SOLVING CIPHER SECRETS Edited by M. E. Ohaver A PROFITABLE LESSON ON THE SOLUTION OF A CRYPTOGRAM IN AN UNKNOWN CIPHER SYSTEM-ALSO READER CIPHERS O solve a cryptogram in a cipher may be so unapparent as to require known cipher system, it is the application of delicate cryptographic only necessary to apply tests to discover their presence. methods peculiar to that If a comparison is again allowable, this cipher. But suppose the would be like identifying the man by his system is unknown. How, Bertillon measurements, or by his finger• then, would it be possible to determine the prints. method of solution? To demonstrate the practicability of these That the fans are much concerned with tesf s, we have applied some of them in this this question would seem to be indicated article to a cryptogram that was submitted by the volume of mail from readers who to this department without solution or ex• stale that they have successfully used the planation. different methods described in these columns This cryptogram was chosen from many for various ciphers, but who wonder if there similar ones for several reasons. In the first is any way of finding what method to use place, it illustrates all the points brought when the cipher is unknown. up by the various tests. Again, it happens Fortunately, in many cases a cipher will to be in a standard system that we wanted leave an indelible impress on a cryptogram, to present to our readers, anyway. And, allowing the system to be identified, or, at finally, the fact that the inditer was abso• any rate, to be recognized within limits, by lutely certain his specimen could not be de• certain more or less easily recognizable ciphered—an opinion he no longer holds—• characteristics. adds zest to the problem. Sometimes these peculiarities are distin• The cipher was submitted through an• guishable at sight. To illustrate this, con• other reader of FLVNN'S WEEKLY, who ac-' sider the Nihilist numerical cipher, the num• companied it with the following letter. bers of which are within the limits 22 DE.SR SIR: and 110. I inclose a message written in cipher. This To determine a cipher system in this way was made up by a man who has used the is somewhat like identifying a man on'the same for private messages. street by the color of his eyes or hair; by a He claims his cipher cannot be solved. For you, and your department, I accepted the missing right index finger; or by a manner• challenge, and am sending on the message. ism of gait or gesture. SAM'L J. MCNARV. On tlie other hand, the peculiarities of a Cincinnati, Ohio. IS) V 154 FLYNN'S WFFKLY Things begin to look interesting already. the groups are given herewith in this in• Suppose we have a look at the cryptogram stance. Itself? A 8 L s J 5 E 3 N I KB ol jmepprqvhoi j I 3 R 4 Q 3 mzphxzuwvbhnauo - O 10 SI X 2 Ivuohphabkskle U 7 T s Z 4 tlulvbfbwopwtp houvryucxbbatd 31 16 22 zbqpyaat jdeyiap (25.4%) (13.1%) (18.0%) fkkkokrgcutqoak pyi rjpwofbkohw A difference of more than 5% in any t p d K id z.— group from the 40%-30%-2% averages could be taken as evidence that the cipher The several tests about to be given in• is not of the transposition class. Here all volve the number of limes various cipher three groups are outside their respective characters are used. Accordingly, a table limits, rendering such a conclusion even of their frequencies Is herewith appended: more probable. Having thus disposed, apparently, of the A 8- H 7 O lO V S B 8 I 3 P II W S transposition possibility, we will now pro• C 2 J 5 Q 3 X 2 ceed to discover if the cipher is of the sub• D 4 K 8 R 4 Y 4 stitution class; and, if so, whether the char• S I Z 4 E 3 L 5 acters are fixed in their values as in the sim• F 3 M 2 T 5 ple substitution cipher, or variable as in G 2 N I U 7 122 multiple alphabet and other varieties of Had this cryptogram been one of num• substitution ciphers. bers or signs, we could have at once as- In the simple substitution cipher, where siuned that it was of the substitution vari• a given character always represents the ety. Since it is literal, however, it can be same letter, quite frequently the number of one of either the substitution, transposi• different characters in a cryptogram will be tion, or null class, not to mention combina• less than twenty-six, since one or more let• tions of these. ters of the alphabet are often unused even If our specimen is a transposition cipher, in long messages. it will react positively to the