Trying again, however, beginning at the tenth trigram and examining each fifth decipherment, we find something more satisfactory: ALL, ION, BEH, DFR. If these are correct, the period is 5. At (c), we have gone back to the continuously-written cryptogram in order to try these in their places; and since a period 5 would mean that each of the letters E D A is used regularly to encipher each fifth letter, we are able to include two shorter decipherments at the two ends of the cryptogram. The next step in logical order is to try deciphering T in front of ION, since the trigram TIO would have been the next one on our trigram list. This brings out key-letter C, which, if correct, will decipher correctly at each interval 5, and which extends our key-letters to C E D A. We can see, too, that this is not the beginning of the word; the sequence we have is D A * C E. In the given example, it is not difficult, also, to guess a probable word, FRIDAY. Now, having twice called attention to the fact that the trigram-search can grow quite tedious, we hasten to point out that it need not be made more so by deciphering each trigram individually. If your trial key is THE, set your slide at the T-alphabet (or point this out on the tableau), and decipher every first letter on the sheet. Then set the H-alphabet in position, and decipher every second letter on the sheet. Finally, set the E-alphabet in position and decipher all of the remaining letters.
The foregoing few paragraphs have illustrated the worst case in almost its worst form, but will show the principle. Now let us consider this work in a much more usual case. As mentioned earlier, the first of the two work-sheets will be prepared with a great deal of space between the rows of trigrams. The full number of decipherments will be made for the first trigram THE, but not erased. Just below these, a second row of decipherments will be made for AND, and these, too, will be left standing. (THA can be omitted.) A third row of decipherments is made for ENT, a fourth row for ION, and so on down the list, until there are six or eight rows of possible key-fragments. These are all examined and compared with one another, in the hope of finding duplications. Perhaps THE and AND have both brought out a key-fragment EDA, or one has brought out CED and the other EDA, having ED in common. It is far from unusual, in some of these cases, to find a whole series of these overlapping key-fragments, for instance, CON, ONS, NST. This will explain why many persons consider the trigram-search the simplest and most direct way of attacking a Vigenère cryptogram.
For the benefit of the novice, we end the chapter at this point in order that he may have some practice. Example 104 comprises a thrilling serial with all the trimmings, gripping and original title, smashing climax, and a brave hero, John Miller. The key to the title is STRANGE. Part I repeats a word found in the title; part II repeats a word of part I; and somewhere are the trigrams NOT, CON, YET, ING, TEN, THE. We have heard, too, that an amateur encipherer will occasionally encipher the nulls which he adds in his final group. Example 105 is easily investigated through short common words. As to the remaining examples, while it is true that they can be attacked by the trigram method, the student will probably prefer to leave them until he has seen the methods outlined in Chapters [XIV] and [XV].
104. By PICCOLA. (For trigram practice. A new key for each fragment).
Title of Serial: S L K R N T K W W Z S N V T W T I A A I I X X X X.
Part I: R I G Z V Z K I U O M H J L B W F P K S R Z T R H E J T W I
O S W I O S G Q I I. Part II: H H T X T N E O L V R M T U L C L P P X
T Y R X K U K B U W U O J Z H X M Z K H. Part III: S Y Z Y R T N F U R
K C U S I I R Q U X W U F K C J N R L Q N F O K V X M P U O N H J A X
J H V O P. Part IV: X B V P Y S X C J J Y U R X O T S P I N Y I L U P
A V M X M M F C I B S T I T O O T B R O.
105. By PICCOLA. (For investigation of short words. - Still Vigenère!)
V Y I D J G I E J S N V R J H J F J D B G E K O W U Y A R F F Z W
V O K U X R P G R J U O E K M R B U Y S U H Q W J L J G C I W H G I W.
106. By NEON. (Any repeated trigram is worth watching!)
P Q X E J F V E G Y M N Y N Y I U F R D S G V R I L P S G Z T M E S I
R K N Y I G P E R W G R R N D L O J N T Y I D X O T Y C I P C R E V C
E S G O I R L I S I R Z Q E U C G L T C I X H Y I X H E L E K Y J E K
P X I E Y R R S L H D L I F Y G P R J G S D I C E.
107. By THE ADMIRAL. (Numbers are always possible!)
L V P R V S F P T Y J S P H L F R C E U S B O S Z P H J F Z N S O A P
K T T V V Z C F R J X C C T P W W R H K E W Y U K W G L N U X C C T P
X W G E R F R Z N V Z O W F J W Q Z N U K W Y O E W M P A I.
108. By NEON. (This cryptogram, circulated in April, 1935, caused great consternation among solvers. Do you see any reason why?)
T W G J C N I U J X C S L S K K B N V G W I P S U Q I U J A U L J U Z
H B E V J V M A O H G G L T P D G L E Y S S L A F I M J S W Q I U M O
N N F L V H I U I Z D Q K V Y R T W H I M R F E U K P N O V Y T K E F
N V Q N O T.
109. By PICCOLA.
A X S E H G O I W W F O I A L G E M Q W E E N B W R E I K L S H Z Z Q
X L G A H V P Z K L D L G G D W T C M H Q D J N W K E H M V V A B M A.
CHAPTER XIII
The Gronsfeld, Porta, and Beaufort Ciphers
Now let us have a brief look at other classic ciphers of the multiple-alphabet type, and see to what extent these will differ from the Vigenère. The Gronsfeld cipher, as may be seen from the specimen encipherment of Fig. 92, uses a number-key. Its ten alphabets are governed by the ten digits. To encipher S, using key-digit 2, simply begin at S and count forward 2 in the normal alphabet; the substitute is U. To encipher E with key 8, begin at E and count forward 8 in the normal alphabet; the substitute is M. For decipherment, count backward in the alphabet. A very superficial investigation will show that the Gronsfeld key of the figure, 28105, and the Vigenère key CIBAF will produce identically the same cryptograms. The key-digit zero governs the A-alphabet of the Vigenère, the key-digit 1 governs the B-alphabet, and so on to the J-alphabet. If it is found convenient to use a tableau (as it may be for the decipherment), the first ten cipher alphabets of the Vigenère
| Figure 92 GRONSFELD Encipherment Key: 2 8 1 0 5 2 8 1 0 5 2 8... Plaintext: S E N D S U P P L I E S... Cryptogram: U M O D X W X Q L N G A... |
tableau can be ruled off from the rest, and the key-digits, in the order 0 to 9, can be added beside the key-letters A to J. Or, if the slide is the preferred method, these digits can be written beneath the first ten letters of the sliding alphabet; it is then possible to slide them into position below the index (the stationary A), in the same way as the letter-keys. The Gronsfeld cipher, then, is no more than a minor variation of the Vigenère, and requires no separate discussion other than a simple reminder that its possibilities are far more limited than those of the Vigenère proper. That is, it covers a range of only ten cipher alphabets where the Vigenère covers 26, and this limitation more than compensates for the fact that its key is not a plaintext word (presuming, that is, that we know what cipher has been used. Otherwise, the difficulties are about the same for both). To understand how this limitation may modify the case, let us examine the work-sheet shown in Fig. 93.