SOLVING CIPHER SECRETS

HE cipher presented in this article might well be heralded with the flourish of trumpets, the rattle of drums, or the booming of cannon.

For it is representative of that aristocracy of ciphers known as code, And code stands ready to serve nations in the weightiest affairs of state; to bear its own proper burgle meaning. For example, there are the everyday needs of business, as well as to the private purposes of the individual.

The word "code" is not limited to a single meaning. For example, there are the so-called "technical codes," or signal communication systems, such as the heliograph or ordinary electric telegraph, where letters, figures, et cetera, are communicated by means of the American or International Morse codes; the printing telegraph, using the five unit code; and the wigwag code, where letters are symbolized by positions of flags or lights.

Again, there is the railway semaphore, with its arm positions and colored lights, for day and night signaling. While signal fires and smoke columns, where "vocabularies "were limited to such words as "warning," "defeat," and "victory," may be mentioned as early forbears of technical code.

The kind of code here referred to, however, is a specialized form of cipher, where the terms of a more or less elaborate vocabulary have corresponding code numbers or code words which are made to act as their substitutes.

A code vocabulary, of course, must conform to the use for which the code is intended. Ready-made codes for almost every conceivable purpose are on the market. Or, should you not want a "hand-medown," you may have a code made to your special order.

With the kind permission of the publishers—Cryptograph Company, North Station, Providence, Rhode Island—we have used the Simplex Cryptograph to illustrate the present article, this code being e.xceptionally well suited to general correspondence, unusually complete in its vocabulary, and at the same time quite inexpensive.

The vocabulary of this code book comprises 53,000 terms, in a single alphabetical order, numbered ooooo to ysggg, and with a corresponding alphabetical series of 53,000 code words. In this vocabulary are to be found proper names, prefixes and suffixes, letters, a sprinking of common phrases, and the usual "blanks" (52650 to 52999), which can be filled out with special terms as desired. However, for the most part it is made up of words, given in their various grammatical inflections.

Thus, we find here not only "blend" (04141), but also "blended" (04142), "blending" (04143). and "blends" (04144). This type of code is thus a wonderful improvement over common dictionary cipher. (See FLYNN'S WEEKLY for May 22, 1926). Such terms of the present code as are required by the several ciphers in this article will be found, with code words and code numbers, in the short illustrative vocabulary herewith:

To encode a message it is only necessary to substitute for each vocabulary term its corresponding code number or code word. Thus the message: "The doctrine of ciphers carries along with it the relative doctrine of deciphering without the key to the cipher," could be transmitted either as a series of numbers, "47434 11893 29145 06953 ..."; or of words, "tympanites decamped misdate butler ..."

Many manufacturing and industrial codes, when economy of transmission rather than secrecy is desired, are of this simple nature.

In such form, however, a coded message could easily be read by any one equipped with a similar code book. Further, an alphabetical vocabulary of the present type would be subject to interpretation without the code book in the same manner as ordinary dictionary cipher.

When secrecy is desired, therefore, some additional method of obscuring the coded message is necessary. And for this purpose any suitable cipher whatever may be employed, the result being termed "enciphered code."

A common method of encipherment, and that proposed in the Simplex Cryptograph, consists in modifying the code numbers by a series of key numbers known only to the communicating parties. And this system, together with suggestions for its resolution will be treated in this article at some length.

Right here it must be said that the present method of analysis is concerned particularly with this one method of encipherment. There is nothing to prevent the use of this same code book with another method of encipherment. And the latter should in any case preferably be known only to the correspondents, since code operates to the fullest advantage when the code book, method of encipherment, and key, are all carefully guarded secrets.

To proceed with the present method, a key of any length may be chosen, consisting of any numbers whatever within the code limits, from 00000 to 52999. Suppose that we select the key "17643 04952" to encipher the illustrative message partly coded above.

1 2 3 4 5 6      ...
(a)  The doctrine of ciphers carries along  ... 
(b)  47434      11893      29145      06593      05693      01360  ... 
(c)  17643      04952      17643      04952      17643      04952  ... 
     —————
     65077
     53000
     —————      —————      —————      —————      —————      —————  ...
(d)  12077      16845      46788      11545      23336      06312  ... 
(e)  deducing   evolutions triplopy   cynical    hymns      buccaning ... 

Having first translated the message (a) into plain code (b), write down the key numbers (c) below the code numbers, repeating the series as many times as the length of the message may require.

Then add the numbers thus brought together at (b) and (c), subtracting the code "capacity"—53,000—whenever the sums are equal to or in excess of that number. The resultant numbers (d) or their equivalents in code words (e) complete the encipherment, in either of which forms the message is ready for transmission.

To decipher the above example—given the key, method, and code book—first substitute for the code words (e) the equivalent code numbers (d). Next, subtract the key numbers (c) from the latter, adding 53,000 to any code numbers which are less than their key numbers. The resultant plain code (b) is then decoded (a) into the terms of the terms of the original message.

