HAVING determined a number of digraphs in the Playfair cipher, the reconstruction of the key square may next be attempted. The following list comprises the digraphs found last week in Cipher No. 129, and a few others obtained by substituting NB in the last group of that cipher. Cipher letters are in ordinary type, and message letters are in italics. An unknown letter in any equation is denoted by an x.
PI = TH GK = xL HG = EM HR = Ex IR = ET IL = ES TE = RI RI = TE EL = GE NB = SA TL = RS
From the method of encipherment by verticals, horizontals, and rectangles, in no case will it be necessary to consider more than three key arrangements for any equation. For example, here are the three possibilities for TL=RS:
R T R — T — R T — S L — — S L — S L
On the other hand two equations in which the members are interchanged, as TE=RI and RI=TE, or interchanged and reversed, as TE=RI and IR=ET, can only have been enciphered in a rectangle; and an equation having a term in common to both members, as EL=GE, can only have occurred in a vertical or horizontal, thus:
T — R G — — G E L E I — E L
Separately considered, a number of equations may thus be capable of more than one key arrangement. Upon taking them together, however, some of these possibilities can often be eliminated. Here, for example, there is only one arrangement, shown at (a), which will satisfy all of the above equations. Note that this arrangement also agrees with IL=ES.
(a) T — R (b) P T — R
— — — — — — —
— — G M — — G
I — E H I — E
S — L — S — L
Having tentatively placed a number of letters in this manner, it is easy to fit other equations into the framework so formed. HG=EM, for example, must occupy the four corners of a rectangle, for we already have GEL in the same vertical. This last will also give us the first three terms of PI=TH, thus locating P in the fourth corner of a rectangle.
By this time the square (b) is, sufficiently developed to show that the unknown letter in HR=Ex is P; also that the symbol GI, not listed above, equals xE; and so on. And such letters may accordingly be substituted in the cryptogram wherever such symbols occur, leading, possibly, to the determination of new letters, words, et cetera.
Enough has already been given, however, to demonstrate the method of decipherment, so the present solution need be carried no further. The cipher square used above was based on the key word CRYPTOGRAM. And here is the full translation: The Playfair is a substitution cipher, two letters in cipher being used for each two letters of the message.
In developing the cipher square it makes no difference which of the columns and rows happen to come first so long as their rotational order is the same. Any Playfair square is thus capable of twenty-five different forms without in the least changing the results in cipher. The present key is appended with one variation.
C R Y P T X Z U V W O G A M B P T C R Y D E F H IJ M B O G A K L N Q S H IJ D E F U V W X Z Q S K L N Message: TH EP LA YF AI RI SA ... Cipher: PI HR NG AN BF TE NB ...
For another Playfair cipher, try No. 136, herewith. In this example, which is also about ciphers, the arbitrary grouping may render solution somewhat more difficult. But bear in mind that any word or phrase can only be enciphered two different ways in the Playfair system. CIPHER, for example, would have to be paired off CI-PH-ER or xC-IP-HE-Rx; and THE would be either TH-Ex or xT-HE. The answer to No. 136 will be published in two weeks.
Last week's No. 131 conveyed the following interesting bit of history: Q: What celebrity took a pinch of snuff on the scaffold? A: Sir Walter Raleigh.
No. 132, Dr. Wood's "Boy Scout" cipher, was an autokey substitution in which each group represented a letter of the alphabet, and the numbers in a group the successive intervals formed by that letter in the message. When a given letter did not occur in the message, the fact was indicated by a "O" for that group.
Thus, the first group, 6-8-17-15-16, meant that the first A was the sixth letter of the message; that the second A came eight letters after the first A; and so on. In the same way the second group of numbers located the B's; the third group, the C's, et cetera. The message: "This may prove rather difficult, but a little perseverance will bring the answer."
M. Walker's modified Playfair, No. 133, used the subjoined four by seven key, based on the key word HELP. The two additional signs, & and *, are for AND and THE, respectively. Encipherment is exactly as in the Playfair for rectangles, but Mr. Walker provides the following special rule: When the two letters to be enciphered are in the same line, see them as corners of a rectangle whose vertical sides have diminished to the vanishing point, and you will come out with the pair reversed; when the two letters are in the same column, see them as corners of a rectangle whose horizontal sides have diminished to the vanishing point, and you will come out with the same letters in the same order.
H E L P A B C D F G I J K M N O Q & R S T * U V W X Y Z Message: And while other men ... Pairs: &W HI LE O* RM EN ... Cipher: &W PD EL NU TJ HO... Fives: &WPDE LNUTJ HO...
Translation: "And while other men have toiled with their hands and brains, we have watched them and guarded them and encouraged them."
This week's layout, besides the new Playfair cipher, also includes a difficult straight substitution cryptogram by Rufus T. Strohm, editor of the Enigma, National Puzzlers' League organ, and a new type of transposition cipher by Ken Davidson.
CIPHER No. 134 (Rufus T. Strohm, Scranton, Pennsylvania).
COWARDS BESPY PLUMB BLUD KYU- GAZ, PLUMIXL, DEPWXF, DZCRD; XIK- PUOB DLAKSU; KMXLR OETY AFSE- OPS SXFE; KYAM RCPY XSAPYOJ.
CIPHER No. 135 (K. Davidson, Montreal, Quebec, Canada).
AAVEE EEJNN XSSSS TTTTI IIIIL OOOUU WWWYC CGDDM PQFFF HHZRR BK
CIPHER No. 136 (Playfair).
ULWRA MHQFW RUGCH YIOKL
BGFIQ BAPYP ABDCE TCOAL
KFPUS LLILH IMFBP BMIHL
DOIBK FLNEL COFCK ALIAL
KFLBM KRNUE OMTHU NCDOI
BAMCP ZABFU MBBGF EHVYV