Chapter 25 of 25 · 9289 words · ~46 min read

CHAPTER XXIII

Investigating the Unknown Cipher

When the type of encipherment is unknown, the decryptor’s first problem may concern the probable language used in the plaintext, and this he is usually able to determine from the source and history of the cryptogram.

His second problem is the major classification, and this, too, is usually simple, since transposition, as a rule, can be recognized by its appearance. It must, however, respond to a group-test, and for cases in which this is needed, the approximate percentages for English can be taken as follows:

Vowels, with or without Y, about 40% (Variation limits: 35% to 45%) Consonants L N R S T about 30% (Variation limits: 25% to 35%) Consonants J K Q X Z about 2% (May be influenced by nulls).

The 5% variation is suggested in the Parker Hitt Manual. In this connection, it should be pointed out that an apparent transposition with exactly 40% of vowels and 100% evenness in their distribution is suspicious. Many of the checkerboard systems result in this way, and also some of the codes based on pronounceable five-letter groups. Then, too, it is easily possible to construct a simple substitution cipher alphabet in such a way that the resulting cryptograms will resemble transposition, and even respond satisfactorily to a group-test. It should be carefully ascertained that a supposed transposition cryptogram does not contain the many repeated sequences which belong to simple substitution. As to those transpositions which do show an appreciable number of repeated digrams, they will probably have undergone one of the route transpositions, especially one in which columns were taken off in alternating directions.

* * *

Concerning the characteristics of simple substitution, these have been seen throughout the text; we have normal frequencies attached to the wrong letters, and we have those numerous repetitions of various lengths, occurring at all kinds of intervals, which are never found in a transposition. Here, too, we may apply a group-test, based only on the relative frequencies of letters. The five most frequent are supposed to represent the letters _E T A O N_ or their equivalents, and should total about 45% of the text. The nine most frequent should total about 70%; the eleven most frequent well over 75%; the five of lowest frequency (which would include all of those totally absent) should correspond to the normal behavior of the group _J K Q X Z_.

* * *

If the simple substitution frequency count is present without the repeated sequences, then we probably have a combination of simple substitution with transposition. It becomes necessary to rewrite the cryptogram into various new arrangements until one is found which will bring back the repeated sequences. Ordinarily, the simplest kinds of transposition will have been used; sometimes the transposition will have taken place in a complete-unit block, and there will be a clue in the total number of letters present in the cryptogram.

* * *

When all letters are present in the frequency count (or all but one or two in the possible cases of 25-letter and 24-letter alphabets), a period-investigation is usually indicated. The case of periodics has been seen at considerable length, though a final hint might be added for the detection of a possible Porta encipherment. One of our many collaborators, F. R. Carter, suggests that any Porta cryptogram, periodic or otherwise, ought to show from 52% to 53% of letters _N_ to _Z_ — the opposite of normal.

The characteristics of digram-encipherment have been mentioned. Other polygram ciphers show corresponding characteristics, according to the polygram length, though the trail grows fainter as polygrams grow longer. A trigram-system, for instance, might be present when the cryptogram is evenly divisible into three-letter groups; it might suggest period 3, and might even show repeated sequences whose length is a multiple of 3 and which begin at serial positions such as 1, 4, 7, 10, which are the beginnings of trigrams. A great many of the trigram systems will show only repeated digrams beginning at these serial positions, or separated by intervals which are divisible by 3.

A 5 x 5 square is often suggested in the fact of a missing letter; but the fact of 26 letters does not deny one, since the careful encipherer may make use of his missing _J_ instead of using _I_ exclusively. Great evenness in frequencies may suggest one of the key-lengthening devices, such as autokey and progressing key; and the practical absence of repeated sequences will usually mean that a transposition has been added to a substitution. It is never a bad idea, in a puzzling example, to make the various digram-counts (in chart form): An actual digram count, in which every letter is considered the beginning of a digram; a pair-count on separated pairs, as in Playfair; the two counts which could be made with the cryptogram marked off into three-letter groups; and the kind of pair-count which could be made in Playfair if the first cryptogram-letter were omitted. Many devices, as mentioned, may be uncovered simply by “running down the alphabet.” And if the cryptogram has come from an amateur “inventor,” it may be a case of digging into one’s memory for previous “inventions.” With this last case, however, the “inventor” very often fails to submit material in proportion to the amount of complication he has introduced.

* * *

Of the examples to follow, there is none in which the system may not be learned through analysis, unless perhaps the final unnumbered cryptogram, and the material, in every case, should be suffcient for solution.

No. 163 follows Mr. Berkley’s encipherment plan, illustrated just above it.

No. 164 is said to have been taken from a German spy serving in the American army in France. This applies, however, to the first fifty groups only; the remainder was added to increase the length and to emphasize the plan followed by the spy.

No. 166 was accompanied by a plot:

“Supposed to have been found on the body of a man floating in San Diego Bay. Autopsy shows death by drowning. Victim was a local banker who had disappeared a few days earlier. Wife says no financial worries. No money missing. Banker had prospered during depression. Was yachting enthusiast. Our hero solved the cipher with the unconscious assistance of a radio crooner. Tragedy occurred in _August, 1932_.” The date was doubly underscored, but those who have read the message have found no reason for this and no explanation for the “crooner.”

157. By PICCOLA.

C S R Z V Y P Q Z J K H K V Q U U C V M R T W Z N G H Q S A K O X P M H D R W A J D F Q D F S R Z Z C G X P A J J T Z U L H T G S A H X J J L T R N N Z P B Z G R E B N F Y G E J N M T N J J Q H P J X M O B J A L X I A I C P F J O O F R N H.

158. By PICCOLA.

O C E E A T T I T K S N D T D S T H O O Y E A O E E P E B O T Y T A O A D S E O E T F T T T H R V W C T H O Y L T O O H L R B T T U H R R V R A W O B R U A O Y E H H L A B N E R L R K V C R I O N S E I D R U E R I P.

159. By TITOGI.

A H Y N U H C E S T I T N D O R F E H R W E A T F N R F P A O T M A T L H R E I O T N R L O D R H E E A T E S C T D I N W T S T O E A T S I T E C D U T M S O T R L D O N G N I I S O F A E T L I T A S.

160. By PICCOLA. (Veiled reference to crypt No. 166?)

(a) H Z M Q L D N N D Z S P R F S K L L L L. (b) L I L V M S T Z U G D H Z U Q X L L L L. (c) T V I U M F R U O Y U Q Y P S F W X L L. (d) L I L V M F P O E Y Z K F D V U E L L L. (e) G K P V D Z T A Y T B F Y Y C F I U L L. (f) Q B F P W Y C L U D V P Z Z O S W Y N C. (g) Q B R T F F G V T U E N S Z H B Q E R L.

