As to consonants, we have assigned the value t to the most frequent one, R, and there has been no difficulty in identifying h in the letter K, which three times has followed R. But our present cryptogram is too short to provide any clear distinction among letters which might represent n, r, s. With the seven substitutions made, as shown at (c), notice how quickly it becomes possible to spot the incongruity of sequences tho, more than once, in a short text which contains not a single occurrence of he or ha. Notice again, at (d), how quickly the mere exchanging of the values e and o will bring out word-suggestions.
At (e), the first line of the cryptogram is repeated, as it would appear after the making of this exchange. The beginning of the message can almost be read: The first word appears to be notify, furnishing two new substitutes. Three more can be furnished in the suggested sequence to go ahead with. And here, the word with would be tried in any case, because it is a common word, and because the frequency of the letter P is suggestive of w. Arrived at this point, we begin to notice patterns: postpone, council, account, matter, and so on; so that the rest of the solution is largely a matter of filling in framework. In the given example, it would also be noticed that F and N have resulted from reciprocal encipherment; this may not be the case with other letters, but it presents a possibility which is always well-worth investigating.
Figure 68 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Most Frequent Digrams |
The Digram-Solution Method. — This method, representing another of our many debts to M. E. Ohaver, may be used either in conjunction with the vowel method, or independently, as the fundamental method of attack. For a satisfactory demonstration, however, we need more material, and Fig. 67 shows our cryptogram again, together with a suspected reply. Thus we have a length of 235 letters, so that the preparation of contact-notations, which we found sufficient in the preceding case, becomes here an irksome task.
For these longer cryptograms, it is usually best to put all of our data into the form of a digram-count, as indicated in Fig. 68. This is most easily done as follows: Using a sheet of cross-section paper, mark off the limits of a 26 x 26 square; write the normal alphabet across the top, so that each of its letters will govern a column; and write it again along one side, so that each letter will govern a row. For added convenience, these two alphabets may be repeated, as they are shown in the figure. Now, remembering that each letter in the text is the first letter of a digram (except the two which are finals), our two texts, with their total of 235 letters, are to provide a count on 233 digrams. Taking letters one by one, just as they come in the cryptograms, find each letter in the upper alphabet; find, in the side alphabet, the letter which immediately follows it in the cryptogram, and count this digram by placing a tally-mark in the cell at which the column and row governed by these two letters are found to intersect. In the figure, the tally-marks have been replaced with numbers showing their totals. It will be noted that the process described is identically the method which would have been used by Meaker in preparing the digram chart; and, just as in the case of the digram chart, the counting of the digrams has automatically counted the single letters. To obtain their frequencies, we may total either the columns or the rows, taking the larger figure in those few discrepancies caused by initial or final letters. With the chart understood, the digram-method of solution can be shown in a nutshell.
An inspection of this chart enables us to find quickly that the leading digrams are those listed: RK, VT, KV, DY, etc. These, almost certainly, are the substitutes for digrams ranking high on the normal list, and many others, having a frequency of 3, are very likely indeed to be substitutes for digrams from that same high-frequency class. Our text, of course, is still short, even with 235 letters, and we do not invariably find, in texts of this length, that the ranking digram (in this case RK, frequency 10) is the substitute for th, though the chances are, at all times, that it is. And should it prove here that RK does not represent th, then we may be quite sure that th is represented in one of the digrams VT, KV, DY, having the next frequency, 6. With the single exception of RR, each digram of the nine which are listed below the chart can be checked against three other digrams: Its own reversal; the doubling of its first letter; and the doubling of its second letter. In addition, it may be checked through the individual frequencies of its two component letters. These points of comparison, made for each of the nine leading digrams, have been tabulated in Fig. 69, so that the discussion may be easily followed.
Examining RK, assumed to represent th: Its reversal, KR, has not appeared on the chart, which is satisfactory for a digram of no greater frequency than its supposed original, ht. The doubling of its first letter, RR, has appeared four times, which is satisfactory for tt, one of the leading doubles of our language. The doubling of its second letter, KK, has not appeared, which is eminently satisfactory for a digram as rare as hh. Its first letter, R, has a frequency of 28, the highest in the cryptogram, which is not at all unusual in the case of t; and its second letter, K, has a frequency of 16, a little high for h, but not unsatisfactory. Thus, we find nothing, so far, to contradict the supposition that the digram RK is the substitute for th. But if K represents h, it should be possible to find digrams beginning with K which will check equally well as the substitutes for ke and ka. We do, in fact, find KV and KS. But which is which? Examination of Fig. 69 shows that one of these, KS, has a reversal, SK, frequency 1; but this is not informative, since it would be equally expected of eh or ah. Further examination shows that V has been doubled, which is far more characteristic of e than of a. Also, the individual frequency of V, 24, is the second highest in the cryptogram, and more likely to be that of e than that of a. Thus we may assume that KV represents he and that KS represents ha. This automatically identifies the digram SR as at. As to VT, this, apparently, involves the only reversal of any prominence in the cryptogram. Its first letter has already been identified as e, and the outstanding reversal of the language is er-re. This is not so certain as in the preceding cases, but the frequency of T is satisfactory as that of r.
Thus we have identified the letters t, h, e, a, r, which is as far as the tabulation has been carried. Having the substitute for h, we may now bring in the vowel-solution method through examination of digrams KD, KJ, KT, KZ; or continue with the digram-solution method by looking over the field for some of the other h-digrams: sh, ch, wh, ph, gh, and so on. The first of these should be easily identified by the frequency of s, and, in addition to the regular three check-digrams, we might check this against a possible st, another of our leading English digrams. With the process explained, we need not go further; the substitution of letters t, h, e, a, r, s, will surely break any simple substitution cryptogram. Possibly, enough has not been said as to the use of the trigram list, the consideration of common
| Figure 69 Digram Doubled Letter Letter Frequency Supposed IdentityOriginal Reversed 1st 2d 1st 2d R K 10 K R... R R 4 K K... R 28 K 16 t h V T 6 T V 2 V V 1 T T... V 24 T 15 e r K V 6 V K... K K... V V 1 K 16 V 24 h e D Y 6 Y D... D D... Y Y... D 2l Y 10 ? W D 4 D W 1 W W 1 D D... W 8 D 2l ? S R 4 R S... S S... R R 4 S 18 R 28 a t K S 4 S K 1 K K... S S... K 16 S 18 h a R R 4 .... .... .... R 28 t t H V 4 V H... H H... V V 1 H 5 V 24 ? (-e) |
affixes, common short words, and so on; but these are all points which the student can best develop for himself.