| Figure 157 Initial Key-word: C U L P E P E R C U L P E P E R C U L P E P E R Plaintext: T H E R E I S O T H E R C A U S E F O R T H I N... PRIMARY Cryptogram: V B P G I X W F V B P G G P Y J G Z Z G X W M E... Progression Key: A B CFINAL Cryptogram: V B P G I X W F W C Q H H Q Z K I B B I Z Y N G... (a) C U (key) plus T H (plaintext) equals V B (cipher). (b) Interval 18 plus interval 14 equals (32 less 26) = 6 |
| Figure 158 Tableau for Finding ALPHABETICAL INTERVALS A B C D E F G H I J K L M N O P Q R S T U V W X Y Z A 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 A B 25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 B C 24 25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 C D 23 24 25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 D E 22 23 24 25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 E F 21 22 23 24 25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 F G 20 21 22 23 24 25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 G H 19 20 21 22 23 24 25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 H I 18 19 20 21 22 23 24 25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 I J 17 18 19 20 21 22 23 24 25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 J K 16 17 18 19 20 21 22 23 24 25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 K L 15 16 17 18 19 20 21 22 23 24 25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 L M 14 15 16 17 18 19 20 21 22 23 24 25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 M N 13 14 15 16 17 18 19 20 21 22 23 24 25 0 1 2 3 4 5 6 7 8 9 10 11 12 N O 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0 1 2 3 4 5 6 7 8 9 10 11 O P 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0 1 2 3 4 5 6 7 8 9 10 P Q 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0 1 2 3 4 5 6 7 8 9 Q R 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0 1 2 3 4 5 6 7 8 R S 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0 1 2 3 4 5 6 7 S T 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0 1 2 3 4 5 6 T U 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0 1 2 3 4 5 U V 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0 1 2 3 4 V W 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0 1 2 3 W X 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0 1 2 X Y 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0 1 Y Z 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0 Z A B C D E F G H I J K L M N O P Q R S T U V W X Y Z |
from K to O is 4, that from O to S is 4, that from S to X is 5, and so on. If these numbers are placed directly below the first letter, as shown, the computation of their lineal intervals apart is less confusing than when they are placed between the two. As to repetitions, each repeated single number may represent a repeated digram, each repeated sequence of two numbers may represent a repeated trigram, and so on. Only the longer of these possibilities have been underscored.
| Figure 159 (5) (10) (15) (20) K O S X M Y M M Q Y T K N G Z W L T Z L 4 4 5 15 12 14 0 4 8 21 17 3 19 19 23 15 8 6 12 22 (25) (30) (35) (40) H C G F A P J Y K W A T Z P Q X U J Z P 21 4 25 21 15 20 15 12 12 4 19 6 16 1 7 23 15 16 16 6 (45) (50) (55) (60) V C Z Q A R F P V Y U Y C R C X M X G I 7 23 17 10 17 14 10 6 3 22 4 4 15 11 21 15 11 9 2 21 (65) (70) (75) (80) D U X Q Y M T E V V S C X J L J D A E Y 17 3 19 8 14 7 11 17 0 23 10 21 12 2 24 20 23 4 20 4 (85) (90) (95) (100) C S F P J W F V J V Q V E G A N G K B B 16 13 10 20 13 9 16 14 12 21 5 9 2 20 13 19 4 17 0 17 (105) (110) (115) (120) S C P Z B H G I D Z J A N Z I Y E Z P T 10 13 10 2 6 25 2 21 22 10 17 13 12 9 16 6 21 16 4 - |
| Figure 160 Repeated Intervals Lineal Interval Possible Factors 4-4 KOS-UYC 51 - 1 = 50 2 5 10 15-12 XMY-JYK 27 - 4 = 23 21-17-3-19 YTKNG-IDUXQ 60 - 10 = 50 2 5 10 23-15 ZWL-XUJ 36 - 15 = 21 3 7 21-15 FAP-CXM 55 - 24 = 31 7-23 QXU-VCZ 41 - 35 = 6 2 3 6 16-6 ZPV-IYE 115 - 39 = 76 2 4 19 17-10 ZQA-BSC 100 - 43 = 57 3 19 10-17 QAR-ZJA 110 - 44 = 66 2 3 6 11 15-11 CRC-XMX 56 - 53 = 3 3 9-2 XGI-VEG 92 - 58 = 34 2 17 2-21 GID-GID 107 - 59 = 48 2 3 4 6 8 12 17-0 EVV-KBB 98 - 68 = 30 2 3 5 6 10 13-10 SFP-CPZ 102 - 82 = 20 2 4 5 10 20-13 PJW-GAN 94 - 84 = 10 2 5 10 9-16 WFV-ZIY 114 - 86 = 28 2 4 7 |
Fig. 160 shows the application of a modified Kasiski examination. Notice the prominence of small factors 2 and 3, caused, often, by repeated alphabetical intervals in the key itself. In the given case, the period 10 would probably be the choice, though period 5 is correct; in practice, we should probably consider possible digrams as well as longer sequences. Accepting period 10, we have still to learn the progression index, and for this we must consider letters, all of which are shown in the second column of the same figure. Taking the longest repetition, most likely to be reliable, the two first letters are Y and I; their alphabetical distance apart is 10, and their lineal distance apart in the cryptogram is 50. If the accepted period, 10, is correct, it has taken five periods to produce the alphabetical shift of 10, therefore the shift per period (the progression index) is 10 divided by 5; or 2. This, of course, has taken for granted that the encipherment is either Vigenère or Beaufort. Considered as a possible variant Beaufort, where the progression
| Figure 161 Figure 162 K4 O4 S5 X15M12Y14M0 M4 Q8 Y21 (A) K O S X M Y M M Q Y T17K3 N19G19Z23W15L8 T6 Z12L22 (2) (C) R I L E X U J R X J H21C4 G25F21A15P20J15Y12K12W4 (4) (E) D Y C B W L F U G S A19T6 Z16P1 Q7 X23U15J16Z16P6 (6) (G) U N T J K R O D T J V7 C23Z17Q10A17R14F10P6 V3 Y22 (8) (I) N U R I S J X H N Q U4 Y4 C15R11C21X15M11X9 G2 I21 (10) (K) K O S H S N C N W Y D17U3 X19Q8 Y14M7 T11E17V0 V23 (12) (M) R I L E M A H S J J S10C21X12J2 L24J20D23A4 E20Y4 (14) (O) E O J V X V P M Q K C16S13F10P20J13W9 F16V14J12V21 (16) (Q) M C P Z T G P F T F Q5 V9 E2 G20A13N19G4 K17B0 B17 (18) (S) Y D M O I V O S J J S10C13P10Z2 B6 H25G2 I21D22Z10 (20) (U) Y I V F H N M O J F J17A13N12Z9 I16Y6 E21Z16P4 T- (22) (W) N E R D M C I D T X |