161. By PICCOLA.

E G W G W G E G T U C L C U O X G K Z T E G O B G B Y L W M I Q N K Q Y E N F S C L H M N Y B X S E T N I W O C E G C B F C T C S Z T V G B E A E G T U R K F K B E G K X B C T G Z Y L X C H Y E G C U O X Y T Q F A D Q T T C U N B O G C O H X C E W E C U V E G C O C X Y X G B E A Y T K X F Q C O T B X N E G T U C O N T O P E L E K U V U N T O C N G N G B K W C E E C S Z K W N H E I K C C R E G C T E G T U R K F K T B R G M W X C F G Q N I C E B P E E W E N B K I Y F K F D O F E G N U C B G M T Z T F X C E W E C F V D T T U Z T E N E G W G L F M C T O V L.

162. By PICCOLA.

S P P A S T A S E F U N M T E H S O O A E S L E I C T R C H V U G S E L Y R E M E N E E R O S N E H I R A E T O R N S H M O D R O P E A O R P O S R Y P D O I N O C K G T.

The "NICODEMUS" Cipher (Harold Berkley) SPECIMEN ENCIPHERMENT

Key: M E T H O D I C M E T H O D I C M E T... 6 3 8 4 7 2 5 1 6 3 8 4 7 2 5 1 6 3 8... Cryptogram: T H I S I S E N A N S P O S E D E T C... C I P H E R E D U S I N G T H E PFGVT VUHDG LMRIV I V V I G E N E S A M E K E Y F ZOPUH MMVNB FOUDQ WSURF R E A N D A F T O R B O T H O P BIOTP FGHRU VWHKR RWEVV E R W A R D T R E R A T I O N S WULVA MPGWV MGEAQ CUYHW LBFUT.

163. By PICCOLA.

T Y D Q V W P A Z O M B W B I R K F I O O G W C O G E F L T Q M S R F X T C J C M A W P P Q M E X V O Q C O C Z F S F W V F E V E R S A B E C V J J W S I P P H M M K O X V Y I D B D B C I S Y N L J C Y F K C W E N Z E I T J V L Z M I L I I R W K R O O S Z A W E K J V J G F M Q K G F N C K H P B R D L V I A P E S L V M D J Z Z V F Z F F R D B A D P Q W E N L A L O E K M F M F W X O K D W D G C K K K C Q R V.

164. By VULPUS.

P E N A R C P F T I Q E V A T E N B L A T K Q F O A R E N E U I P E P F U K X I L C N F Q E P C V B T A W A O B N C O E T I N D W B N A R D Q F O F N B V C P E P G V G P A V A P B P F O A O B S C L B V B T F W A N E W B T C S D N F M A N A O E V A R A R C T K Q E N B M B Q F V E V B X K O A P E T B U I P F O F Q E L E O B R D R B Q F U A W A S C U K L F P E W B O C O D N A M E L G V F V A N C N D M F N B V D T D L E P F V I T I Q E Q F O C O A U C L F L A O B M E P E N A S D L B T K L H N E P D. ..... U I L A L B O B M A V K M G U K R F P F U B U D M F W E T A T I Q E V B R C M B W A N F Z I L E N A Q F W B T C R D T B T K O E P E U A V A O F N B S C Z K V B W C U B O A L F O B M E X I T D Q C Q D W A P F Q E N A L A.

165. By PICCOLA. (Again that No. 166?)

R O V L L A B T L D L B C Q M P X L B A F B T C T A T C O R L T O L C R H P D T X L Y O A E L B X P H L X B T X X Q L D R G L T K X R L G D B K L D P P L O H L Y O A E L K O M X B L H O E L V C R R C R J L T K D T L R C I N X P L L L T K X L R C I N X P L V D B L V O R L P O R J L D J O L F Y L I O P O R X P L M D E N X E L K C T T L V K O L O H H X E X G L T O L I O Q M E O Q C B X L H O E L T V O L I X R T B L B C R I X L K X L V D B L D F P X L T O L B X R G L T K X L B O P A T C O R L F Y L E X T A E R L Q D C P L L B T C P P L C T L V O A P G L F X L V O E T K L D R O T K X E L R C I N X P L T O L H C R G L O A T L T K X L N X Y L L T K C B L Q A B T L F X L T K X L X W M P D R D T C O R L O H L T K X L E X H X E X R I X L T O L D L I E O O R X E L D R G L T K X L X Q M K D B C B L O R L D L G D T X L L M L B L T K X L T V O L I X R T B L K D B L R O T L Y X T L F X X R L M D C G L.

166. By CACHE. (Contributor, C. H. Price, died without explaining his key).

03 65 12 45 58 28 06 41 72 14 22 03 02 17 36 88 25 20 55 77 74 51 23 45 41 42 30 24 36 61 96 09 07 78 05 44 08 06 55 92 16 93 02 15 36 37 40 87 41 01 33 77 06 36 27 54 48 29 16 78 92 66 03 10 38 17 45 23 72 96 73 01 49 25 72 38 92 72 24 55 48 08 40 92 28 01 72 96 02 04 74 61 06 99 30 45 72 69 74 93 77 23 55 36 24 93 47 84 76 35 32 89 87 76 77 64 51 96 58 43 76 02 81 38 87 69 89 55 99 23 79 55 51 06 99 71 74 69 89 84 27 25 22 39 42 53 19 93 41 66 09 75 87 37 91 87 90 91 43 19 40 30 38 16 96 22 69 38 78 02 74 92 47 25 77 91 15 40 24 45 07 07 96 48 44 15 12 06 99 44 93 19 25 23 55 30 45 87 96 18 01 78 44 29 45 86 47 69 48 30 66 44 03 41 66 37 38 22 06 42 41. 59.

Here is one which nobody has ever been able to decrypt:

V Q B U P P V S P G G F P N U E D O K D X H E W T I Y C L K X R Z A P V U F S A W E M U X G P N I V Q J M N J J N I Z Y K B P N F R R H T B W W N U Q J A J G J F H A D Q L Q M F L X R G G W U G W V Z G K F B C M P X K E K Q C Q Q L B O D O Q J V E L.

