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