Wherever the trial segment is taken, there is always the question as to how many letters ought to be included. In Fig. 39, the decryptor has decided to take the beginning segment of the cryptogram, and has started with 15 letters. He has written beside it another 15-letter segment, chosen because of NG, HO, VI, and is attempting to tell, by the appearance of his digrams, and their frequencies as taken from two different digram charts, just about how far his digrams are uniformly good. If the nulls in use are actually XX, he knows immediately that this is the end of his two columns; otherwise, his digrams are acceptable throughout. If he sets down beside each digram its frequency as taken from Meaker’s chart, he might decide that his digrams are
| Figure 40 (The numbers assigned to these set-ups merely indicate the order in which the second segments were taken). 1 8 9 10 11 2 3 E U 7 E Y 17 E B 11 E X 17 E G 20 E S E O* N S 51 N T 110 N N 9 N G 75 N G 75 N O N E T O 111 T A 56 T S 32 T G 1 T E 94 T E T U *H E 251 *H E 251 *H E 251 *H E 251 *H O 46 H U H Y* V U - V I 19 V I 19 V O 6 V I 19 V Y* V E C Y - C D - C R 7 C I 15 C C 12 C E C I C E 55 C E 55 C A 44 C C 12 C R 7 C I C S* O I 13 O X - O S 37 O R 113 O L 17 O S O G 488 508 410 490 290 4 5 (1) (8) (9) (10) (11) 488 508 410 490 290 E E E I H E 251 H E 251 H E 251 H E 251 H O 46 N U N S 237 257 159 239 244 T Y T G* H E H A Ranked in the order: 8, 11, 10, 1, 9 V I V U* ......... C S* C A C G* C M* O A O A Same Test, Using Mr. Ohaver's Digram Frequencies: 6 7 1 8 9 10 11 E S E H* E U 6 E Y 24 E B 24 E X 14 E G 15 N G N Y N S 47 N T 97 N N 8 N G 83 N G 83 T A T T T O 92 T A 64 T S 27 T G - T E 74 H U H A *H E 305 *H E 305 *H E 305 *H E 305 *H O 42 V A V E V U - V I 14 V I 14 V O 9 V I 14 C M* C I C Y 1 C D - C R 12 C I 19 C C 6 C A C D* C E 46 C E 46 C A 36 C C 6 C R 12 O H* O E* O I 15 O X 1 O S 35 O R 99 O L 36 512 551 461 535 282 (Set-up No. 2 (1) (8) (9) (10) (11) would have 512 551 461 535 282 been tested.) H E 305 H E 305 H E 305 H E 305 H O 42 207 246 156 230 240 Ranked in the order: 8, 11, 10, 1, 9 (as before). |
good as far as UT, depending somewhat on the letters represented in our XX. Using Ohaver’s frequencies, he would feel sure that his digrams are good as far as OL. In many cases the frequencies shown for the lower digrams will grow so erratic as to be plainly unlikely; and in other cases, more difficult than the present one, a check on the probable column-length can be had by preparing a similar set-up for the end-segment of the cryptogram, in which the lower digrams are excellent, while those extending upward may grow erratic. This decryptor is safe, however, in accepting as much or as little of the length as he likes; there will be a more definite line of demarcation when he attempts to write beside these a third column of 15 letters. The only cases which ever give trouble are those in which a short text has been enciphered with a long key. Key-lengths, generally speaking, hardly ever run outside of limits 5 to 15, that is, lengths which come from single words. Thus a tentative key-length 10, 11, 12, lying half-way between these extremes, is always safe to try. The key-length 10, applied to 75 letters, gives columns of 7 or 8, and, in the discussion which follows, the tentative column-length was fixed at 8 letters.