APPENDIX

ENGLISH FREQUENCY AND SEQUENCE DATA

(Compiled from the MEAKER Digram Chart)

Order and Frequency of Order and Frequency of Single Letters Leading DIGRAMS

E 1231 L 403 B 162 TH 315 TO 111 SA 75 MA 56 T 959 D 365 G 161 HE 251 NT 110 HI 72 TA 56 A 805 C 320 V 93 AN 172 ED 107 LE 72 CE 55 O 794 U 310 K 52 IN 169 IS 106 SO 71 IC 55 N 719 P 229 Q 20 ER 154 AR 101 AS 67 LL 55 I 718 F 228 X 20 RE 148 OU 96 NO 65 NA 54 S 659 M 225 J 10 ES 145 TE 94 NE 64 RO 54 R 603 W 203 Z 9 ON 145 OF 94 EC 64 OT 53 H 514 Y 188 EA 131 IT 88 IO 63 TT 53 TI 128 HA 84 RT 63 VE 53 AT 124 SE 84 CO 59 NS 51 Group Percentages: ST 121 ET 80 BE 58 UR 49 EN 120 AL 77 DI 57 ME 48 A E I O U 38.58% ND 118 RI 77 LI 57 WH 48 OR 113 NG 75 RA 57 LY 47 L N R S T 33.43% List of Common REVERSALS: J K Q X Z 1.11% ER RE ON NO TE ET ST TS E T A 0 N 45.08% ES SE IN NI OR RO IS SI AN NA EN NE TO OT ED DE E T A O N I S R H 70.02% TI IT AT TA AR RA OF FO

Order of the Leading TRIGRAMS In 10,000 Letters of Semi-Military Text - PARKER HITT

THE ENT FOR NCE OFT AND ION NDE EDT STH THA TIO HAS TIS MEN

INITIAL LETTERS OF WORDS:

Order, as found by M. E. OHAVER ... T A O S H I W C B P F D M R, etc.

Order, as found by H. O. YARDLEY .. T O A W B C D S F M R H I Y, etc.

FINAL LETTERS OF WORDS:

Order, as found by M. E. OHAVER ... E S T D N R O Y, etc.

Order, as found by H. O. YARDLEY .. E T D N S R Y, etc.

NOTE: Lists of terminals (letters, digrams, trigrams); of common affixes, short words, and common pattern-words, can be found in the booklet "CRYPTOGRAM SOLVING", obtainable from the author, M.E.Ohaver, at Columbus, Ohio.

X J M M T V O Z B N Q M F B T F S F N J U G P S U I J T B E ?

COMPARATIVE TABLE OF SINGLE-LETTER FREQUENCIES (Per 100)

ENGLISH GERMAN FRENCH ITALIAN SPANISH PORTUGUESE

A 7.81 A 5. A 9.42 A 11.74 A 12.69 A 13.5 B 1.28 B 2.5 B 1.02 B .92 B 1.41 B .5 C 2.93 C 1.5 C 2.64 C 4.50 C 3.93 C 3.5 D 4.11 D 5. D 3.38 D 3.73 D 5.58 D 5. E 13.05 E 18.5 E 15.87 E 11.79 E 13.15 E 13. F 2.88 F 1.5 F .95 F .95 F .46 F 1. G 1.39 G 4. G 1.04 G 1.64 G 1.12 G 1. H 5.85 H 4. H .77 H 1.54 H 1.24 H 1. I 6.77 I 8. I 8.41 I 11.28 I 6.25 I 6. J .23 J ... J .89 J ... J .56 J .5 K .42 K 1. K ... K ... K ... K ... L 3.60 L 3. L 5.34 L 6.51 L 5.94 L 3.5 M 2.62 M 2.5 M 3.24 M 2.51 M 2.65 M 4.5 N 7.28 N 11.5 N 7.15 N 6.88 N 6.95 N 5.5 O 8.21 O 3.5 O 5.14 O 9.83 O 9.49 O 11.5 P 2.15 P .5 P 2.86 P 3.05 P 2.43 P 3. Q .14 Q ... Q 1.06 Q .61 Q 1.16 Q 1.5 R 6.64 R 7. R 6.46 R 6.37 R 6.25 R 7.5 S 6.46 S 7. S 7.90 S 4.98 S 7.60 S 7.5 T 9.02 T 5. T 7.26 T 5.62 T 3.91 T 4.5 U 2.77 U 5. U 6.24 U 3.01 U 4.63 U 4. V 1.00 V 1. V 2.15 V 2.10 V 1.07 V 1.5 W 1.49 W 1.5 W ... W ... W ... W ... X .30 X ... X .30 X ... X .13 X .2 Y 1.51 Y ... Y .24 Y ... Y 1.06 Y ... Z .09 Z 1.5 Z .32 Z .49 Z .35 Z .3

Vowel Percentages:

English German French Italian Spanish Portuguese

40% 40% 45% 48% 47% 48%

Percentages for L N R S T:

33% 34% 34% 30% 31% 29%

NOTES: ENGLISH frequencies, which may be compared with those of Mr. Meaker, (A, 8.05; B, 1.62; C, 3.20; etc.), were taken from M.E.OHAVER. FRENCH, ITALIAN, and SPANISH frequencies were taken from a count made by the author. All four counts are based on 10,000 letters of literary text, and the dropping of the decimal point gives the actual count. The frequencies given for GERMAN and PORTUGUESE are approximations, reduced from other texts, probably military.

Chart Showing Normal CONTACT PERCENTAGES - Compiled by F. R. CARTER

(Based on a Digram Chart by M.E.OHAVER)

