NUMEROUS ciphers have been devised in which some or all of the letters of the alphabet have more than one cipher substitute, any given substitute fixedly signifying only one and the same letter at each occurrence.
An unusually interesting cipher of this type is the "ten by ten square" of the French cryptographer Grandpré. This cipher recommends itself from the fact that the key can easily be memorized, and set down on paper in a few minutes when the proper time comes to use it.
Grandpré's system employs an alphabetic square, formed of ten ten-letter words so selected and arranged that their initials spell another ten-letter word, which thus acts as sort of a master key word to the entire square. The rows and columns of the square are numbered from 1 to 0 down the side and across the top, so that it is possible to represent any letter by the two figures indicating its precise row and column.
Grandpré supplies an alphabetical list of several hundred ten-letter words, similar to the short list herewith, from which to prepare these keys. But, of course, any ten-letter words whatever can be used, so long as the square is made to contain all twenty-six letters of the alphabet.
ATMOSPHERE NAVIGATION BIRMINGHAM OBJECTIONS CONVENTION POLYCHROME DETERMINER QUADRATURE EQUATORIAL RETROGRADE FAHRENHEIT SUPPLEMENT GUILLOTINE TRISECTION HAWKESBURY UNILATERAL INFLEXIBLE VEGETATION JUDICATURE WASHINGTON KILOGRAMME XYLOGRAPHY LEMNISCATE YESTERDAYS MOZAMBIQUE ZANESVILLE
The illustrative key square, shown herewith, is composed of words occurring in the above list. Note that the initial, or master key word is BICHROMATE. Also observe that the key provides substitutes for the different letters of the alphabet roughly in the order of their frequencies, there being twelve symbols for E, seven for T, and so on.
The short message (a), ARRIVED TODAY, will serve to demonstrate the method of encipherment. Numerical substitutes (b) are selected from the key square at random. Grandpre writes his completed cipher continuously, as shown at (c). But the cryptogram can be arranged by fives, sixes, or in any other desired grouping. Decipherment, of course, is merely a reversal of the process just described.
1 2 3 4 5 6 7 8 9 0
1 B I R M I N G H A M
2 I N F L E X I B L E
3 C O N V E N T I O N
4 H A W K E S B U R Y
5 R E T R O G R A D E
6 O B J E C T I O N S
7 M O Z A M B I Q U E
6 A T M O S P H E R E
9 T R I S E C T I O N
0 E Q U A T O R I A L
(a) A R R I V E D T O D A Y
(b) 74-13-89-27-34-20-59-97-61-50-09-40
(c) 741389273420599761590940
With sufficient time and material, ciohers of the above class can be solved by various methods. For example, they may be reduced to and solved as simple substitution systems by determining which symbols represent the same letters. Also it is sometimes possible to get started by guessing one or more words of the message.
Cipher No. 175, below, will afford our readers a fascinating study in Grandpré's system. A different key square from that given above has been used, but the ten key words have been selected from the above list. We suggest that you try the message for such common short words as OF, THE, and so on.
The answer to last week's crypt, No. 170: "Burglars loot dwelling, ransack ice box, make getaway, while watchdog snoozes peacefully." The best place to start here is no doubt with the ending—CCZ—of the last group, which can hardly be anything but -LLY.
Taking C=L, the doubled letter in CVVY will have to be either EE or OO, probably the latter, since V is not used as a final which would probably be the case if V=E. Taking T=S, from the fact that T is used both as initial and final, and substituting in TIVVUMT, we have S-OO--S, which just has to be SNOOZES.
The give-away in last week's No. 171, by Edward Peatross, was in the signature, 51,11,71,11, which obviously was PETE. Substituting in 42,11,11,71,42,11, we get MEET ME; and so on. The message in full: "We are being trailed. Meet me at Court and Plum Street. Two thirty. Pete."
E. J. Frankenfield waxes romantic in his No. 172, knight's tour transposition cipher. Here is the answer: "Fair was she to behold, this maid of seventeen summers. No, this is not a limerick." To decipher the message, number the letters of the square as follows, and read in numerical order. The path of the knight is easy to follow.
15 38 31 56 17 58 11 34 30 55 16 37 12 33 18 59 53 14 39 32 57 20 35 10 40 29 54 13 36 9 60 19 27 52 41 4 45 62 21 8 42 3 28 49 24 7 46 61 51 26 1 44 5 48 63 22 2 43 50 25 64 23 6 47
Besides the Grandpré cipher, this week's bill also presents two other exceptionally interesting ciphers by J. Lloyd Hood and M. Walker. 'Mr. Hood's contribution is of the standard crypt, or simple substitution type, and should give you a good workout. See what you can do with it, and send in your own crypts.
Mr. Walker's cipher, like No. 172, above, is based on the move of the knight in the game of chess. But a different tour is used than in Mr. Frankenfield's example. Try to solve these ciphers, fans, and send us your answers. We expect to publish another solvers' list in a week or two, so keep your answers coming.
CIPHER No. 173, by J.Lloyd Hood, Bastrop, Texas.
ORB STAMP GLUED HUNK EUYH ZTVCBX UQBL HAQB YWFK RUTDX XUIJ.
CIPHER No. 174, by M. Walker, Akron, Ohio.
UFHLF RLWTL OEKEO ARRYE ECOAE OTONR EYHIT NIMTO HKAEE DRWLE OSOTT ONRDS WTMO.
CIPHER No. 175.
207187 038355 797039 199752 762532 041073 34840s 14092s 719654 366730 345671 678346 900566 655879 377180 B34962 472183 007124 610527 8383.