AS stated in the issue of February 4, the formation of the key square used in the Playfair cipher is dependent not only upon the key word or phrase used to vary the alphabet, but also upon the order of transcribing that alphabet into the square.
In the two examples of this cipher— Nos. 129 and 136—which have appeared here, the key word occupied the first line, or lines, of the square. For example, the key (a), herewith, formed on the key word COMMUNICATION, was used in enciphering No. 136.
(a) C O M U N (6) C IJ E L V
IJ A T B D U B H R O
E F G H K X S Z Y A
L P Q R S Q K D N F
V W X Y Z G T M W P
However, this key could just as well have been filled in by columns instead of rows, or in any other manner, provided that all the communicating parties shared the secret. Thus, at (b) the columns of (a) have been transcribed in a clockwise spiral beginning at the upper left corner.
Of course the Playfair cipher can be resolved regardless of the method of forming the key square. But in general the more obvious arrangements will not be so difficult to determine as those in which the letters are more thoroughly mixed.
By the way, how did you make out with No. 136? If you assumed, as suggested, that the recurrent ALKF resulted from a repetition of the word CIPHER, you were in possession of the following equations: CO=xC; LI==xC; AL=IP; KF=HE, PU=Rx; and LB==Rx. And taking the third KF as part of THE would give the additional equation, IB=xT.
Looking for a symbol among the remaining repeated groups to represent TH, BG is more likely than AB, since the latter occurs reversed, and the resultant HT would not be so probable in the message. Thus you would also have BG=TH, FI=Ex, and FE=Ex.
The methods of applying these equations to the solution of the cipher have already been outlined in preceding articles. Suffice it here merely to append the full translation: Cryptography embraces the art of writing in cipher or secret character, and the science of deciphering such communications without the key.
Last week's simple substitution Cipher No. 137 conveyed the message: Rebel chief fortifies mountain stronghold, inaccessible except through narrow, rocky trails. The final O, occurring twice, suggests S, and also the value ES for the terminal KO. Substituting in NUYQQKOONWGK, where IN and IBLE are probable affixes, would give IN—ESSIBLE, probably INACCESSIBLE. After this, REBEL, NARROW, and other words, would follow in rapid succession.
J. H. Warburton's No. 138 used the key word CIPHER, and conveyed the message: ' POLICE ON TRAIL; AM LEAVING FOR CALIFORNIA AT ONCE. SLIM." As suggested last week, this system employs a cycle of twenty-six alphabets, the order and identity of which are determined by the key word.
A sufficiently long message could, of course, be solved without this information in the manner of other ciphers of the Vigenère class. But with this knowledge it becomes possible to reduce the present short example to a six-alphabet cipher with an interrupted key, by merely counting backward from 0 to 25 places for successive letters in each series of 26.
Treated in this manner the cipher becomes: NGWBYN MF EKWRJ SX EAJTAYZ BXP UYDTYKALAL TP XLUP. In this form, fragments of the key may be found by guessing short words. And from these, parts of longer words may be deciphered, and the rest of the key and message developed by context without serious difficulty.
Here is the answer to No. 139, by J. Lloyd Hood: "I do not believe that this can be very easily deciphered without the key used in transposing." This message was first enciphered in the subjoined simple substitution alphabet, and then transposed as shown, by taking the columns downward in the order indicated by the numerical key.
A B C D E F G H I J K L M
J A I R X L B K S Z O C M
N O P Q R S T U V W X Y Z
T Y E N U D F P V H G Q W
J A M E S
3-1-4-2 5
S R Y T Y
F A X C S
X V X F K
J F F K S
etc.
To decipher this system, first determine the order of transposition by finding series of letters which produce probable cipher sequences. Thus, in columns 2=5 the sequence ST occurs twice, and FK occurs three times. And the latter, from letter frequency, is likely material for TH.
In the same way columns 4=2 furnish two XU's and another FK. And other columns may be matched in the same way. Once the original order is restored, decipherment may proceed as with any other continuously written simple substitution cipher. Did you get it?
If you are looking for some real fun, try for the long word in No. 140, a straight substitution cipher. Twenty-seven letters! Count 'em! And yet they represent a genuine English word, properly used. Try to solve this, and send in your own "jawbreakers" for the fans to puzzle over.
William B. Marks, in No. 141, is offering you something different in an autokey cipher. All the paraphernalia you require is the ordinary alphabet written in the form of a circle. The numbers represent counts on this circle between letters of the message. But some counts are in a clockwise direction, and others counterclockwise, as indicated by the first two numbers which constitute the key. What can you manage to do with it?
In No. 142, J. A. Dockham challenges you with a cipher which is shorter than the message it conveys! Straight A to Z alphabetic slides have been used, and each group of five letters represents six in the message! How is it done?
The answers to this week's ciphers will appear next week. Send in your answers, fans, and also your new ciphers. We are always glad to hear from you. Keep the pot boiling!
CIPHER No. 140.
ZHJGQQECQZJGZWJZWPGJCXAGAQQ WQ QJWU ZP CA ZVA XPGNAQZ GPGZAMVGWMJX SPHU WG ZVA AGNXWQV XJGNEJNA.
CIPHER No. 141 (William B. Marks, Waterbury, Connecticut).
21-7-13-14-1-16-31-26-6-6-1-11-18-29-22- 10-36-14-22-18-20-27-21-21-42-20-24-12-25- 3-19-25-32-12-23-28-19-10-6-35-24-4-23-10- 17-30-4-11-41-21-16-6-27-20-17-13-36-24-8- 26-11.
CIPHER No. 142 (J. A. Dockham, Oakland, California).
QEFPP JKVDG DSJRT BDSZQ LDOXJ UVPUV VKRUW JLZSF TQYQE MSQUF RPPXQ KIBMA