IN the three preceding weekly articles we have shown methods of finding the key length of the transposition system described in the issues of September 17 and 24, using cipher No. 73 of the latter issue for that purpose.
Keys of 2, 3, 4, 6, 8, 9, 12, 18, et cetera, letters were eliminated from the "line-up" of suspects by factoring. Next, keys of 5, 10, and 15 letters were turned loose upon being scanned by the method of computing intervals given last week.
But there still remain keys of 7, 11, 13, 14, 16, 17, 19, et cetera, letters. Of these, 7, already sort of isolated from the rest, begins to look rather guilty. In fact, the few remaining suspects themselves seem to be casting doubtful glances in its direction.
Were there no other evidence at hand, however, it might be necessary to give all these key lengths a trial. But fortunately we have another method which is going to point an accusing finger at the "guilty" one, and thus bring our case to a speedier ending.
This last method is based on the fact that the column lengths of a given cryptogram in this type of cipher can be determined, approximately, by merely observing at what points two otherwise compatible series of letters begin to produce improbable digraphs.
To illustrate this, the two series already used to find the interval 31 are again employed, but at greater length, herewith. Each digraph in the series is followed by its frequency number, taken from the complete digraph table in the January 23, 1926, issue of this magazine.
etc. A R 78 L R 4* O O 29 L R 4* T E 74 S H 40 U N 48 H I 75 L A 30 H E 305 Q U 9 N D 116 O S 35 U R 33 C I 19 A E 1* D O 30 D N 5* C I 19 etc.
The eleven digraphs included between the two horizontal lines all have relatively high frequencies. But the LR's, above, and the AE and DN, below, are of low frequency. Assuming, consequently, that these latter do not occur in the message, and they therefore belong to other columns than the two being matched, the column lengths in this case may be taken as about eleven letters.
If the columns were shorter than this in the original set-up, low frequency combinations would probably be encountered within correspondingly narrower limits; and if they were longer, the series would probably not be interrupted by so many low frequency (*) digraphs.
Now, a seventy-two letter message with a seven letter key, as observed last week, would produce columns of ten and eleven letters. A key of eleven letters would give columns of six and seven letters. Similarly, the use of keys of thirteen, fourteen, sixteen, et cetera, letters, would result in still shorter columns.
We are therefore reasonably certain that a seven letter key is responsible for the present mix-up. But absolute proof will be lacking until the message is actually unlocked with a key of this length. So let us withhold our final judgment in this matter, at least, until next week, when the analysis of cipher No. 73 will be continued on the supposition that it employed a seven letter key.
Cipher No. 76, published October 1, and of the same type of transposition cipher as the above No. 73, was enciphered with the key word NAVIGABLE, conveying the message:
Mystery submarine 027 was again sighted to-day drifting almost awash near the Midway Islands about twelve hundred miles from Honolulu.
A good rule to follow in enciphering any message containing figures, and one usually observed, for example, in military ciphers not making special provisions for figures, is to spell out all numbers.
The numbers in the above message were purposely allowed to stand in order to illustrate how they offer a means of attacking the cryptogram. Assuming that some of the figures are used together in the message, series containing them can be tried in various combinations to get probable sequences of letters by the method given two weeks ago.
There being but seven figures in the cryptogram, it would only be necessary to try any one of them before and after the remaining six, twelve trials in all, to get a start. This would be comparable to trying some of the less frequently used letters in a cryptogram by the same method.
Here is the translation of Ernest Brewster's "crypt" No. 80, published in FLYNN'S last week:
Second immurement having elapsed, convict awaits discharge within wardens office. Plans further skullduggery upon release. Turnkey loiters near by.
To decipher No. 81 (M. Walker), merely take the third word of each sentence and you will have the message: "Come over, this evening, we have one quart left." Now you know why nothing short of an earthquake would have kept Dear Uncle" away.
In No. 83, the first of this week's brain teasers, you have another of the "Q. and A." cryptograms. Different simple substitution alphabets are used for the question and answer. Some chemical terms are involved in this cryptogram, but the short words should help you through in short order.
Nos. 84 and 85 are both "null" ciphers. In the first example only certain letters have any significance; and in the second, certain words form the message. In both cases, however, the significant terms are placed in accordance with prearranged keys. The dashes are necessary to both of these ciphers.
CIPHER No. 83.
Question: LZTO TFW OZW SBAABR- WGO BX OZW KQOFQBNG ? Answer: NMIO DLABLTM, TB KTJJOB CIMJQRAO; SBOOH DLABLTM, TB LBTH CIMJQRAO; RHY GQLAO DLAB- LTM, TB XLHK CIMJQRAO.
CIPHER No. 84 (Dr. H. E. Burnett, San Antonio, Texas).
Bnhkof ytv-xakhlf mln-dwbfhy yoh-gthrg nyv-dsabum vcbnegcn hecdej nde.
CIPHER No. 85 (Ken Davidson, Montreal, Quebec, Canada).
—After the first attempted deciphering fails, a good many give up. A man who reads this and makes use of his deductive powers, who realizes there must be something of importance hidden in it succeeds, where others have failed, through his absolute refusal to give in. This has made many high ability solvers quit. Will you? KEN.
Solutions to ciphers Nos. 83 and 84 of this issue, and No. 79 (W. A. Cooke) of two weeks ago, will be published next week. Answer to No. 85 will be published in three weeks. Be sure to send explanations along with ciphers sent to this department.