Usually these trials are made by setting up the trial column (in pencil) several times in succession, so that several of the possible combinations can be seen side by side, in order to determine which is best. Sometimes this can be decided by simple observation. Otherwise, the combinations can be subjected to a digram test. This is made by setting down beside each digram, as formed by each pair
| Figure 41 1 2 3 4 Y E 12 D E 39 R E 148 E E 39 E N 101 E N 120 A N 172 O N 145 I T 88 X T 1 S T 121 I T 88 S H 30 T H 315 T H 315 C H 46 G V - N V 4 D V 4 R V 5 A C 39 B C - A C 39 L C 8 U C 17 H C 2 N C 31 B C - A O 2 B O 11 V O 6 X O 1 308 492 836 332 ..... Same Test, Using Mr. Ohaver's Digram-frequencies: 1 2 3 4 Y E 8 D E 64 R E 139 E E 57 E N 120 E N 101 A N 168 O N 162 I T 90 X T 4 S T 119 I T 90 S H 40 T H 377 T H 377 C H 53 G V 1 N V 1 D V 1 R V 6 A C 35 B C - A C 35 L C 1 U C 11 H C - N C 34 B C - A O 2 B O 13 V O 9 X O 1 288 560 882 370 |
of columns, its frequency as taken from a digram chart. These figures are then added in each of the set-ups, and the supposition is that the combination furnishing the highest frequency-total will be the correct one, provided this high total has been produced by all of its digrams collectively, and not by some one or two individual digrams. With short columns, such tests are never conclusive, but with as many as ten or twelve digrams they are nearly always dependable, and even with only five or six digrams they will often select a correct combination.
It was decided here to choose as the trial column the first eight letters of the cryptogram: E N T H V C C O. This column is filled with consonants, indicating that those which follow or precede it might contain a number of vowels; and of the six consonants present, practically every one could be called a “vulnerable” letter, or, as we say in the Association, a “clue-letter.” If we wish, for instance, to choose a column which will fit well on the right-hand side of this trial column, we can search the rest of the cryptogram for two consecutive vowels to follow, respectively, H and V, and these two vowels we should expect to find followed, either immediately or at interval 2 by some letter (usually a high-frequency one) which will follow at least one of the C’s. This kind of pattern, unfortunately, was found eleven times. In practice, we should probably abandon it rather than copy down
| Figure 42 Trigram Observation 1 2 3(*) 4 5 REU REY ¦ REB REX REG ANS ANT ¦ ANN ANG ANG STO STA ¦ STS STG STE THE THE THE THE THO DVO DVI DVI DVO DVI ACY ACD* ACR ¦ ACI ACC NCE NCE NCA ¦ NCC* NCR VOI VOX* VOS ¦ VOR VOL (*) Acceptance of combination 3 would entail shortening columns. |
and test eleven combinations; here, however, the eleven set-ups can all be seen in Fig. 40, accompanied by serial numbers to show the order in which their second columns were taken from the cryptogram. Some of these have not been tested. Of the five retained, particular attention is called to the fact that the one having the very lowest total is actually the correct one, as may be seen by turning back to the encipherment block. But when a single row of corresponding digrams (HE in the first four set-ups and HO in No. 11), has been subtracted throughout, it is seen that No. 11 moves upward toward its proper rank, having now the second highest total. In practice, it might even be selected in preference to No. 8, which grows erratic after its fifth digram (frequencies of 0, 55, 0). But the column-length 5, in practice, is not unlikely, so that a test made on the right-hand side of our trial column has not been at all conclusive.
Postponing the decision, then, let us take a fresh sheet of paper and make some tests for columns which can be fitted on the left-hand side of our trial column. Here, we find that the best “clue-letters” are N and H, standing at interval 2. To precede N, we should like to find one of the vowels of which it is so fond, and to precede H, we hope to find either T or one of the letters S, C, W. That is, we hope to find a pattern in the rest of the cryptogram in which some vowel, other than Y, is followed at interval 2 by one of the letters T, S, C, W. This time we find only four segments, and when the test is made for these, as shown in Fig. 41, the resulting totals point decisively to the correct combination, which is No. 3. Notice, in both of these tests, that results are identical whether the frequency-figures are those counted by Meaker or those counted by Ohaver: In the test of Fig. 40, the five combinations (using either chart) are ranked in the order 8, 11, 10, 1, 9, while the test of Fig. 41 has ranked its four combinations in the order 3, 2, 4, 1. Selecting, then, combination No. 3 of Fig. 41, let us return to the doubtful tests of Fig. 40 and attempt to effect a combination between our No. 3 and some one of the five previously considered worth retaining. Thus we can make an observation of trigrams, as shown in Fig. 42.