(e) deducing   evolutions triplopy  ...
(d) 12077      16845      46788     ...
    53000
    —————
    65077
(c) 17643      04952      17643     ...
    —————      —————      —————
(b) 47434      11893      29145     ...
(a) The doctrine of        ... 

Enciphered code of this type might readily be accepted by the uninitiated as insuring absolute secrecy in so far as anything can be absolute.

In this case, for example, a given vocabulary term can assume 53,000 different forms in code; and, further, dependent on the wording, key length, and key numbers, it might not be represented by the same substitute twice in the same message. For instance, "the" is here expressed both by "12077" or "deducing" (1-9-15), and "52386" or "wimpled" (18).

This system thus provides 53,000 possible variations with but a single key number. Should two key numbers be used there are 53,000 × 53,000, or 2,809,000,000, combinations. And with only three key numbers the staggering total of 148,877,000,000,000 is reached. The possibilities seem stupendous.

To find a key among such almost unlimited possibilities might seem like searching foolishly for the proverbial needle in a haystack.

Fortunately, however, the reduction of this problem does not depend upon an individual trial of every possible key until the right one is found, but upon the determination of the particular key by more direct methods.

Suppose, for instance, it B desired to decipher the above example, now appended in full in its numerical form.

1 2 3 4 5 6 12077 16843 46788 12545 23336 06312 7 8 9 10 11 12 16816 27539 12077
    42231 29536 34097 13 14 15 16 17 19 27576 04144 12077 28164 12642 52386 19 24233

The first step is to determine the period, or key length. When one has the code book at hand for reference, this may sometimes be done by guessing the identity of one or more code groups, and observing if the resultant key numbers produce probable words at regular intervals throughout the message.

But as a general rule, the best way to find the period is to factor the intervals between repeated groups; or those between groups providing "characteristic," "common "or "complementary" differences, as will be seen.

Let us first consider repeated groups. Here we find "12077" (or "deducing" ) occurring as groups 1, 9, and 15. The period is found from these numbers by exactly the same method described for the numerical cipher in FLYNN'S WEEKLY for December 18, 1926. The greatest common factor in this case is "2," indicating a cipher key of that many numbers.

Places     Intervals      Factors
 9-1 =         8;         1, 2, 4, 8
15-1 =        14;         1, 2, 7, 14
15-9 =         6;         1, 2, 3, 6

The finding of the key length, either as just shown, or by any of the methods yet to be described, will reveal just which code groups have been enciphered by the same key numbers. With a key of two numbers, for instance, groups 1, 3, 5, 7 . . . must have been enciphered by the first key number; and groups 2, 4, 6, 8, ... by the second.

Having determined the several series of code groups, the next step is to find the key number for each series. Whenever they occur, "characteristic differences" may be used for this purpose. These exist between the code numbers of any desired vocabulary terms; as, for example, frequently used words, or certain other words whose presence in a given message may be easily suspected.

A table of these differences must be specially made for each different code book, and may be as extensive as desired. That herewith lists only five frequently used words in the present code. The differences in the second column are found by first adding 53,000 to the code number of the word marked with an (*) asterisk as follows:

to  - the = 00563; the* - to  = 52435
and - to  = 06671; to*  - and = 46329
and - the = 07236; the* - and = 45764
of  - in  = 08539; in * - of  = 44461
the - of  = 18289; of*  - the = 34722
to  - of  = 18854; of*  - to  = 34146
in  - and = 18936; and* - in  = 34064
and - of  = 25525; of*  - and = 27475
in  - to  = 25607; to*  - in  = 27393
in  - the = 26172; the* - in  = 26828

To apply this method, compute the differences between all the code numbers in each series, endeavoring to find differences that occur in the table. For example, in the first series, the difference between 46788 (3) and 12077 (1) is 34711, a number given in the table. But the difference between groups 1 and 5 is 11259; and that between groups 3 and 5 is 23452; neither of which are in the table. Proceeding in this way, the following list of differences is readily discovered in the present code message:

Groups Difierences Intervals Factors
46788  (3); — 12077  (1) = 34711;  2   1, 2
46788  (3); — 12642 (17) = 34146; 14   1, 2, 7, 14
12642 (17); — 12077  (1) = 00565; 16   1, 2, 4, 8, 16
32386 (18); — 34097 (12) = 18289;  6   1, 2, 3, 6 

By referring to the table, these differences show what words are supposedly represented by the groups in question, thus making it an easy matter to find the key numbers.

To illustrate, the table says that 34711 is the difference between the code numbers for "of" and "the." Hence, we may assume that 46788 and 12077, respectively, are the present substitutes for these two words, giving the key number 17643 by the following simple manipulation:

                    (3)       (1)
Enciphered code: 46788  -  12077 = 34711
                           53000
                           —————
                           65077
Plain code:      29145=of  47434=the
                 ———————————————
Key number:      17643     17643

This method operates on the theory that other words producing the same differences, while quite possible, are not so liable to occur in the same message. Groups 3 and 77, or 1 and 77, would also give key number 17643; while groups 12 and 18 would similarly supply the second key number, 04952. The 53,000 is only added when the characteristic number is in the second column of the difference table.

