A NUMBER of methods may be brought to bear in determining the key length of the type of transposition cipher described in the two preceding issues. For example, you will remember that one of the requirements of the system under discussion is that the last line of the form into which the message is written in enciphering must be incomplete.
From this it is evident that all numbers which are factors of the number of letters in a cryptogram of this type may at once be rejected as key lengths. All other numbers, not evenly divisible into the length of the cryptogram, however, may be held over for further investigation.
Let us see how this rule works with cipher No. 73, reprinted here from last week:
TVYIE TRROR EHNIA EUDSR lEONI ORENA EEORP TEALO LTSUH LHQNO UCADD CSAAE TDVFU GNNYC YI
This cipher contains seventy-two letters. In the following list, numbers marked with an "X "are eliminated because they are factors of 72, thus leaving 5, 7, 10, 11, 13..., as possible key lengths. This list may be made as long as the cryptogram itself, if desired. But most key words will run from about five to fifteen letters.
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 ... X X X X X X X ...
When a cryptogram happens to contain a prime number of characters, of course it is not possible to apply this method. But whatever the length, elimination can be carried on by an analysis of the intervals between characters forming probable message combinations.
For this purpose digraphs, trigraphs, syllables, prefixes and suffixes, words, and other combinations, characters to form which occur in the cryptogram, may be considered. The present cryptogram, for example, contains five T's and three H's, some of which may form the much used digraph, TH. Any other frequently used digraph, HE, ER, IN, AN, ON, RE ..., may be tried for in a similar manner. (See table of digraphs in FLYNN'S for January 23, 1926).
But sometimes it is expedient to work with letters occurring only a few times in the cryptogram. Take the letters F, G, P, and Q, for example, which occur but once each in this case. F might belong to a common word like OF, FOR, FROM, or IF. G might be the last letter of the common suffix, ING. Q is also an excellent letter to work with, when not used as a null, being always followed in English by U, and then by another vowel.
A method of determining the probability of such combinations will be given next week. And complete details for deciphering this type of cipher will follow in the next few articles. Try out your own ideas on cipher No. 76, on next page. The underscoring of figure 1, and the line struck through zero, in this cryptogram, are in accordance with United States army code practice to distinguish these figures, respectively, from the letters I and O.
Last week's "jumbled crypts," No. 71, conveyed the following two messages, enciphered in the subjoined alphabets, which are of the "coupled pair" variety, based on the key words STOLEN and PEARLS.
(a) You will find the missing necklace behind the large portrait in the library. S T O L E N A B C D F G H Z Y X W V U R Q P M K J I (b) The necklace was stolen by the girl in black wearing the jade ring. P E A R L S B C D F G H I Z Y X W V U T Q O N M K J
After these messages were enciphered in their respective alphabets, they were "jumbled" by interchanging the third, fifth, sixth, ninth, eleventh, and twelfth groups of the two cryptograms. Thus KHUM became the third group of (b); and RXU the third group of (a). The other jumbled groups were interchanged in the same manner. The idea here was to present a somewhat more difficult problem than the simple substitution cipher without resorting to unusual words.
Cipher No. 72 (John H. Rosa) conveyed the message: "Look out for the girl with the pearls; she knows our game." In enciphering, first transpose the first letter of each word to the end of that word (b); add an A to each group, forming the "speaking cipher" (c); and regroup by fives (d).
(a) LOOK OUT FOR THE ... (b) OOKL UTO ORF HET ... (c) OOKLA UTOA ORFA HETA ... (d) OOKLA UTOAO RFAHE TA ...
Cipher No. 67 (M. Walker) used the four alphabets given in the issue of September 10, in connection with a four-figure key, 1-7-5-4, derived from the key word, AGED, by replacing each letter by its place number in the alphabet. Message in full: "The designer believes that without doubt it will prove to be really quite a difficult task for any one to decipher this without the key."
To encipher, group the message by fours (a); write the key above each group (b); substitute for each letter by counting forwards in its alphabet the number of letters indicated by its key number (c); and regroup by fives (d).
(a) 1754 1754 1754 1754 ... (b) THED ESIG NERB ELIE ... (c) AOQJ TZEL SLAW TSEU ... (d) AOQJT ZELSL AWTSE U ...
With the alphabets known, this cipher is decipherable in the same manner as the Gronsfeld. (See issue of June 6, 1925). Without them, decipherment of the system is still possible, but much more difficult.
A few more words about this week's layout, besides what has already been said of No. 76, the transposition cipher. No. 74 tells of a deep-laid plot. We do not know what the parties concerned have up their sleeve, but maybe you can read their message, and cause their undoing. This example is in simple substitution cipher.
No. 75 is an adaption of a very ancient system, described in a recent installment. To tell you any more would make the problem too easy.
All right, folks! Up and at 'em!
CIPHER No. 74.
MFB: EDAA EID PYLW EY BDDE BD GE EID TYYE YT ZGCGA WEVDDE EYBYVVYU CFRIE. CY YCD FW UFWD EY YXV QAGCW. PFAA.
CIPHER No. 75.
GSVIV ELOFG RLMZI BKOLG HSZEV YVVMU IFHGI ZGVWZ OVZWV IHLUG SVNLE VNVMG SZEVY VVMZI VHGVW
CIPHER No. 76.
YMWIA GAELT SLRHG EIOEW S0MYE ADFSA AAMHU 2NOIA TIOLN EIATR MNDD0 OUTRS HDLHI N2RLS 0ITTT RYBIO MB7SD HWHSU EOSAA GYASM A1FU
Ciphers Nos. 74 and 75 will be explained next week; No. 76 in three weeks. You still have one more week on transposition cipher No. 70 (Charles Winsor), published two weeks ago, the translation and key to which will be given next week. If you have not already solved this, try it.