vowel-conso• A'peculiarity, however, of ciphers em• nant group test, given by Parker Hitt in ploying characters of variable values, is that his " Manual for the Solution of Military almost always all of the characters will be Ciphers," a work formerly published by present even in short cryptograms. The the Army Service Schools Press, Leaven• present cipher would thus seem to be one of worth, Kansas, but now, unfortunately, out this kind, using, as it does, all twenty-six of print. letters, presumably the whole number of This test is based on the fact that in characters employed by the cipher. average English text the total frequencies Another characteristic of the simple sub• of the vowels AEIOU, and the consonants stitution cipher is that repeated words will LNRST and JKQXZ, will ordinarily not at each recurrence be represented by the vary more than 5% one way or the other same cipher characters. The present cryp• from 40%, 30%, and 2%, respectively, of togram, as shown, contains a number of the total number of letters. The figures two-letter recurrent groups, and one of have been obtained by countless experi• three letters, but none of any greater length, ments. which would be likely if the cipher were A common method of applying the test is of the simple substitution type. to first count the vowels directly from the .Another aid in recognizing the variable cryptogram, not taking the consonant substitute cipher is that ordinarily it af• counts unless the vowel count falls within fords no characters of either extremely high the prescribed 35%-45% limits. For illus• or low frequencies, corresponding respec• trative purposes, however, the counts for all tively to the substitutes for F, T, A, 0, N, SOLVING CIPHER SECRETS 155 et cetera, and J, K, Q, X, Z, et cetera, of substitute cipher will in this case be more the simple substitution cipher; the tendency than 2%, approaching 20% as a limit. In being, on the other hand, for all characters applying these tests due allowance must lie to approach an average frequency of made where substitutes for the word-space, (ioo% 26 letters—3.85%) approxi• punctuation marks, figures, and so on, may mately 4% for each character. have been used. This being so, we are able to offer the fol• Having eliminated the simple substitu• lowing test, based on the fact that the com- tion cipher we will next investigate the pos• hkKd frequencies of the five most used let• sibilities of a variable substitute system. ters, ETAON, comprise approximately 45% At this point it is necesary to mention of all letters in average English text. that such ciphers are legion. Some of them, In the simple substitution cipher the five for example the Vigenere chiffre carri, the most used characters will either represent Cronsfeld, and Saint Cyr ciphers, use a the above five letters, or other letters of fixed series of alphabets, determined by a practically the same frequencies, whose short key. total will thus approximate 45% of all the In others, the fixed series of alphabets is characters in the cryptogram. avoided by using a continuous and non-re• In variable substitute ciphers, however, peating key; 01, as in autokey ciphers, by where a given character can represent sev• allowing the letters of the message itself to eral different letters, and a given letter can determine the alphabets. have several substitutes, the combined fre• Again the cipher may be based on di• quencies of the five most used characters graphs, as is the Playfair cipher, for exam• will fall below the 45% average, approach• ple, in which each letter can have five sub• ing (5 lettersX 3.85% = 19.25%) approxi• stitutes, and each substitute can represent mately 20% as a limit. any one of five letters, depending on the The following comparative table shows letter with which it is paired. the five, most used letters, ETAON, with fre• However, this multiplicity of classes and quencies taken from the table of 10,000 in types can hardly be more than mentioned FLYNN'S WEEKLY for January 23, 1926, here. For the present we must content and the five most used characters, POABK, ourselves with following up the main stream of the present cryptogram. to only one of its many branches, reserving the others for later exploration. E 12=11 P It One method of finding if our cipher uses T Qso 0 10 A 806 A 8 a fixed series of alphabets is to apply the 0 800 B 8 Kasiski test for recurrent groups, described, N 712 K 8 in detail in FLVNN'S WEEKLY for August 7.