THE Playfair cipher, described in this article, has been widely used as a military cipher. It is simple, fast, and reliable. And its operation requires only pencil and paper, and the knowledge of a few rules which are easy to remember.
The cipher is a digraph system of the fixed substitution class employing two-unit symbols, any given pair of message letters always being represented by the same two letters in cipher, and any given cipher symbol always standing for the same two letters of the message.
Encipherment is accomplished by means of a five by five alphabetic square, formed by transcribing the letters of the alphabet in a prearranged order, and according to a key word or key phrase agreed upon by the communicating parties. In preparing this square, all repeated letters in the key are omitted except on their first occurrence, and two letters—usually I and J—are made to occupy the same space.
For example, the accompanying square (a) is based on the key word PLAYFAIR, and- is filled in by straight horizontals. Observe that the second A in the key has been omitted; that the remaining letters of the key, P-L-A-Y-F-IJ-R, occupy the first seven spaces of the square; and that the rest of the square is filled in by straight horizontals with the remaining letters of the alphabet.
The Playfair cipher provides no substitutes for repeated letters. Hence, in grouping a message by twos for encipherment, when the two letters in any pair are the same it is necessary to separate them by a null, as X, Y, or Z, so that the second of the two similar letters will become the first of the next pair.
This point is illustrated in the message (b) where the two R's have been separated by an X, as shown at (c). When the final letter of a message occurs alone, any desired letter, as B in this case, may be used to fill out the last pair. With the message properly paired off, the following three rules govern the selection of substitutes.
When the two letters of any pair are in the same vertical column of the alphabetic square, each letter will be represented by that immediately below it. Should either letter of such a pair be the last in the column, it will be represented by the first letter in that column. Thus: CK=KS; RO=GV; WB=AH; PU=IP; and so on, in the present square.
When the two letters are in the same horizontal line of the alphabetic square, each letter will be represented by that immediately to its right. Should either letter of such a pair be the last in the line, it will be represented by the first letter of that line. Here, for example, NO=OQ; ON=QO; EM=GE; MH=EK; and so on.
When the two letters are in the diagonally opposite corners of a rectangle, each letter will be represented by the letter in the other corner of that rectangle in the same horizontal line. Thus, AT=FQ; TA=QF; MO=GT; UF=ZP; and so on, in the present key.
The symbols for the pairs of letters in the present example are given at (d). For transmission the cryptogram is grouped by fives (e). Should the last group contain less than five letters, any desired nulls — as NPO in this case—may be used to complete it.
(a) P L A Y F
IJ R B C D
E G H K M
N O Q S T
U V W X Z
(b) ATTACK AT NOON TOMORROW
(c) AT TA CK AT NO ON TO MO RX RO WB
(d) FQ QF KS FQ OQ QO NQ GT CV GV AH
(e) FQQFK SFQOQ QONQG TCVGV AHNPO
Decipherment with the key is merely a reversal of the process just described. Taking the cryptogram by twos, when both letters are in the same vertical, each letter is replaced by that above it; when they are in the same horizontal, each letter is replaced by that to its left; and when they occupy corners of a rectangle, each letter is replaced by that in the other comer in the same horizontal. The message is then divided into words, all nulls, of course, being disregarded.
The Playfair cipher can be solved without the key by reconstructing the key square and developing the message through identification of digraphs by their frequency, context, and so on. But the process is highly involved, and usually requires a long cryptogram, for here we are dealing with an "alphabet" of six hundred symbols instead of only twenty-six.
However, to afford the fans a short workable problem in this system we are appending Cipher No. 129, which conveys a message about this type of cipher, and in which the five-letter grouping has been abandoned for normal word divisions. The other ciphers in this issue are also far from what you might call "easy." No. 128 is only a straight substitution cipher, but where do you start?
With No. 130 Mr. Bellamy only sent us the hint that the numbers did not stand for letters, but jumps between letters.
Last week's No. 125 conveyed the message: "IT IS GOOD TO RUB AND POLISH OUR BRAIN WITH THAT OF OTHERS." The many short words in this one no doubt broke it at sight.
No. 126 (Bernard G. Kobus) expressed this well known fact: "FLYNN'S WEEKLY IS THE BEST DETECTIVE FICTION IN THE WORLD!" Bernard used a simple numerical alphabet. 1=O; 2=P... 26=N. After substituting numbers for letters, these rules were applied to the numbers of each word: triple first number; add five to the second, fourth, et cetera, numbers; add ten to the third, fifth, et cetera, numbers; add twenty-five to the last number. In this way FLYNN'S became 54-29-21-31-36-30 and so on with the rest. Did you get it?
CIPHER No. 128 (Milton L. Cohen, Dorchester, Massachusetts).
C
I C
K Q Y
A B H P
J E T K N
E C H S O G
A B V E C
K T A B
Q P G
A T
J
CIPHER No. 129.
PIH RNGANBFT EN B KZIZBSCZBSAK TDMQLG YZG KIRRITL FS TDMQLG GIFSO VLIE HGC FGPD YZG KIRRITL AD PIH GLINBEL
CIPHER No. 130 (Arthur Bellamy, Boston Massachusetts).
23-42-32-23-14 24-23-20-43-20 00-42-34-03-21
04-11-03-32-43 33-04-30-10-04 43-13-13-12-30
11-02-10-13-00 10-11-23-10-01 20-31-31-02-43
33-23-11-00-34 42-11-40-22-10 44-34-43-24-43
40-14-33-41-03 33-11-24-43-10 41-02-20-23-14
44-02-20-11-00