AS we have already pointed out, Cipher No. 148 of two weeks ago, which adapts a phonetic alphabet to the famous Nihilist system, is capable of a mathematical resolution.
That is, with sufficient material to work on, it is possible to determine the length of the key and the identity of the key numbers by mathematical processes, and without any knowledge whatever of the language used in the message.
In the present case the length of the key may be found by factoring the intervals between recurrent sequences, high numbers, low numbers, et cetera. Or the decipherer may apply the special method for this particular system, which would consist of eliminating intervals between numbers which have a units difference of more than four or a tens difference of more than seven.
Thus, the units difference between 79— the third number of the cryptogram—and 42—the ninth number—is 7, thereby eliminating 6, the interval between these two numbers, as a possible key length. Similarly, the tens difference between 125—second number—and 42—ninth number—is 8, eliminating 7, the interval between these two numbers, as a possible key length.
By a continuation of this process all intervals but 8 and its multiples may likewise be eliminated. Assuming, therefore, a key of eight numbers, the cryptogram may now be transcribed in lines of eight numbers each, forming eight columns, as shown herewith:
1 2 3 4 5 6 7 8 65 125 79 108 113 l08 107 137 42 137 79 68 135 86 107 99 46 96 117 8S 105 48 85 137 54 78 89 37 136 55 94 146 94 117 97 S6 136 58 107 76 115 87 117 58 156 106 103 130 103 77 89 47 97 106 77 87 83 134 68 49 137 58 87 137 106 117 79 108
In this arrangement all numbers enciphered with any given key number are brought together in the same column. And by considering the highest and lowest units and tens in any column the key number for that column may be found, or at least, it may be fixed within certain limits.
For example, the key to the numbers in the fourth column must be 24, for the tens figures there run from 3 to 10, and the units from 5 to 9. In this way the first (31=F), fourth (24=E), and eighth (65=S), key numbers may be found in a few minutes. Also, the second key number may be limited to two possibilities, 53 (O), and 63 (P), of which the second can be rejected on account of the improbable sequence, FP, which would result in the key.
For the same reason the fifth key number, which might otherwise be 82 (W), is probably 72 (T). Reference to the alphabetic key published two weeks ago in connection with this cipher is, of course, necessary in assigning letters to all of these numbers, both in the key and message.
Having tentatively accepted these several key numbers, their respective columns may be deciphered. And values in the remaining columns may be determined by context, thereby leading to a discovery of the remaining key numbers.
For instance, the translation of the eighth line of figures,as already given, would run 0-V-68-E..., suggesting DH(23) for 68. And this would give OV DHE—of the—in the message, and 45—N—for the third key number. By similarly treating the two remaining columns the decipherer will have the full key, 31-53-45-24-72-34-42-65, which was derived from the key word FONETIKS—PHONETICS.
Here is the message in phonetic spelling, in groups of eight characters to facilitate comparison with the crvptogram: IT IZ JUST—AZ IMPOSI—BL TOO HAWLT—DHE MAHRCH OV—PROGRES A— Z IT IZ TOO S—TEM DHE TID—OV DHE SENT—URIZ. (It is just as impossible to halt the march of progress as it is to stem the tide of the centuries.) The following short example will show the method of decipherment with the key:
Cipher: 65-125- 70-108-113-108-107-137 ... Key: 31 53 45 24 72 34 42 65 ... —————————————————————————————— Subtract: 34 72 34 84 44 74 65 72 ... Message: I T I Z J U S T ...
Last week's straight substitution Cipher No. 149, by Hannah C. Jones, conveyed the message: "Your ciphers are certainly successful as gloom chasers. One can spend an enjoyable evening with them." Predominating E, and the groups DYQL QLAJ—WITH THEM—would give a good start here.
No. 150, by P. A. Napier, used a modification of a system which our correspondent found in an interesting article on secret writing by John H. Haswell, in The Century Magazine for November, 1912. To decipher, merely count forward in the alphabet for each letter the number of places indicated by its position in the group as shown below, where the sixth group, TZQH, becomes TASK. Mr. Napier's message: "It is sometimes an arduous task to relieve a cipher of its secret."
T Z Q H A R I S J K
M. Walker's phonetic substitution Cipher No. 151 used the numbers 1 to 36 as substitutes for the characters of his alphabet in the order given last week: I=E (long); 2=I (short)... 36=K. The message: "For some we loved, the loveliest and the best that rolling Time hath from his Vintage pressed have drunk their cup a round or two before." Did you get it?
We think you will find the first of this week's ciphers rather difficult. It is a straight substitution, and every word is in common use. But Mr. Boyer has fashioned this problem with rare skill. Can you crack it? No. 153 is also practically a straight substitution cipher, although the alphabet is based on phonetic properties of letters. There are also some slight variations in spelling here, but it is much easier than No. 152.
No. 154 hails from far-off Honolulu. In this cipher the message was first spelled phonetically, and then subjected to a simple transposition. Mr. Harris has taken certain liberties with the spelling, which do not, however, impair the intelligibility of the message. See what you can do with this product of sunny Hawaii!
CIPHER No. 152 (John Q. Boyer, Baltimore, Maryland).
VQLGB WPJWD, JPWXKW WHZNX, KWB EJS, NPLFZQ WRJVA, JHIZKX PKVDB, LNX XZASX VDKKQE JWPLIJX.
CIPHER No. 153 (Raymond Wallace, Oakland, California).
DHUZ JOBHUL IMRA LUGWOLUZ Y ZHILD DYPRU WHOJH JYM NUNILOSUT OM Y VUW NOMEDUZ.
CIPHER No. 154 (M. L. Harris, Honolulu, Territory of Hawaii).
TZH OZUSA IU IU MHL HRJH LRMH LI IR YUR URFSUAMV HNRO PSZMU- OYV UILOHV LUIRKAB U NDNZM SNHIAZ WIM AGFN CKYBZ VWWABOB FVHOZ.
Answers to this week's ciphers will appear next week. See how many you can get, and send in your solutions.