% V. C. 19 81 P4 L4 C5 D5 M5 N6 S6 W7 T8 R8 E11 H14 A N21T17S12R10L8 D5 C4 M4 55 45 Y4 B4 N5 T5 U8 D9 O9 S10A16E16 B E34L17U11O9 A7 Y5 B4 R4 61 39 U4 O5 S8 N13A13I18E20 C H19O19E17A13I7 T6 R4 L4 K4 52 48 R4 I5 L6 A10N29E39 D E16I14T14A10O8 S6 U5 8 92 C4 B4 E5 M5 V5 D5 S5 L5 N6 T6 R11H24 E R15D10S9 N8 A7 T6 M5 E4 C4 O4 W4 69 31 S4 N5 F5 D5 A6 I7 E12O41 F T22O21E10I9 A7 R5 F5 U4 36 64 O4 D4 U5 R5 I9 E9 A10N48 G E14H14O12R10A8 T6 F5 W4 I4 S4 7 93 G4 E5 W5 S7 C9 T62 H E50A23I12O7 13 87 F4 M4 W5 E6 N6 L8 D8 S8 R9 H11T14 I N25T13S10O8 C7 R4 E4 M4 A4 L4 28 72 Y7 W7 T7 S7 N7 E7 C7 B7 A14M29 J U35O29A12E12M6 W6 53 47 Y5 U5 I5 N7 A11R13E13O15C18 K E34I21N10A9 T7 S6 52 48 N4 P4 T6 I7 B7 U7 O10E11L11A17 L E19I15Y12L12O9 A8 D7 U4 69 31 S4 D4 M5 R5 I12A13O16E24 M E26A17O12I11P5 M5 89 11 U7 E14O22A23I24 N D16T14G12E10A7 S7 O7 I6 C5 21 79 M4 O4 D4 L4 P4 H5 N6 E6 C7 F7 S8 I8 R9 T11 O N20F14R11U10T6 M5 L5 S4 W4 O4 47 53 R4 L4 T4 N4 I4 P6 M6 A7 O8 U10E16S17 P O17E16A15R15L8 U6 P6 T5 I5 S4 20 80 O10N10L10E10D10R20S30 Q U100 70 30 P5 I5 U5 T7 A13O16E30 R E23O12A11T11I10S7 Y4 48 52 D4 T4 O6 U6 R7 N8 S9 I11A16E18 S T19E11O10I9 S9 A8 H6 P5 U4 43 57 U4 O5 D6 T6 F7 R7 E8 I10N10S13A14 T H39I10O10E8 A7 T6 R4 35 65 P5 F5 T5 L5 B6 D8 S9 O30 U N18S13T13R12L10P7 B4 C4 88 12 R6 U10O16A16I16E30 V E65I14O9 A8 48 52 G4 D4 Y5 N9 S10T11O16E23 W A27H16I16E15O11N4 95 5 U5 N5 I16E74 X P29T19I14A14U10C5 K5 O5 24 76 B4 N8 A8 T13E14R15L25 Y A15O12S12T9 W7 H5 I5 E5 D4 M4 B4 88 12 O12N12A25I50 Z E43I43W14 % V. C. 6 94 70 30 59 41 54 46 21 79 52 48 42 58 90 10 17 83 88 12 68 32 65 35 71 29 32 68 18 82 59 41 100 -- 61 39 41 59 38 62 8 92 99 1 80 20 38 62 38 62 86 14

All figures indicate PERCENTAGES. - Taking any one letter, as A: On the left, it was contacted 14% of the time by H, 11% by E, etc., and 81% of its total contacts on that side were consonants. On the right, it was contacted 21% of the time by N, and 94% of the time by consonants.

Chart Showing FREQUENCIES of English DIGRAMS - Prepared by O. PHELPS MEAKER

(Actual Count Made on 10,000 Letters of Literary Text).

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 1 8 44 45│131│21 11 84 18 34 56 54 9 21 57 75 56 18 15 32 3 11 805 B 32 18│ 11│ 2 2 1 7 7 9 7 18 1 4 13 14 5 11 162 C 39 12 4│ 64│ 9 1 2 55 8 1 31 18 14 21 6 17 3 5 10 320 D 15 10│107│ 1 1 1 16 28 2 118 16 16 6 9 11 4 4 365 E 58 55 39│ 39│25 32 251 37 2 28 72 48 64 3 40 148 84 94 11 53 30 1 12 5 1231 F 10 1 12│ 23│14 3 2 27 5 8 94 6 13 5 1 1 3 228 G 18 2│ 20│ 1 1 10 1 75 3 6 6 1 12 5 161 H 46 3│ 15│ 6 16 5 1 9 3 7 3 30 315 2 48 5 514 I 16 6 15 57│ 40│21 10 72 8 57 26 37 13 8 77 42 128 5 19 37 4 18 2 718 J 2 1│ 1│ 1 1 3 1 10 K 10 8 │ 2│ 8 3 3 5 11 2 52 L 77 21 16 7│ 46│10 4 3 39 55 10 17 29 12 6 12 28 4 6 1 403 M 18 1 9│ 43│ 3 1 1 32 4 5 7 44 15 14 14 9 1 4 225 N 172 5│120│ 2 3 2 169 3 1 3 9 145 12 19 8 33 10 3 719 O 2 11 59 37│ 46│38 23 46 63 4 3 28 28 65 23 28 54 71 111 2 6 17 1 28 794 P 31 1 7│ 32│ 3 1 1 3 2 16 7 29 26 8 24 8 17 2 4 7 229 Q 1 1│ 14│ 2 2 20 R 101 6 7 10│154│ 4 21 8 21 2 5 113 42 18 6 30 49 1 5 603 S 67 5 1 32│145│ 8 7 3 106 2 12 6 51 37 3 39 41 32 42 3 17 659 T 124 38 39│ 80│42 13 22 88 1 19 6 110 53 14 63 121 53 45 6 1 21 959 U 12 25 16 8│ 7│11 8 2 4 8 13 12 96 7 20 6 30 22 1 1 1 310 V 24 4│ 16│ 1 14 2 4 13 5 2 4 1 3 93 W 7 1 9│ 41│ 4 2 7 1 3 5 2 15 36 1 10 27 16 2 14 203 X │ 17│ 1 1 1 20 Y 27 19 6│ 17│ 1 1 1 3 47 3 14 4 2 17 4 21 1 188 Z 1 │ │ 4 2 1 1 9

To learn the frequency of any digram, find its first letter at the top, find its second letter at the side, and observe the figure in the cell at which the column headed by the first letter crosses the row headed by the second. Frequency for EA, 131; for AE, zero.

SOME FOREIGN LANGUAGE DATA

NOTE: Frequencies of letters, and their order, are fixed quantities in any language. Group frequencies, however. are fairly constant in every language. (These may be computed from the Comparative Table for any desired group in the languages given.) Of the material which follows, portions came from Lange and Soudart, and from Valerio, but exact sources were not in every case furnished to the author.

G E R M A N

Order of single letters: E N I R S A D T U G H O L B M C F W Z K V P (J Q X Y)

Order of digrams: EN ER CH DE GE EI IE IN NE ND BE EL TE UN ST DI NO UE SE AU RE HE

Order of trigrams: EIN ICH DEN DER TEN CHT SCH CHE DIE UNG GEN UND NEN DES BEN RCH

Order of tetragrams: ICHT KEIT HEIT CHON CHEN CHER URCH EICH DERN AUCH SCHA SCHE

SCHI SCHO SCHU (Furnished by JOSEPH ARTHOLD).

Peculiarities:

C is practically always followed by H (or K), and SC by H. Word-length is normally greater than in English.

