1. Certain pairs are identified, or assumed, as the substitutes for certain digrams.
2. These pairs and their supposed originals are set together in such a way as to start the reconstruction of the key-square.
3. Substitutions are made on the cryptogram and further pairs are identified.
When probable words exist, the work of solution becomes more or less mechanical, as we shall see. At worst, we may begin at the beginning of the cryptogram and work straight through until we find the word. But very often, a really probable word is repeated, and even repeated more than once. In the latter case, we are sure to find the long repeated sequence in the cryptogram; while a word repeated only once may have been divided into two different sets of pairs, as: ex-ec-ut-io-n and e-xe-cu-ti-on. But notice, here, what the two encipherments would be, using our key-square of the figure: LZ CU EO HQ x and x ZL UL QM QO. These two sequences have five letters in common, L Z U O Q, and, in addition, when considered together, show the letters E C U O of the word “execution.” This does not invariably happen, but is far from uncommon. Nor is the word “execution” the only one which produces reversal (ex in one sequence, xe in the other). Then, too, there are many words like “commission” which, regardless of the point at which the division begins, will always end in the same set of pairs: mi-s?-si-on.
Granting an absence of probable words, the difficulties of solution are almost entirely dependent upon the amount of material available. A pair-count will be made in the usual chart-form (but only on the divided pairs, and not “straddling” from one pair to another), and pairs will be identified by frequency, by the frequency with which they are found reversed, by the possibility of their letter-combinations in a key-square, and so on. We will not attempt, here, to go into a detailed demonstration, since every case is individual in its details, and success, in all of them, is dependent largely upon the decryptor’s own persistence. But in order to see sketchily what some of the routine might be, we will make use of the very short example shown in Fig. 167.
In the usual case, there has been a preliminary frequency count on single letters in order to find out what the cipher is. The appearance of this frequency count has more or less negatived the possibility of simple substitution, and the next step has been a Kasiski tabulation in the hope of finding a period. This tabulation, in any pair-system, will bring out a predominant factor 2, and, since many of the supposed digram systems actually do produce periods, the two supposed alphabets would have been examined for that possibility. But pair-systems, as a rule, will leave a wide-open trail: Repeated sequences, in the majority of cases, will include an even number of letters (that is, an exact number of pairs), and will begin largely at the odd serial positions (that is, at the beginnings of pairs). The Playfair shows this a little less distinctly than some of the others, because of the fact that substitutes for single letters are so limited in number.
It is sometimes said of the Playfair that it can be distinguished from other ciphers by (1) the fact that cryptograms contain an even number of letters, (2) the fact that only 25 letters are represented in its general frequency count, (3) the fact that when the cryptogram is marked into pairs, no pair will be a doubled letter, and (4) the presence of long repeated sequences at irregular intervals. As conclusive evidence, these are debatable points, but all are good supporting evidence, provided a proper confession can be extracted from the pair-chart: (5) When the cryptogram has been marked off into pairs, and the pairs counted, the result should bear much resemblance to a count made on the same number of normal digrams. Even on an extremely long cryptogram, over half of the cells will be blank, since a normal text never uses more than about 300 of the possible 676 combinations; there will be a certain group of predominant pairs followed by a group of moderate
| Figure 167 HR5 KY3 LD ZX NQ2 EO ND EC TC TI2 AD CT AK RH LB2 GT SN AN UN2 ON DR HX PE BN ZC DT KV EQ2 HD AO HR5 DU RP TQ OB DE2 QD2 HR5 KY3 YA2 HZ HB BU KZ EQ2 XG TI2 BI KY3 RI CQ HR5 CE CO SX RM BC TH CG QD2 RK NQ2 IT DC WT FV2 UB2 YA2 GU HE CZ NU2 LB2 IQ2 YK FV2 UB2 IQ2 WD QB UN2 KM DE2 TD KA HR5 NU2 OU Frequency Count - Rearranged: D H B C N Q R T K U E A I O Y Z G X L V F M P S W J 14 12 11 11 11 11 11 11 10 10 9 7 7 6 6 5 4 4 3 3 2 2 2 2 2 - List of REVERSALS "Chart of Probable Position" HR 5 - RH 1 EC - CE E T/ D H B C N Q R K U KY 3 - YK 1 TC - CT D H UN 2 - NU 2 AK - KA B C N Q R UB 2 - BU 1 ZC - CZ K U TI 2 - IT 1 DT - TD |
frequencies; and, with any appreciable length, there will be a generous sprinkling of reversals. In preparing the cryptogram, a great deal of convenience may be had by placing frequency figures beside their digrams, by marking long repeated sequences, noticeable reversals, and so on; and many persons like to list the most prominent pairs and the most prominent reversals.
The Playfair has also a rather characteristic frequency count. Notice, in the figure, where the general count has been rearranged in the order of decreasing frequencies, that the gradation from high to low is somewhat less even than in a periodic; frequency 8, for instance, is skipped altogether, and we have a sort of modified high-frequency group. Sometimes we find from one to three letters of great prominence before the downward gradation begins.