THE first step in solving the Playfair cipher is to group it by twos, to facilitate the calculation of frequencies, the location of reversed symbols and recurrent sequences, et cetera. Here is last week's Playfair cipher, No. 129, pointed off in this manner, with dashes indicating spaces between words:
PI.H—R.NG.AN.BF.T—E.N—B.— KZ.IZ.BS.CZ.BS.AK—TD.MQ.LG— YZ.G—K.IR.RI.TL—FS—TD.MQ.LG— GI.FS.O—V.L.I.E—H.GC—FG.PD— YZ.G—K.IR.RI.TL—AD—PI.H— G.IL.NB.EL.
In a message of about fifty or more words, one or more digraphs can usually be identified at the start by frequency. Thus, TH will generally be the predominating digraph; or at any rate, it will usually be found somewhere near the top' of the list in such company as HE, ER, IN, AN, and so on.
Here PI may be assumed to stand for TH. But not so much from its frequency— it occurs only twice—as from the fact that in both cases it begins a three-letter word, PIH, probably THE, which is commonly used also at the beginning of a sentence.
If PI=TH, however, we also know that IP=HT. For a peculiarity of the Playfair system is that any symbol, reversed, stands for the same pair of message letters reversed. And this is true whether the letters have been enciphered from a vertical, horizontal, or rectangle, of the cipher key. In the case of a rectangle, two additional equations, TH=PI and HT=IP, will also hold good.
As it happens, however, IP, TH, and HT do not occur in the present example, so these values cannot be put to trial. But we do find a reversed symbol, IR.RI, in the group K.IR.RI.TL, for which the word LETTERS should not be long in suggesting itself, especially in view of our hint last week as to the contents of the message.
Assuming now that the above IR=ET was enciphered in a rectangle, we obtain the additional equations, ET=IR and TE—RI, the second of which can be applied to TE, which is divided between the second and third groups of the cipher. This would mean, of course, that the second word of the message must end with an R, and that the third must begin with an I. Ad this is not at all an unlikely supposition, since the third word could thus be IF, IN, or IS, any of which would fit the following single-letter word, B, which is probably A.
Other substitutes may be worked out in a similar manner, and additional clews are plentiful. For example, the ninth group, FS, occurs as part of the eleventh, GI.FS.O. And the third and fifth pairs in the fifth group are identical.
Having thus determined a number of digraphs, the reconstruction of the key square should next be attempted. And this should proceed hand in hand with the gradual development of the message. For the present, however, any further decipherment of the above example will be left to the reader. Additional hints on solving the Playfair cipher will be given next week.
To decipher last week's No. 128, by Milton L. Cohen, first take the cryptogram by successive horizontals, left to right, thus: C-IC-KQY-ABHP... Next, substitute from the accompanying key, where the equivalent for any letter is that occupying the same position in the other "diamond."
In this way you will get the message: "FIFTY PACES NORTH OF ELM BACK OF TRACY'S B.ARN." Not so hard, perhaps, if you have the combination. But pretty tough without it. Do you agree?
V W X Y Z Z X U Q L
P Q R S T U Y W T P K F
K L M N O V S O J E
G H I J R N I D
D E F M H C
B C G B
A A
(Message) (Cipher)
Cipher No. 130, by Arthur Bellamy, was of the autokey class, each letter of the text being represented by two figures which locate it in the subjoined key with relation to the position of the letter preceding it in the message, the first figure indicating the difference in rows and the second the difference in columns.
1 2 3 4 0 1 A B C D E 2 F G H IJ K 3 L M N O P 4 Q R S T U 0 V W X Y Z
Thus, beginning with Z as starting point, the first two figures of the cipher, 23, indicate a count of two rows downward and three columns to the right, which will bring you to H, the first letter of the message. Similarly, starting with H for the second pair of figures, 42, a count of four downward and two to the right indicates E as second letter of the message; and so on.
Counts are all taken in rotation, the first row of the key following the last, and the letter at the extreme left of any row coming next after that at the extreme right of that row. This cipher is easy to use, and is very clever. Translation in full: "Here is a little contribution for your weekly department. The fans may have some fun solving it." Did you get it?
In the first of this week's ciphers, a straight substitution, you will find concealed an interesting and curious historical fact. How long will it take you to dig it out?
Dr. Wood writes us that his cipher was used by a bunch of Boy Scouts who did not find it too difficult for transmission by signal flags, and flash lights at night. This cipher will test your powers of observation. Look over the various groups, and see what you can make of them.
In No. 133, Mr. Walker is giving you a chance at an original and quite difficult variation of the Playfair system. If you find this hard, don't say we didn't tell you so beforehand..Answers and full explanations to all of this week's ciphers will be published next week.
CIPHER No. 131.
Question: CVSM IRQRZNAMD MEEL S OAPIV EX HPBXX EP MVR HIS - XXEQY ? Answer: HAN CSQMRN NSQRAWV.
CIPHER.No. 132 (Geo. P. Wood, M. D., Detroit, Michigan).
6-8-17-15-16 38-26 24-24 19 12-5-20-2-3-2- 5-12-5 21-1 58 2-14-44 3-17-3-10-18-5 0 0 26-6-4-16-1 5 47-10-6 10 8-30 0 9-4-5-22-5- 10-12 4-37-23 1-14-12-3-4-1-24 25-4 11-32 50-15 0 7 0.
CIPHER No. 133 (M. Walker, Akron, Ohio).
&WPDE LNUTJ HOAHU LOTGP HFWIN CWDNA S&SPR AD&&Y HELXP UCRHC HFZDQ IXENJ HFZDO PTHOU RAFLD *GT
Don't hesitate to send in any cipher system of your own that you would like to see put to a real test by hundreds of eager, crafty fans. Then watch and see what happens to it!