ QBEGBF TQBDQE QZFTUS TCGMXU FKARFT QUDEFA DUQEFT QKIUXX PQEQDH QFTQMP PQPNGE UZQEET TUOTUF IUXXND UZSFTQ Y.
The incident referred to in the next cipher, submitted by Gilbert Hagedorn, Kenosha, Wisconsin, is an actual occurrence. Some day, he writes, it may furnish material for a special article in FLYNN'S.
CIPHER No. 5 (Gilbert Hugedorn).
56 63 42 61 94 Q8 98 98 80
98 86 60 42 08 38 60 40 98
94 60 44 50 44 98 86 60
72 59 so 92 86 72 60 92
60 44 63 86 43 82
72 80 40 50 44 72
98 86 60
92 82
The following letter should act as a challenge to every fan who reads it. The cipher is a variation of a system already described, with one method of solution, in a previous article.
Those who prefer to attempt to solve it without any hint should pass over the last part of the letter, where Dr. Weitz refers to his key.
DEAR SIR :
Having always been interested in cipher messages and the solving of them, I am taking this chance to place in your hands a cipher message written in a cipher of my own devising.
Give your readers a chance at this one. 1 have never had any one even get one whole word right. This cipher seems to baffle every one I have submitted it to.
I even feel safe in giving the key to reader, because the key itself is puzzling to the uninitiated.
Key : RW RL 123,321
Hoping to see this in an early copy of FLYNN'S, I am
Sincerely yours.
DR. G. M. WEITZ.
Gainesville, Fla.
CIPHER No. 6 (Dr. G. M. Weitz).
RPBSJNR PBENHB IZRJ CNMD MS MNGQRJNR CEQ LDUGD BTZG QQOCOWC OBFOHA UJPZ KYOBTDR BBSJNR LBBZ QCSBL RZF OBFOHA PFFS DEABTVNLH VK NS.
If you still have some strength left after your bouts with the preceding six ciphers, the next and final one for this issue, submitted by Fletcher Pratt, Buffalo, New York, is guaranteed at least to make your head reel, if not to finish you off altogether.
CIPHER No. 7 (Fletcher Pratt).
21-29-22-28 36-S-26-22-3-28 17-2 24-36- 14-34-iS 28-12 4-20-5 23-2-33-9-17-16-12- 8 18-11-32-12-28 22-14-32 i9r9-2-34 7-11- 30-29 11-30-7-0-33-28-27-6-23-30-4-31 8- 16-23-26-31-34 iq-12-30-2 11-21 23-6-12- 29-8-25-21-0-15-24 4-29 27-25-14-2 33-19 00-33-23 25-27-29-33-4-00-30 18-13-1 35- 16-3-20-25-36-35-6-33 10-36 3-10-4-7 12- 15 29-15 19-21-34-7 5-24 7-20-27-17-12 31-3-12 17-25-10-29 26-1-13-3-10 11-13-27 27-24-1-1-6-10-26-34-30-2 32-13 26-20-5-28- 9-15-6-32 34-20-1-26-36-27-9-16-8 35-22-0- 34 2-22-3 7-15-30-22-14-5 9-22 23-32-22 9-5-23-00-3-32-10.
This cipher is one of very ingenious construction. It is a variation of the wheel cipher, the wheel In this case being that used in the game of roulette. The numbers on some of these wheels run from 1 up to 27; on others up to as high as 30, 33, or 36. Besides they have one or more of the three zeros, single-0, double-0, and Eagle Bird, all of which are on some wheels of American make.
The numbers on these wheels may be in any order to suit the fancy of their makers. The famous wheel at Monte Carlo, with 36 numbers and one zero, the single-o, is by no means the standard, being altogether different from that used here. The numbers on the wheel used by Mr. Pratt, in clockwise order, read as follows:
00-1-13-36-24-3-15-34-22-5-17-32-20-7-11- 30-26-9-28-0-2-14-35-23-4-16-33-21-6-18- 31-19-8-12-29-25-10-27.
A circular card is now made to fit this wheel. Around the edge of the card are written 38 letters in any desired arrangement, comprising the 26 letters of the alphabet and 12 of its most frequently used letters in addition.
To encipher a message place the wheel at its initial position, this being here with an A opposite the 00. Now the letters of the first word may be enciphered by using in their stead those numbers which appear opposite them at this position of the wheel. Any commonly used letter, if repeated in the word, is represented by its other value. The first word enciphered, the numbered wheel is rotated one place in a counterclockwise direction, thus bringing the A opposite the number next to 00, when the second word is similarly enciphered. At the thirty-ninth word the wheel would again be at the starting point, having thus made one complete revolution.
To solve this cipher one must determine the order of the numbers on the wheel, and the order of the letters in the cipher alphabet. Given sufficient material and time, such a cipher could be solved without knowledge of either arrangement. Bu t here, seeing that the cryptogram is so short, and, relatively speaking, so difficult, the explanation sent along with the cipher by its inventor has been passed on to the reader at the same time.
Solutions to ciphers appearing in previous installments of the department have been received by the following correspondents, the numbers after each name indicating the ciphers solved.
The list for August 15, following, is headed by John G. Bailey, who solved all but numbers 3 and 6, no solutions to which were received. Solvers of No. 4 are to be commended, in that this was really a Vigenère cipher, using a numerical instead of a word key.
Three fans are tied for first place in the September 12 list, each with correct solutions to the same five ciphers. No correct solutions were submitted to Nos. 3 and 5.
C. P. Winsor, of Boston, unqualifiedly heads the October 10 list with correct solutions to all five ciphers.
Of all the ciphers in this article, the No. 2, modified Nihilist by Mr. Alexander, attracted the widest comment. Mr. Winsor speaks of this cipher as "a beautiful demonstration of how an elaborately constructed cipher may sometimes be made to fall apart at a touch."