F R E N C H

Order of single letters: E A I S T N R U L O D M P C V Q G B F J H Z X Y (K W)

Order of digrams: ES EN OU DE NT TE ON SE AI IT LE ET ME ER EM OI UN QU

Order of trigrams: ENT QUE ION LES AIT TIO ANS ONT ANT OUR AIS OUS

Peculiarities: Q followed by U and a second vowel. Four and five vowels may be found in sequence ("J'ai oui dire.."), but E seldom touches the other vowels. D and M contact E about 75% of the time, and L contacts it over 50% of the time. It is unusual to find more than four consonants in sequence; when five are found in succession, one is almost surely the final S of a plural word.

Order of doubled letters: S L M R T N P E C F Order of initials: P A S M C E D T V F R B L G J I Q N O H U Y X Z Order of finals: E S T R N D A I X Z L C U P F Y

Average word-length: 4.3 letters. Commonest short words, in order: DE IL LE ET QUE JE LA NE UN LES EN CE SE SON MON PAS LUI ME AU UNE DES SA QUI EST DU

I T A L I A N

Order of single letters: E A I O N L R T S C D P U M V G H F B Q Z (J X K W Y)

Order of digrams: ER ES ON RE EL EN DE DI TI SI AL AN RA NT TA CO

Order of trigrams: CHE ERE ZIO DEL ECO QUE ARI ATO EDI IDE ESI IDI ERO PAR NTE STA

Peculiarities: Q followed by U and a second vowel. H largely preceded by C, in CHE,CHI, or sometimes by G in GHE GHI. Z most often part of ZIO or NZA. The frequencies of the vowels E A I O often exchange places. Doubling of consonants is very frequent.

Order of doubled letters: L T S C R G P N B M Z F V I D Order of initials: S P A C D V T M F I G Q R E B L N O U Z H Order of finals: O E A I (Others, if used: R L D N)

Average word-length: 4.5 letters. Commonest short words, in order: LA DI CHE IL NON SI LE UNA LO IN PER UN MI IO PIU DEL MA SE

S P A N I S H

Order of single letters: E A O S N I R L D U C T M P B H Q G V Y J F Z X (K W)

Order of digrams: ES EN EL DE LA OS AR UE RA RE ER AS ON ST AD AL OR TA CO

Order of trigrams: QUE EST ARA ADO AQU DEL CIO NTE OSA EDE PER IST NEI RES SDE

Peculiarities: Q followed by U and a second vowel. The only doubles are LL, RR, CC, EE, NN, OO, in the order given, but the latter three are very rare. Group frequencies somewhat less stable than in the other languages.

Order of initials: C P A S M E D T H V R U N I L B O F Q G J Z Order of finals: O A S E N R D L I Z

Average word-length: 4.4 letters. Commonest short words, in order: DE LA EL QUE EN NO CON UN SE SU LAS LOS ES ME AL LO SI MI UNA DEL POR SUS MUY HAY MAS

P O R T U G U E S E

Order of single letters: A E O R S I N D M T U C L P Q V F G H B J Z X (K W Y)

Order of digrams: ES OS DE AS RO EN CO DO RE ER NT SE AD OR AO SA TE AR EM QU UE OD ST

Order of trigrams: QUE ENT NTE DES EST ODE ADO CON STA MEN ADE DOS ARA COM

Much like Spanish. Spanish cion becomes cao; ll becomes lh. Articles drop the L: os, as, in place of Spanish los, las, etc.

BIBLIOGRAPHY By W. D. Witt

An extended bibliography of cryptography would fill many pages and is therefore beyond the scope of this work, but it is hoped that the following short selected list will be found useful. Some of these works are out of print or otherwise unobtainable, but may, in some instances, be found in public libraries or in old bookstores. The Riverbank Publications may be consulted at The Library of Congress, Washington, D. C.

More or Less Elementary Works

Boyer, John Q. “The Cryptogram” in Real Puzzles by John Q. Boyer, Rufus T. Strohm and George H. Pryor, pp. 147-154. Baltimore, 1925. (Simple substitution ciphers only.)

Buranelli, Prosper, Margaret Petherbridge and F. Gregory Hartswick. The Cryptogram Book. New York, 1928. (Simple substitution ciphers only.)

Hitt, Parker (Colonel). The A B C of Secret Writing. New York, 1935.

Lysing, Henry, pseud. (John Leonard Nanovic). Secret Writing. New York, 1936.

―. The Cryptogram Book. New York, 1937.

Mansfield, Louis C. S. The Solution of Codes and Ciphers. London, 1936.

―. One Hundred Problems in Cipher. London, 1936.

Ohaver, M. E. Cryptogram Solving. Columbus, Ohio, 1933, (Simple substitution ciphers only.)

Thomas, Paul B. Secret Messages. New York and London, 1928. 2nd printing, 1929.

Windolph, J. Fred (“Phil Down”). “Cryptograms: Their Construction and Solution” in A Key to Puzzledom, pp. 53-64. New York, 1906. (Simple substitution ciphers only.)

Yardley, Herbert Osborne (Major). Yardleygrams. Indianapolis, 1932. (The London edition (1932) bears the title Ciphergrams.)

Advanced Works

Friedman, William F. (Lt.-Colonel). Elements of Cryptanalysis. Washington, Gov. Printing Office, 1924. “For Offcial Use Only.” (Contains a bibliography. Out of print and unobtainable.)

―. See also Riverbank Publications.

Givierge, Marcel (General). Cours de Cryptographie. Paris, 1st edition, 1925, 2nd edition, 1932.

Hitt, Parker (Colonel). Manual for the Solution of Military Ciphers. Fort Leavenworth, Kans., 1st edition, 1916, 2nd edition, 1918.

Riverbank Publications. Papers (except No. 19) by W. F. Friedman. Department of Ciphers, Riverbank Laboratories, Geneva, Illinois. No. 15, 1917. “A Method of Reconstructing the Primary Alphabet.” No. 16, 1918. “Methods for the Solution of Running-key Ciphers.” No. 17, 1918. “An Introduction to Methods for the Solution of Ciphers.” No. 18, 1918. “Synoptic Tables for the Solution of Ciphers, and a Bibliography of Cipher Literature.” No. 19, 1918. “Formulae for the Solution of Geometrical Transposition Ciphers,” by Captain Lenox R. Lohr, with an introduction by W. F. Friedman. No. 20, 1918. “Several Machine Ciphers and Methods for Their Solution.” No. 21, 1918. “Methods for the Reconstruction of Primary Alphabets.” No. 22, 1922. “The Index of Coincidence and Its Applications in Cryptographic Analysis.”

