From FLYNN's February 25, 1928

EXPLAINING SOME OF THE CHARACTERISTIC EARMARKS OF THE PLAYFAIR

CIPHER, WITH ILLUSTRATIONS FROM LAST WEEK'S CIPHER No. 136

CIPHER, WITH ILLUSTRATIONS FROM LAST WEEK'S CIPHER No. 136

T HE Playfair cipher, which has been more or less engaging our attention for the past three weeks, presents the following well defined characteristics which aid in its identification in most cases.

It is a cipher of the substitution class. Long repeated groups will almost invariably recur at even intervals, and in most cases will consist of an even number of letters. A table of the pairs of letters will conform in general with digraph frequencies. Some of the symbols will occur reversed, depending upon the digraphs represented. No cipher pair will contain the same letter repeated. And, unless nulls have been used, the cryptogram will always consist of an even number of letters.

Trying last week's Cipher No. 136 on these various points, we find, first, a substitution cipher definitely indicated by the group percentages AEIOU= 26.5%, LNRST=17.5%, and JKQXZ=7.5%, which differ sufficiently from the averages of 40%, 30%, and 3%, respectively, to show a cipher of that class. This should be extremely clear.

No. 136 is too short to afford a representative assortment of repeated groups. Nevertheless, we find ALKF at the interval 40, with the additional KF giving intervals of 16 and 24. Also we find the intervals, BG=92, AB=76, LI=30, and CO=34, as shown in italics herewith, where the cipher is grouped by twos for convenience in solving.

UL.WR.AM.HQ.FW.RU.GC.HY.IO.KL.BG.FI.QB.AP.YP.AB.DC.ET.CO.AL.KF.PU.SL.LI.LH.IM.FB.PB.MI.HL. DO.IB.KF.LN.EL.CO.FC.KA.LI.AL.KF.LB.MK.RN.UE.OM.TM.UN.CD.OI. BA.MC.PZ.AB.FU.MB.BG.FE.HV.YV.

There are only sixty pairs of letters in this whole cryptogram and consequently they cannot be expected to follow digraph frequencies closely. In fact, the above mentioned symbols are the only ones occurring more than once. As to reversed symbols, we find IO and OI, AB and BA, DC and CD, LH and HL, and IM and MI. But even these are probably of greater value in solving the cipher than in identifying it in the first place.

On the other hand, the fact that no repeated letter forms a symbol is good evidence of the Playfair cipher. The present cryptogram also contains an even number of letters. But this does not carry so much weight since nulls may have been used in finishing out the last group.

Having assumed from these tests, however, that the cipher is probably of the type under discussion, the solution may now proceed along the lines suggested in previous articles. And it should not be hard to assign whole or part values to eight or nine symbols right off the bat. But here we shall leave the reader to his own resources rather than spoil a good problem by revealing too much. There is more fun in working it all out for yourself.

There is still another peculiarity of the Playfair cipher, however, which we have not yet touched upon, and which should prove a valuable asset in reconstructing the key square. And this is the mere fact that letters occurring in the same vertical and horizontal with the letter E, will, from the method of encipherment, be among the most frequently used letters of the cryptogram.

Even in this very short example this principle works out admirably. Thus, the most frequently employed letters here are: L, used twelve times; B, eleven times; F, nine times; A and I, eight times each; C and M, seven times each; and K, O, and U, six times each. And you will find that five of these ten letters actually occur in the same line and column with E in the key to the present cryptogram.

This, of course, greatly facilitates combining equations in reconstructing the key, and the solution is rendered just that much more expeditious and less difficult. The answer to No. 136 will be published next week. Can you get it before then? With a knowledge of the various methods that have been described here we think you should. Try it, anyway! And see how close you can come to it!

We venture to say that last week's cryptogram No. 134, by Rufus T. Strohm, kept you guessing for awhile. At any rate, it is one of the most difficult of this type yet printed in this department. Here is the message: " Unkempt ditch crowd drop shovel, crowbar, pickax, plump; abscond presto; swarm nigh extinct taxi; shew much atechny."

The first four groups of this cryptogram spelled real words, the first three of which formed a correct English sentence. Which brings up the interesting question: Is it possible to so select the words of your message and to so arrange the letters of your cipher alphabet that the entire cryptogram will also constitute a correct English message? J. A. Dockham, Oakland, California, has already sent us some experimental cryptograms of this kind, more about which later.

K. Davidson's No. 135 conveyed the
message: " A word to the wise is sufficient."
This cipher uses two series of letters of the
same length, the key series *(a)* and the
message series *(c)*. The key series, obtained
by taking one of each letter in the
order used in the cryptogram, is changed
in deciphering into numerical key *(b)* by
numbering the letters according to their
places in the ordinary alphabet.

(a)A V E J N X S T I L O U ...(b)1 -22-5 -10-14-24-19-20-9 -12-15-21...(c)A C D E E E F F H I I I ...

The remaining letters of the cryptogram
are then written in alphabetical order under
the key *(b)*, whereupon the number
above any letter will show its place in the
message, A being the first, C the twenty-second,
D the fifth, and so on. A cryptogram
is here twice as long as the message,
and longer messages must be divided into
sections of the proper length and separately
enciphered.

Turning to this week's ciphers. No. 137 is another of the straight substitution variety. No. 138 embodies a new method of using the Vigenère square of twenty-six alphabets, the letters of the key word being taken in successive lines, and the cipher substitutes from the left side. The normal word divisions should help.

In No. 139 you have a double cipher in which the message has been first enciphered in a simple substitution alphabet, and then transposed by transcribing in short rows of a fixed length and taking out by columns in the order designated by a numerical key. The answers to this week's ciphers will be published next week.

CIPHER No. 137.

DKWKG QINKH HSDFNHNKO ASJUF- YNU OFDSUBISGM, NUYQQKOONWGK KVQKCF FIDSJBI UYDDSP, DSQTX FDYNGO.

CIPHER No. 138 (J. H. Warburton, Franklin, New Hampshire).

NHYECS SM MTGCV FL TQALTSU XUN TYEVBOFRHT CZ IXHD. SLIM.

CIPHER No. 139 (J. Lloyd Hood, Bastrop, Texas).

RAVFI VJRKH POXUY TCFKT USIUF FQSTS SFXJD XXQER YXDFE BYXXF JXDXX SFXRJ DYSKS AQCSX KKPTD T