Elementary cryptanalysis

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				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

																											10000

         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