Sacco, Luigi (General). Manuale di crittografia. Rome, 2nd edition, revised and enlarged, 1936. (The first edition was privately printed under the title Nozioni di crittografia. Rome, 1930.)

Zanotti, Mario. Crittografia. Milan, 1928.

Miscellaneous (Primarily descriptive of systems, historical, special essays, etc., usually with little on cryptanalysis.)

Anon. “Cryptography” in Encyclopaedia Britannica, Vol. 6, 14th edition, New York and London, 1929. (Contains a bibliography.)

Ball, W. W. Rouse. “Cryptographs and Ciphers” in his Mathematical Recreations and Essays. 7th edition, 1917 and later. (Latest edition is the 11th, 1939.)

Blair, William. “Cipher in Diplomatic Affairs” in Rees’s Cyclopaedia. 1803-1819.

Candela, Rosario. The Military Cipher of Commandant Bazeries, An Essay in Decrypting. New York, 1938.

Friedman, William F. (Lt.-Colonel). “Codes and Ciphers” in Encyclopaedia Britannica, Vol. 5, 14th edition, New York and London, 1929. (Contains bibliography.)

―. “Edgar Allan Poe, Cryptographer” in American Literature, A Journal of Literary History, Criticism and Bibliography, Vol. 8, No. 3, Nov. 1936, pp. 266-280. Duke University, Durham, N. C.

Hulme, Frederick Edward. Cryptography, or, The History, Principles and Practice of Cipher-Writing. London, 1898.

Lange, André and E. A. Soudart. Traité de Cryptographie. Paris, 1st edition, 1925, new edition, 1935. (Contains an extensive bibliography.)

Lange, André. Cryptography. Translated from the French by J. C. H. Macbeth, London and New York, 1922.

Pratt, Fletcher. Secret and Urgent, The Story of Codes and Ciphers. Indianapolis, 1939.

Yardley, Herbert Osborne (Major). The American Black Chamber. Indianapolis and London, 1931. Reprinted, New York, 1933, London, 1934.

THE COMMONEST ENGLISH WORDS

Below are listed the hundred most frequently used words in English. The figures give occurrences in 242,432 words of English text taken from fifteen English authors and many newspapers. Compiled by Frank R. Fraprie, after the rest of the book had been completed.

THE 15568 OR 1101 WHEN 603 ONLY 309 OF 9767 HER 1093 WHAT 570 ANY 302 AND 7638 HAD 1062 YOUR 533 THEN 298 TO 5739 AT 1053 MORE 523 ABOUT 294 A 5074 FROM 1039 WOULD 516 THOSE 288 IN 4312 THIS 1021 THEM 498 CAN 285 THAT 3017 MY 963 SOME 478 MADE 284 IS 2509 THEY 959 THAN 445 WELL 283 I 2292 ALL 881 MAY 441 OLD 282 IT 2255 THEIR 824 UPON 430 MUST 280 FOR 1869 AN 789 ITS 425 US 279 AS 1853 SHE 775 OUT 387 SAID 276 WITH 1849 HAS 753 INTO 387 TIME 273 WAS 1761 WERE 752 OUR 386 EVEN 272 HIS 1732 ME 745 THESE 385 NEW 265 HE 1727 BEEN 720 MAN 383 COULD 264 BE 1535 HIM 708 UP 369 VERY 259 NOT 1496 ONE 700 DO 360 MUCH 252 BY 1392 SO 696 LIKE 354 OWN 251 BUT 1379 IF 684 SHALL 351 MOST 251 HAVE 1344 WILL 680 GREAT 340 MIGHT 250 YOU 1336 THERE 668 NOW 331 FIRST 249 WHICH 1291 WHO 664 SUCH 328 AFTER 247 ARE 1222 NO 658 SHOULD 327 YET 247 ON 1155 WE 638 OTHER 320 TWO 244

ENGLISH TRIGRAMS

The ninety-eight most frequent English trigrams, combining a count of 20,000 trigrams by Fletcher Pratt, in “Secret and Urgent,” supposed not to include overlaps between words, and 5,000 by Frank R. Fraprie, including overlaps. This table and the following one are not referred to in the text, having been compiled since the completion of the book.

THE 1182 HER 170 HIS 130 ITH 111 ING 356 ATE 165 RES 125 TED 110 AND 284 VER 159 ILL 118 AIN 108 ION 252 TER 157 ARE 117 EST 106 ENT 246 THA 155 CON 114 MAN 101 FOR 191 ATI 148 NCE 113 RED 101 TIO 188 HAT 138 ALL 111 THI 100 ERE 173 ERS 135 EVE 111 IVE 96

REA 95 INE 73 ORE 65 ART 58 WIT 93 WHI 71 BUT 64 NTE 58 ONS 92 OVE 71 OUT 63 RAT 58 ESS 90 TIN 71 URE 63 TUR 58 AVE 84 AST 70 STR 62 ICA 57 PER 84 DER 70 TIC 62 ICH 57 ECT 83 OUS 70 AME 61 NDE 57 ONE 83 ROM 70 COM 61 PRE 57 UND 83 VEN 70 OUR 61 ENC 56 INT 80 ARD 69 WER 61 HAS 56 ANT 79 EAR 69 OME 60 WHE 55 HOU 77 DIN 68 EEN 59 WIL 55 MEN 76 STI 68 LAR 59 ERA 54 WAS 76 NOT 67 LES 59 LIN 54 OUN 75 ORT 67 SAN 59 TRA 54 PRO 75 THO 66 STE 59 STA 75 DAY 65 ANY 58

ENGLISH DIGRAMS

The one hundred and nine most frequent English digrams, compiled from a count of 20,000 trigrams by Fletcher Pratt, in “Secret and Urgent,” supposed not to include overlaps between words, and 5,000 by Frank R. Fraprie, including overlaps.

