Since the reconstruction of these mixed-alphabet slides is probably the most fascinating subject in the whole field of cryptanalysis, several problems are being appended in Fig. 148. In all of these, Semper has selected key-words or phrases to contain no repeated letters. With reference to the practice cryptograms, only one of those submitted was thought to have enough alphabet-length for purely analytical attack. The others, even with their probable words or partial translations, will still require some work. The periods of these examples are said to be, respectively, 6, 7, 8, 3, and (?).
135. By NEMO. (Type II. Partial solution: WHEN JACK BOOMER,GREEN RIVER,WYO,B..)
T E R P J Y D B N Q S A I M B X B L Y M D O B I T Z P T I H K O K A G
M Y Q R X T D W U U X B O B Q Y D B W Z S V Z G C U P R Z S W V O D M
T Q Z C A T S M Y Q F D B H Z Q U T I H F S V S Y N F U L Z G L B G D
M T R M U C N A J M I Y N Q O F B D P Q L G X U Y W U I P C A Y N J N
X S B K W I J G R L G I B.
136. By NEMO. (Type III. Partial solution: ALOIS STEPHEN,YOUNG VIENNESE CHARGED W..)
H G K S T I L O Y D B O L E G A Z N G P D U W P B D R V Z Q Y Z X F L
Q S B H S L T U Q P S Z G X V A Y T G B C B X K H U R I E D M D X B T
O E P S A R I N K X K J B I T P Y I X R I U Z Y O M I M H P H B E J D
N E B S E F L B F D B H F J B F N L G P L J M I B O G T A W D U E Q E
Z T Y U S I.
137. By THE SQUIRE. (Type III. Probable words: AMERICAN CONSTITUTION. GLADSTONE).
H T F M R S R T Y E O V P D S Z L A X B A C N T N A K X R C S Z K G O
Q U O F A Z R E T D S V I W K W T E L K F R P R B I H I N A S W R R S
B O H T F L A D D L U B U F M Q O J A G I L I D W T Z I M M R H L L V
K W U J S.
138. By ALII KIONA. (Is this a diplomatic telegram?)
L L D R K Y C R F A S E V S U K T D U L X V K E V C A B L Y U P Y M R
K B E X U B T E L W P J F P T I I U Q Q K T F C T P S K Q L W N D A P
B F A E S N M P R K A P T T S H F K B Z R M G P P Y V M S A I F N P Z
A L T S U S A U D N L X A A Z Y P U C H K N P Y V M S I A X K K D B E
T P S A T P K P S Y V T A Y E A P B T E L W P J F P T A X N.
139. By PICCOLA. (This is a straight-alphabet cipher. Won't tell which one!)
A N D N Y L M Y X N K D L R P G C X G Q N A A R Z L D E P L G I A W Q
N E I O G A G P Q G Z V D E I E Z R H A Y P L B P N A G E L N V A G T
D H O K H V G T I N D O L S F C P L R T.
CHAPTER XIX
Polyalphabetical Encipherment Applied by Groups
Any one of the multiple-alphabet ciphers may change keys at each new group instead of with each consecutive letter. As a rule, this kind of encipherment is never found except in connection with very simple ciphers, and the intact plaintext groups, each one standing on its own key-line, are readily discovered by the decryptor who takes the precaution of cutting out a segment from his cryptogram and “running down the alphabet,” first treating the original letters and then, if necessary, their complements. Porta encipherment, in any form, is rare, but its cryptograms can be subjected to the same process, provided the letters of the tested segment are first enciphered in the AB-alphabet, and the subsequent extensions properly carried out.
