is backward, the alphabetical interval from Y to I is 16, which is not divisible by 5, the number of periods. But this progression might have covered the entire alphabet and then included 16, or it might have covered the alphabet twice, and so on, before including 16. We must make it divisible by 5, adding 26, then another 26, and so on, until we obtain a total progression of 120. This, divided by 5, gives the progression index as “minus 24” — the same as a normal progression of 2. In Fig. 161, the cryptogram has been re-written into the accepted period 10, and the figures in parentheses at the right of each group will indicate the amount of alphabetical shift when the progression index is 2. A constant progression of 2 per group would correspond to the application of a Vigenère key A C E G. . . . . , so that the Saint-Cyr slide will serve for quickly converting the cryptogram to its
| Figure 163 MATHEMATICAL FORMULA - C. H. PRICE X = AD x P LD P = Period AD = Alphabetical Distance X = Progression Index LD = Lineal Distance As Applied to the Supposed Repeated Trigram KOS-UYC, Positions 1, 51: X = 10 P = P 50 5 BUT: P and X must be integers • • If P = 5, then X = 1 (and P must be a divisor of 50) • If P = 10, then X = 2 (Periods of 25, 50, are unlikely) |
periodic form, and this is shown in Fig. 162. The period, as mentioned, is actually 5, though this makes no difference in the final results.
For those who like mathematics, Fig. 163 shows a method used by one of our collaborators for determining both the period and the progression index directly from the cryptogram. Price also preferred to find alphabetical intervals by writing the normal alphabet into a block, five letters to the line, with Z standing alone on the last line; thus, except for watching Z occasionally, the distance from one letter to another could be counted by fives. It is understood, of course, that we do not accept the evidence obtained from only one of the supposed repeated sequences; too many of these will be accidental, and many of those which are actually periodic have not represented repeated digrams, but merely repeated intervals. Naturally, too, the progression index need not be a small number; the disk encipherment, mentioned in the beginning, showed a progression of 17 for each period 5. This disk encipherment, incidentally, has been dealt with in a most interesting manner in Givierge’s Cours de cryptographie.
We have seen, then, all of the essentials of polyalphabetical encipherment. With the cipher alphabets known to the decryptor, practically all of the multiple-alphabet ciphers will be solved by suitable modifications of processes described for Vigenère. When alphabets are not known, his problem, always, is that of collecting as many as possible of the substitutes belonging to each alphabet, so that he may determine both the order of the letters and the relationship of alphabets to one another.
144. By THE SQUIRE.
S O V F O G S G U F V I J R I F M O U I C F T T I K Z Y Z Z Z U I F Q
Q L O W U V A F J F I W W L N C R G J F E M V V N N C D H W T A J N W
A R D B. yallyyayyayalyyaaallayaaaylalllaylyayyallyyayaylalllyyall.
145. By NEMO.
Y Y I Z C U O F Y V H Q Y H T B E B S X P T S Y C R M R X L X E A G U
Y L P U Q B U U Q N Y U S O Q M O O S P U G I J I I F F F A L I R G G
F G E H H N T E G Y Z S M C O F U D E M X O G I K K V B N K W K P Q X
M G D L A I F N H M X T U M E Z X Y Z G N A P D W C D M N C T T H N J F D.
146. By PICCOLA. (We wouldn't throw monkey-wrenches for anything!)
X E I T B B B B V M X R S J P Y L K E N Y K S Z K F R W L G S A Y E A
V I X I X D U V D U R J G E I B A N Z F H D C C Y C O Y R V A B K W B
R H F K K F X S E J Y T F N L R N I V K V K Q H I Q H I J L P G O U J
V F C F T S H L I D V D D M P.
147. By DAN SURR. (Might try this without bothering about its progression!)
E C G M H T Y T A J B T H N G A W K L I B E M N R H T D G N G P D A O
Q A X R P Z P F H D D X I E A U B S Y C I X C W V R H P B O I X Y P Y
D V W N R N X O O K K I H F O X D S V L V W W C L I H Z H V W R L H W
M M I E E A H G Q Y R S R L K L W Z T J A Y W F N S S U C V Z L P X P
S E E E Y R T H D H T Z N U P U R M G K Z N T Y E Q D E Z E N N H W M
I N R L P S S W P Y M C R U B J Z Y C R N L M A S M E U C L R M D Y R
N E S T O B V J E U D V L O T S Q B J H B N R L B V D X J P X N I G F
I C Q J Y Q Z X Q G K B L F Q U B Q K N E L S S L Y G T L F L T D Z Z
Y K E E R H K L W L I M R N J S O O J P Q C A U D M E I B B Q X A H C
V A J C M G X B I C D K V C L G Q I B S C F V F W Q N A X I D R Z S X
R B I W R C Q R.
148. By PICCOLA. (When is a tramp not a tramp?)
E R N I C D M R A S T A A P H T P I L T Q V A A S N E A E E R O O L R.