TH 1582 RO 275 WI 188 SA 146 CT 111 IN 784 LI 273 HO 184 NI 142 TU 108 ER 667 RI 271 TR 183 RT 142 DA 107 RE 625 IO 270 BE 181 NA 141 AM 104 AN 542 LE 263 CE 177 OL 141 CI 104 HE 542 ND 263 WH 177 EV 131 SU 102 AR 511 MA 260 LL 176 IE 129 BL 101 EN 511 SE 259 FI 175 MI 128 OF 101 TI 510 AL 246 NO 175 NG 128 BU 100 TE 492 IC 244 TO 175 PL 128 AT 440 FO 239 PE 174 IV 127 ON 420 IL 232 AS 172 PO 125 HA 420 NE 232 WA 171 CH 122 OU 361 LA 229 UR 169 EI 122 IT 356 TA 225 LO 166 AD 120 ES 343 EL 216 PA 165 SS 120 ST 340 ME 216 US 165 IL 118 OR 339 EC 214 MO 164 OS 117 NT 337 IS 211 OM 163 UL 115 HI 330 DI 210 AI 162 EM 114 EA 321 SI 210 PR 161 NS 113 VE 321 CA 202 WE 158 OT 113 CO 296 UN 201 AC 152 GE 112 DE 275 UT 189 EE 148 IR 112 RA 275 NC 188 ET 146 AV 111

INDEX

Amateurs, devices proposed by, 132, 140, 152 “Amsco” transposition cipher, 51 Anagramming, 22, 29, 45-50 Anagramming, multiple, 32, 56-68 “Aristocrats,” 69, 72, 88 Auto-encipherment, 146-158

Bacon’s biliteral cipher, 6 Basic cipher alphabet, 164 Bassières processes for autokey, 147-151 Beaufort ciphers, 121 “Bifid” substitution, 210 Book cipher, 106

“Caesar” alphabets, 69, 71, 100, 108, 118, 130 Characteristics of systems, 53, 100, 103, 105, 130, 153, 168, 201-203, 213-214 “Checkerboard” alphabets, 102, 104, 164, 209 Cipher, meaning of, 1 Cipher alphabets, 69, 130, 159, 172, 185 Cipher disks, 108, 111 Cipher disks, special application of, 192 Classification of ciphers, 1 Classification of substitutions, 68 Code, 1, 106 Collon systems, 209 Columnar transposition, 11, 17, 23, 37-52 Columnar transposition, double, 54 “Columns” in autokeyed ciphers, 146 Combination block, 44 Combination cipher, 1, 4, 6, 68, 207, 209, 213, 216 Complements, complementary alphabets, 123 Complete-unit transposition, 9 Concealment cipher, meaning of, 1 Concealment ciphers, 4-8 Consonant-line method for simple substitution, 88 Contact count, 74, 77, 83, 173 Conventional writing, 4 “Crypt,” 72, 91 Cryptanalysis, meaning of, 3 Cryptogram, meaning of, 1 Cryptographic security, 2 Cycle (see period or unit) Cyclical encipherment, 186, 200

Deciphering alphabet (or key), 71, 104 Decipherment, meaning of, 1 Decoding, meaning of, 2 Decrypt, meaning of, 1 Definitions, miscellaneous, 1, 68-70 Dictionary cipher, 106 Digram, meaning of, 1 Digram count, 83 Digram-solution method for simple substitution, 83 Digram tests, 45, 46, 47, 50 Dissimulated writing, 4 Double-key substitution, meaning of, 68 Double Myszkowsky transposition, 60 Double substitutions, 155, 164, 193 Double transpositions, 18, 54

Empty, or negative, words, 76 Encipherment, meaning of, 1 Encoding, meaning of, 2 “Entry,” 74 Equivalent slide (or alphabet), 169, 180

Factoring, in transpositions, 12, 42 Factoring of intervals to find a period, 128, 132 “Force Method,” 90 Fractional substitution, meaning of, 68 Fractional substitutions, 209-212 Frequency (see statistics) Frequency counts, 74, 83, 129, 161, 173 “Frequential checkerboard,” 105

German field cipher (the ADFGVX), 210 Grandpré’s word-square, 104-105 Graph, graphic appearance, 106, 131, 173 Grille, Fleissner’s, 26 Grille, Richelieu’s, 4 Grille, Sacco’s indefinite, 12 Grille, turning, 26 Gronsfeld cipher, 117 Group-application in polyalphabetic ciphers, 185 Group percentages (see statistics)

Hermann cipher, 143

Index-letter (or cell), 111, 119, 124, 143, 169 Indicators, 101, 143 Intervals, alphabetical and lineal, 169, 180, 193, 194 Intervals in cryptograms, 43, 127 Inverse alphabets, 69 Irregular transposition, 37-67 Isolating a cipher alphabet, 122

Kasiski method, 127 Key, meaning of, 1 Key-alphabet, 108 “Key-frame” (or “skeleton”), 86, 175, 206 Key-interruption, 143 Key-length, 11, 17, 42, 127, 147 Key-lengthening devices in Vigenère, 143 Key-letter, 108 “Key-phrase” cipher, 103 Keys for simple substitution, 69 Keys, preparation of, 17, 26, 70, 104 Keys, recovery of, 23, 33, 39, 40, 45, 50, 58-63, 64, 85, 106, 124, 150, 157, 163, 164, 167, 175-183, 188-190, 205 Keywords, uses of, 17, 70, 146, 169 Knight’s tour, 10

Legrand’s open-letter cipher, 5 Levine’s concealment ciphers, 7 “Lining up” frequency counts, 162-163 Low-frequencies, assistance from, 99, 100, 129, 136, 138, 160 Low-frequency contacts, 78, 174

Magic squares, 10 Mathematical aspects of multiple-alphabet ciphers, 142, 151, 193, 196 Mechanical methods, 21, 32, 45, 56-58, 133, 138, 149 Military aspects of ciphers, 3, 55 Mirabeau’s cipher, 209 Mixed alphabets, 70, 169 Monoalphabetic substitution, meaning of, 68 Morse alphabet, 210 “Multifid” alphabets, 209 Multi-literal substitutes, 6, 7, 104 Multiple-alphabet ciphers, 108-197 Multiple-alphabet substitution, meaning of, 68 Multiple messages, 56, 85, 140, 146, 185 Multiple-substitutional encipherment, Multiple substitutes, 68, 99, 102, 103, 159 Myszkowsky’s transposition, 51

Negative, or empty, words, 76 “Nicodemus” cipher, 216 Nihilist number-cipher, 164-168 Nihilist transposition cipher, 17, 53 Novelty ciphers, 100, 214 Null cipher, 4 Nulls, legitimate uses of, 37, 55, 110, 201 Nulls, meaning of, 9 Numbers and symbols, encipherment of, 101 Numbers used as substitutes, 154-157, 159-168

