ON numerous and diverse occasions have our readers offered through these pages ingenious and original ciphers based on such accessories as clock dials, roulette wheels, checkerboards, calendars, typewriters, and other devices that seemed adaptable to the needs of the cryptographer.
In this article we take pleasure in presenting still another system of this kind, the magic square this time being the vehicle, and Raymond L. Heitlinger the contributor.
A magic square, as you may well know, is formed of a series of numbers from 1 up, so arranged that the sum in each horizontal, vertical, and diagonal, is constant. In the square given below this constant total is sixty-five.
Magic squares now rank as curiosities. But in earlier times they were thought to possess magical properties.
Numerous methods of constructing magic squares of various sizes have been devised. And the idea has been extended to other geometrical forms, such as the circle, ring, cylinder, and cube. Adequate treatments of all these forms will be found in various works on the subject.
What chiefly interests us here, however, is the application of magic squares to cryptography, and particularly our correspondent's method of using the magic square as key to a transposition cipher system.
This latter Mr. Heitlinger accomplishes in two easy steps. First, the letters of the message are filled into a blank square in the order indicated by the numbers of the magic square selected as key. And, second, the resulting arrangement is taken out by successive horizontals.
Thus, to transpose the message, "Meet me in New York next Friday," using the accompanying five by five Bachet square (a), place the first letter of the message, M, in the space indicated by the figure 1; the second letter, E, in that of the figure 2; and so on, as shown in the completed square (b). Then take (b) by successive horizontals (c), and the cipher is ready for transmission.
(a) 23 10 17 4 11 (b) D E E T W
6 18 5 12 24 E X M Y A
19 1 13 25 7 T M O Y I
2 14 21 8 20 E R R N F
15 22 9 16 3 K I N N E
(c) DEETW EXMYA TMOYI ERRNF
KINNE
To decipher the above communication, merely reverse the process just described, transcribing the cryptogram (c) into the square (b), and taking out in the order indicated by the key (a). A longer message, of course, might require more than one square, depending upon the size; but the procedure for each square would be exactly the same. Vacant spaces in any square could be filled with nulls.
In Cipher No. 166, Mr. Heitlinger has used a different square than the above for his key. And he has also varied the procedure from that just described in another detail, which you must discover before you can decipher his message. The dash forms no part of the cipher, being merely used to divide the next to last group.
You will find some more information about the structure and use of magic squares as applied to ciphers in the next article. Also the full explanation to Mr. Heitlinger's cipher, and a new magic square cipher for you to solve. In the meantime try your skill with No. 166, and let us know what luck you have.
Turning to last week's ciphers, you may not agree with the logic in No. 161, the question and answer crypt by C. E. Roe, but at any rate, it is as reasonable as our "proof" of several weeks ago that a cat has nine lives. Read the translation, and judge for yourself!
Q: WHY DO CHIMNEYS SMOKE? A: BECAUSE THEY KNOW NOT HOW TO CHEW TOBACCO.
The price mark cipher. No. 162, used the subjoined keys. Note that the cost key is formed of the words PAINT and BRUSH, used alternately. The selling key is merely a reversal of the phrase IMPORTED BY. Both keys use "X" as repeater. The 25-50-75-00 terminals were plainly evident in both keys, and their discovery would lead to a speedy determination of the remaining values by the methods outlined last week.
Cost: P B A R I U N S T H X
1 2 3 4 5 6 7 8 9 0 R
Sell: Y B D E T R O P M I X
In Fred J. Heckel's No. 163, the names of the calendar months were used as key, each cipher substitute being composed of a number 1 to 12 to indicate the month and a units figure to indicate the letter in that month.
Thus the first cipher number, 21—2nd month, 4th letter—represented the letter F. In the same way, 45—4th month, 5th letter—signified L; and so on. Letters not occurring in any of the months used their alphabetical place numbers, followed by zeros. Thus K=110; Q=170; W=230; and so on.
The translation: "Flynn's Weekly is a good magazine. Detective fiction with the thrill of truth is always interesting." A difficult cipher, even with the hints offered last week! Did you make the grade?
Besides the magic square cipher, this week's lot includes an interesting simple substitution cipher. No. 164, and a new price mark problem. No. 165. We'll give you just twelve minutes on the crypt! Can you better that record? In No. 165 the prices are disguised as numbers, cost price being given above the line in one system, and selling price below the line in another. See what you can do with it.
CIPHER No. 164.
ZPUJ EPTT KFPVN ZD TPNBZ EBGZJCJF PY BPLLJV; PZ EPTT IDCJF AW GVL IDVIJGT EBGZ PY VDE YBPVPVN PV YWTJVLDF.
CIPHER No. 165.
3827 790 951 634 56705 8356 —————— —————— —————— —————— —————— —————— 18923 10015 1575 10519 105120 15917 105 2153 6678 4881 —————— —————— —————— —————— 1520 15261 10542 15734
CIPHER No. 166, by Raymond L. Heitlinger, Bronx, New York.
HNS THAYSIE CPWBNTH FIGDADE OTNETOBTTIISRHMD REUATREER- VNPEETLAWHSMTYAEREEEGC HEST
Answers and full explanations to this week's ciphers, will be published next week. Keep your answers coming, fans, also your new ciphers. Or let us otherwise hear from you occasionally. Maybe you have a question you would like to ask. Don't hesitate to communicate with your cipher editor in matters cryptographic.