| Figure 149 The "PHILLIPS" Cipher 1 C U L P E* 2 R Z Y X W 2 R Z Y X W 2 R Z Y X W 2 R Z Y X W 1 C U L P E* 3 V T S Q O 3 V T S Q O 3 V T S Q O 3 V T S Q O 1 C U L P E* 4 N M K I H 4 N M K I H 4 N M K I H 4 N M K I H 1 C U L P E* 5 G F D B A 5 G F D B A 5 G F D B A 5 G F D B A (1) (2) (3) (4) Plaintext: T R Y M A....... C D O N A....... L D O N T....... H A T M U.. CIPHER: K T Q D C....... T X N F R....... I X C F L....... C R K L D.. 2 R Z Y X W 3 V T S Q O 3 V T S Q O 3 V T S Q O 3 V T S Q O 2 R Z Y X W** 4 N M K I H 4 N M K I H 4 N M K I H 4 N M K I H 2 R Z Y X W** 5 G F D B A 5 G F D B A 5 G F D B A 5 G F D B A 2 R Z Y X W** 1 C U L P E* 1 C U L P E* 1 C U L P E* 1 C U L P E* (5) (6) (7) (8) ..... R P H Y P....... R O P O S....... I T I O N....... C U R L Y. ..... T W G Q W....... M R O R X....... W K W N Z....... T S U Q P. |
With mixed alphabets of any kind, a number of cases may arise, according to whether groups are of uniform length, or of varying lengths, or, in fact, represent word-lengths; or, in the one case of uniform groups, according to the length of these groups, or the amount of material available, or as to how much is known in advance, and so on. From among so many possibilities, suppose we select the case of accumulated short messages, and, at the same time, take a brief look at a cipher which, according to its description, was actually intended for group-by-group application. This cipher, which may be examined in Fig. 149, was described in an early issue of The Cryptogram as having been used for military purposes, and was called the “Phillips” system. The text of the figure “Try Macdonald on that Murphy proposition. Curly” includes eight five-letter groups, thus requiring eight cipher alphabets. The key, as originally prepared, is a mixed 25-letter alphabet written into a 5 x 5 square, of which the five rows can be cut apart to form five horizontal strips. It may also be set up with anagram blocks. This is alphabet 1 (or block 1), and serves to encipher the first five-letter group. The method of substitution will be explained in a moment. Alphabet 2 (block 2) is derived from the first by moving line 1 so that it stands between lines 2 and 3. Alphabets 3, 4, and 5 are derived by continuing to move the original line 1 so that it stands, successively, between lines 3 and 4, between lines 4 and 5, and at the bottom of the square. Alphabets 6, 7, and 8 are derived by moving the original line 2 according to the same plan. For puzzle purposes, these movements may continue as they apparently began. Line 2 may be given its one remaining shift, which places it at the bottom of the square, and lines 3, 4, and 5 may then be moved downward in the same way as the first two; some puzzlers, in fact, will afterward continue by treating columns. But according to the description (the only one the writer has ever seen of this cipher), the eighth cipher alphabet is the last. For the encipherment of the next eight groups, either the square is restored to its original set-up and the same eight alphabets used again, or the first key is abandoned altogether in favor of an entirely new one.
Now, considering any one block, as No. 1, the method of substitution is as follows: Each letter is to be replaced by the one standing immediately to its right on the descending diagonal. If the given letter happens to stand at the extreme right side of the square, it is to be replaced by one standing at the extreme left and on the next line below. If it happens to stand on the bottom row of the square, it is to be replaced by one standing on the top row and in the next column to the right. One letter, in fact, requires both of these (mental) adjustments; the letter which occupies the lower right-hand corner is to be replaced by the one occupying the upper left-hand corner. If the foregoing is well understood, is is quite obvious that our key-square is, to all intents and purposes, a rhombus formed with five diagonals. One diagonal is complete, as C Z S I A of block 1. The other four break off at the right and are continued from the left, as L X O N F of block 1; or, if you prefer, break off at the bottom and are continued from the top, as N F L X O of block 1. It should be obvious, also, that any one of these five diagonals can be considered as beginning with any one of its five letters without in the least changing the encipherment. Thus, each diagonal furnishes what is called cyclical encipherment. But, as a matter of fact, the entire square involves cyclical encipherment: The placing of line 1 at the bottom of the square, or of column 1 on the right side of the square, or the transfer of several lines or columns, or of both, will not have any influence whatever on substitutes; for this, it is necessary to alter the 1-2-3-4-5 order of these rows or columns. Alphabet 5, then, will be the same as alphabet 1; and if the plan of the puzzlers be followed, this same alphabet continues to reappear for the encipherment of each fourth group, blocks 1, 5, 9, 13, 17, and so on, of a long cryptogram, eventually giving a great deal of material in one cipher alphabet. Moreover, groups having a length of five letters will carry some very visible simple substitution patterns. Now suppose we look at Fig. 150.
These eight cryptograms have all come from one source. The general frequency count has shown a missing letter, J, suggesting the use of a square, and we have suspected the cipher as “Phillips.” With cryptograms arranged one below another, as shown, the first five columns are presumably enciphered with block 1 of that cipher, the next five columns with block 2, and so on; thus, we presumably have 40 letters each belonging to alphabets 1, 2, and 3, and almost that number belonging to alphabet 4, that is, enough material for frequency counts which will show whether or not they have been taken on simple substitution alphabets. While 40 letters of text are very few, we could, eventually, solve any simple substitution cryptogram of that length, or any mixed-alphabet periodic whose alphabets have furnished 40 letters each. In the present case, our first alphabet has furnished eight known word-beginnings; we have one column known to contain only initials, and followed by two others which are very likely to be the hiding-place of vowels. This does not mean that we should have no preliminary struggles, but in the end there are plenty of clues to set us on the right road: The predominant letters of alphabet 1 are A, B, O, K, U (practically sure to contain e, t, and one of the vowels a or o). The column of initials repeats both A and T (to be compared against a list t s a. . . .). The second and third columns, combined, include B and O, three times each, with O found in the initial column also (both could be vowels, and O probably represents a, though i is also frequently found as an initial). If A, by frequency and initial position, be tried as t, then the other repeated initial, T, can be tried as s. This assumption brings out, in the fourth message, a pattern s - t t -, in which the second letter, B, would have to be a vowel, either e or o, since it has been doubled, with e appearing more likely in the given pattern and also in that of the sixth message, s - - - s. The letter O, which under the encipherment scheme could