Ohaver method for period finding, 160 Open-letter cipher, 4

Pair-count, 202 Pair-encipherment, 198, 199, 200 Parallel frequency counts, 162, 165, 177 “Pattern words,” 73 Pentagram, meaning of, 1 Periodic ciphers, 108-184 “Period” in autokey ciphers, 146 Period, periodicity, 108, 112-114, 127, 138, 166, 195 “Phillips” cipher, 185 Phonetic alphabets, 106 Playfair cipher, 200 “Pointers” for vowel-spotting, 78 Pollux systems, 209 Polyalphabetic ciphers, names of, 108 Polyalphabetic substitution, meaning of, 68 Polyalphabetic substitutions, 108-197 Polybius square, 164, 209 Polygram substitution, meaning of, 68 Polygram substitutions, 198-208 Porta cipher, 118 Primary cipher alphabet, 164, 169 Primary cryptogram (see double transpositions or double substitutions) Probable word methods, 23, 29, 34, 37, 99, 113, 119, 124, 147, 202, 206 Progression, Progression index, 192 Puncture cipher, 4

“Quagmires” cipher, 182

“Rail fence” transpositions, 12 Reciprocal substitution, 70, 118, 121, 123 Rectangular transposition, 11 “Route cipher,” 14 Route transposition, 11 “Running down the alphabet,” 72, 100, 118, 124, 139, 185, 192, 214 “Running key,” 143

Saint-Cyr cipher, 110 Scytale, 14 Secondary cipher alphabets, 164, 169 Sequence (see statistics) Seriation, Seriation index, 207, 210 Shift, Shifted alphabets, 69, 70, 72, 108, 119, 133, 172, 177 Short word method for divided cryptograms, 72 Simple substitution, meaning of, 68 Simple substitutions, 69-107 Slides, slide-rules for decrypting, 141 for encipherment, 110, 119, 123, 169, 170 used in transposition, 13, 61 Specific key, 169 Statistics, some uses of, 14, 18, 21, 40-42, 45-50, 57, 73, 75, 78-85, 88, 113, 130, 141, 150, 153, 174, 187, 201, 202, 213 “Step-up” and “step-down” letters, 89 “Straddling” devices, 105 Strips used in decryptment of transpositions, 15 used for encipherment of polyalphabeticals, 108 used for decryptment of periodics, 136 Substitutes, 68 Substitution cipher, meaning of, 1 Substitution ciphers, 68-212 Symbols, 68 “Symmetry of position,” 176

Tableaux: Vigenère, 109 Porta, 118 Beaufort, 121 used for decryptment of periodics, 134 formed in autokey decryptment, 150 high-frequency co-efficients, 152 imaginary, or formed in key-recovery, 170-172, 178 Delastelle, 177 for finding alphabetical intervals, 194 for pair-encipherment, 198 “Taking off” (Transcription), 9, 17, 23, 60 Terminals (see statistics) Tetragram, meaning of, 1 Transformation device, 102 Transposition, meaning of, 1 Transposition ciphers, 9-67 Trial key, 111, 150 “Trifid” substitution, 210 Trigram, meaning of, 1 Trigram encipherment, 199 Trigram method of solution: applied to Beaufort, 125 applied to Gronsfeld, 117 applied to Porta, 119 applied to Vigenère, 113 with the use of a slide, 141 Trithème’s alphabet, 7

Unit, 9, 18 United States Army Cipher Disk, 108, 123 United States Army Double Transposition, 54

Variant Beaufort cipher, 121 Variety of contact, 75, 78, 88, 174, 204 Variety count, 75, 88 Vigenère cipher, 108 Vowel-distribution (see statistics) Vowel-line method for simple substitution, 91 Vowel-solution method, 78, 174

Word-spacers, 100 “Writing-in” (Inscription), 9, 17, 23, 60

Transcriber's Note

The original figures were made with a typewriter, and then lines, arrows, or circles were added. This file reproduces them as well as is possible as plain text. Please see the HTML version if you wish to see the figures with all of their details.

Minor corrections, such as removing extra spaces or punctuation, or adding missing spaces or punctuation or diacritical marks, were made without note. Archaic and inconsistent spelling was retained. In two places, the number of a referenced figure was corrected. Grammar and spelling were only corrected as in the following list of notable changes.

In two places, “diagram” was corrected to “digram”.

In three places, “direct” was corrected to “directly”.

In Chapter III, we italicized the first occurrence of “magic square” because it seemed like the author’s intention. In the same chapter, “said be clockwise” was corrected to “said to be clockwise”.

In Figure 43, “ISGAY” was corrected to “ISGAU” to match previous figures and to correct spelling in the plaintext.

In Chapter VII, “those who like method” was corrected to “those who like this method”.

In Chapter XVIII, “misuse of the Type II slide” was corrected to “misuse of the Type I slide”.

In Figure 139, “IQCIO” is corrected to “IQVIO”.

In the Appendix, in the list of English trigrams, “WHI 51” was corrected to “WHI 71”.

Some corrections were made to the exercises in order to rectify the spelling in their plaintexts or (in one case) to resolve an inconsistency in its key.

In exercise 33, seven letters were missing. The uncorrected cryptogram is VINSC FEAEO OHSEF HLEHU NSTNC LTSLC IAESH RHSIR ERMTS ETEPD TOINM RTTHT TLRUB E.

Exercise 110: “LRSFQ” corrected to “IRSFQ”.

Exercise 115: “FBEHZHWU” corrected to “FBEHZHWG”.

Exercise 116: “HVIYF” corrected to “HVXYF”.

Exercise 128: “JQAOJ” corrected to “JQAOI” and “QNUSG” to “QNUSU”.

Exercise 130: “FBWXJ” corrected to “FRWXJ”.

Exercise 138: “XVKFV” corrected to “XVKEV”.

Exercise 141: “KFTFB” corrected to “KFTFX”.

Exercise 144: “TAJNI WRDB” corrected to “TAJNW ARDB”.

Exercise 145: “TTHNY” corrected to “TTHNJ”.

Exercise 146: “PGOUR” corrected to “PGOUJ” and “VDDMH” corrected to “VDDMP” (we are not sure about “VFCFT”).

Exercise 147: “UVSYC” corrected to “UBSYC”, “IXYDY” to “IXYPY”, “VXOOK” to “NXOOK”, and “NNHMM” to “NNHWM”.

Exercise 149: “MS” corrected to “PF”.

Exercise 153: “QY BN QM” corrected to “QY BM QM” and “BL PK QM” to “BL PO QM”.

Exercise 40 has error(s) in the first 25 letters. We do not know what was the intention of its creator.

The above list should not be assumed to be correct or complete.

We wish to thank the anonymous proof-readers who volunteered at the British National Cipher Challenge (www.cipherchallenge.org).