A Method for Attacking Difficult Cases
By George C. Lamb
Several routine methods have been evolved for special use on the very difficult “aristocrat” — that fascinating form of simple substitution with word-divisions in which the message is of no importance whatever and the encipherer’s full attention has been given to manipulation of letter characteristics. Of the several such methods which have proved workable over a long period of years, the author’s favorite is the “consonant-line” method, the exact value of which has been tested in a special analysis of 130 very difficult cryptograms. However, it should be stated clearly that no method is a mechanical crypt-solver; these devices merely serve to bring out clues which to the haphazard worker are totally invisible. For discussion, we will consider an example by M. E. Bosley which appeared as No. 19 Aristocrat in The Cryptogram for June, 1936. This is shown at Fig. 71.
| Figure 71 U W Y M N X K A E H X R B Z U V X M U W B Z O Y Z T W H V C X Y A C Y A U Z D B R A H V K B A; Z W S V A H K U Z B K C, M S C X C Y X B S, X V Z Y T R Y C X P. |
The work must be initiated by isolating a small group of consonants, and the problem of selecting these with certainty is one which for years has baffled the shrewdest solvers of both the National Puzzlers’ League and the American Cryptogram Association. Many successful solvers have based their selection on frequency alone, rearranging the letters of a frequency count in the order of decreasing frequency and marking off a section of low-frequency letters which will presumably include only consonants. But the clever manipulator is able to distort frequencies out of all resemblance to the normal table, and here we will base our selection on variety of contact — something which the constructor cannot successfully manipulate.
Fig. 72 sums up the entire process. At (a) we have a list of contacts taken in the order of appearance of the letters, and at (b) a rearrangement of the cryptogram letters in the order of decreasing variety of contact. Immediately above each letter is its “variety count” and directly above this is its frequency figure. In this set-up, a certain number of letters taken at the extreme right may confidently be marked off as a group of consonants. As to just where the line of demarcation may be set, recent analysis has shown that it is safe to include 20% of the total variety-count. In this case, the sum of all variety-figures is 104, and 20% of this, roughly, is 21. If we begin with P at the extreme right and add numbers backward for a count of 21, we find that the line of demarcation falls between R and C. However, we have at this point four letters, M, R, C, S, whose variety-count is uniformly 5, and any two of which might have occupied the places of C and S. To accept a vowel at this stage would mar the effectiveness of our system, and either we must discard all four of these letters, or we must find a means of differentiation other than their variety of contact. At this point, letter-frequencies come into play.
Examining the set-up just as we have it prepared at (b), note that the two figures just above M are 3-5. This is a “step-up” of 2 points. Note that just above R we have the same two figures 3-5, another step-up. Above C, we find the two figures 6-5, this time a “step-down” of 1 point; and above S we again find 3-5, a step-up. According to years of observation, confirmed by investigation of special cases, a vowel nearly always shows a tendency to step up, while consonants are
| Figure 72 (a) List of Contacts U6 W7 Y9 M5 N2 X10 K7 A7 E1 H6 R5 B8 Z6 V8 O1 T4 C5 D1 S5 P1 -W U-Y W-M Y-H M-X N-K X-A K- -H E-X X-B R-Z B- U-X -Y Z-W V-X -B W-V X- -V U-B O-Z X-U H-R V-B Y- W-V B-A W-Z B- H-C Y-R -Y M-C M-W T-H X-A -S V-M H-D Y-U A-V T-Y D-R Y-T H-K K- B- A-Z Z-S C-A C-Y B-C R-H A-K K-A U- S-A S-X K-Z C-X C- B- Z-K -W X-Z -Y Z-T Y-B V-H X-S U-B Y-X R-C -V V-Y C-P (The figures give the "variety-count," or number of different letters contacted. Roversals may be indicated by circling letters. Note that in dealing with normal word-divisions, we may omit contacts falling between one word and another). (b) Basis for Primary Isolation of Consonant-Group: Letter-frequencies: 8 7 6 5 4 4 6 5 4 7 3 3 6 3 2 1 1 1 1 1 VARIETY OF CONTACT: 10 9 8 8 7 7 7 6 6 6 5 5 5 5 4 2 1 1 1 1 (104) X Y B V W K A U H Z M R C S T N E O D P (c) (d) (e) (f) 3d word: FIRST CONSONANT LINE SECOND CONSONANT LINE THIRD CONSONANT LINE x . x x x C T N E O D P C T N E O D P A U C T N E O D P A U W Z U V X M U W B Z │ │ │ H v│ vv│v vvv│v x│xxxx x│xxxx x│xxxx (Vowel) (g) 7th word: yy│yyy yyyy│yyy yyyyy│yyyyy (Vowel) k│ kkk│ kkk│ x x x x x x . x s│ s│ s│s Z W S V A H K U Z B K C z│ z│zz zz│zz (Consonant) │w │www │wwww (Consonant H) (h) 4th word: │r r│r r│r m│ mm│ mm│ x . x x x x x . . x │h │hhh │hhhh O Y Z T W H V C X Y A │b b│b bbb│bbb (Vowel) H │ │u uuuu│u (Consonant) a│ s│ (Consonant) │ t│t (Consonant) │ |
prone to step down. Thus among our four doubtful letters, there are three, M, R, and S, of which one will probably be a vowel. But the remaining letter, C, has the step-down peculiar to consonants; and while a step-down of only 1 point would not be definitely informative when found at the left end of the set-up, it almost certainly indicates in the present position that C is a consonant. Thus, we are able to include seven letters, C T N E O D P, in our group of “sure-fire” consonants, but have to dispense with several points of our 21-count.
At (c) we have the beginning stage of the actual investigation, while (d) and (e) are amplifications of the first stage. In these the original consonants are used to determine other consonants, progressing from stage (c) to stage (e). First, the original group of consonants is set down on a sheet of paper, and the space below it is bisected by the consonant-line. Consulting (a), we then find the letters of this group one by one, and all contacting letters which precede any one of them we set down on the left side of the consonant-line, and all those which follow any one of them we set down on the right side, always once for each time that the contacting letter appears. Thus we have stage (c). While we do not often encounter doubled letters in this form of cryptogram, it may be well to say here that while a doubled letter would be counted among the frequencies of letter appearance, its contacts with itself would not be entered on the consonant-line. That is, a doubled L would add a frequency of 2 to the general count, but contacts L-L would be ignored.
At (d) we have the first step in amplification, for which we are indebted to Chester A. Griffin. If there is any letter in the cryptogram which does not appear at all in (c), such a letter is practically sure to be another consonant. In this case we find A and U, and in (d) these two letters have been added to the consonant group and their contacts placed on the consonant-line. From this point onward, the work becomes more tentative, and, as a detail of operation, Mr. Griffin suggests that further additions to the consonant-line be made in another color of lead; if it then becomes a matter of necessity to erase, only the new letters will be included in the erasing.