Since groups providing these differences have supposedly been enciphered by the same key numbers, their intervals may be used, if desired, in determining the key length by factoring. This is also shown above, where factor "2" again rings the bell. Had 12077 (1) here been treated as a recurrent group (1-9-13), it would have afforded two more intervals with 46788 (3) for factoring.

In the event that there are not enough recurrent groups and characteristic differences in a given message to indicate the period. "common" or "complementary" differences may neatly turn the trick. Like recurrent groups, neither of these methods requires the decipherer to have a copy of the code book.

Of these two classes, "common" differences are identical numbers derived from two or more different pairs of code groups, which are consequently assumed to represent the same pairs of words, but enciphered by different key numbers as previously arranged.

Thus the following groups—which happen to signify "of" and "doctrine"— have a common difference of 17252, with intervals of 8 and 10, pointing, as before, to a key of "2" numbers. Further, the difference—12691 in this case—between corresponding groups of this kind is equivalent to the difference between the key numbers involved. (With the present key numbers, for example: 17643-04952=12691).

46788  (3) − 34097 (12) = 12691
29536 (11) − 16845  (2) = 12691
——————————   ——————————
17252  (8)   17253 (10)

Complementary differences exist between two pairs of code groups which represent the same pair of words, when one word of one pair has been augmented by 53,000. Like those in the same lines of the characteristic difference table, the sums of complementary differences always equal 53,000. The following complementary pairs give the intervals 10 and 16, again indicating the same period, "2."

29536 (11)   52386 (19)
12077  (1)   16845  (2)
——————————   ——————————
17459 (10) + 35541 (16) = 53000

The above groups also provide the key differences 12691 (29536 − 16845) and 40309 (52386 − 12077), either of which can be used to transform its respective series of code numbers to the key value of the other series.

We have thus shown how it is possible, even without the code book, to determine the period of this type of message; also how to discover the size of the code, and the differences between the various key numbers. Such a message is therefore capable of being mathematically reduced to one enciphered with a single key number, in which form it is more practicable to determine words by their frequencies, sequences, context, or by approximating one or more of their first letters according to their relative places in the supposed alphabetical series.

If necessary, intervals obtained by any or all of these methods may be combined for factoring in one table. Also, numbers that differ by only a few units usually represent different forms of the same word modified by the same key number, and can therefore generally be treated as recurrent groups. Differences that fail to agree by a few units can likewise be attributed to the same cause with small liability of error.

To return to the present example, when all the key numbers of a message cannot be determined, undeciphered groups can often be read by context. Had only the first key number been found here, the partly translated message would appear as follows, where 34097 and 52836 are obviously "of" and "the," either of which suppositions would supply the missing key number.

12077     16845     46788     11545     23336     06312
The       ——        of        ——        carries   ——

16816     27539     12077     42231     29536     34097
with      ——        the       ——        doctrine  (of)

27576               04144     12077     28164     12642
deciphering         ——        the       ——        to

52386     24233
(the)     cipher

Getting down, at last, to some code messages for our readers to solve, we have prepared three examples, each of which has its points of interest. All the terms used in these messages will be found in the short code vocabulary accompanying this article.

The first two messages are enciphered code of the type here described, and should yield readily to the present methods. The clews in these ciphers are sufficient, but not numerous. So be careful in computing your differences that you do not pass up the very groups that furnish the necessary "leads."

The second message uses Simplex Cryptograph code words, which conform to the 1900-1901 official vocabulary of the Bureau International de I'Union Télégraphique. Code words of this type were used in the famous "Teapot Dome" code telegrams that gained such widespread publicity about three years ago, and which were said to have been in a government code.

This type of code word, however, has been largely supplanted by the more economical five-letter artificial code word, any two of which may be combined for transmission as a single ten-letter code word.

Message No. 3 employs artificial ten-letter words of this general class, each code word representing ten figures, or two complete code numbers, according to a simple plan of encipherment which we shall leave our readers to discover for themselves.

Maybe you wonder what these code messages are all about.

Well, one of them, we will not say which, might be a brief government communication relative to an important event in a certain foreign country.

Another might be a confidential stock message.

And a third—we still refuse to say which—might be news from a party of explorers in search of pirates' gold.

So there you are, fans! Three fine messages in real code for you to solve.

What can you do with them?

IT'S YOUR MOVE !

CODE MESSAGE No. 1.

52609 05926 10218 05176 02403 47876
23439 01201 17514 00199 51585 22678
46656 48808 36736 00174 01267 28507
07495 26214 07679 48742 26060 28507
11837

CODE MESSAGE No. 2.

cowslip nymphs icarian disobliged clawing
muttered comprisal shavelings bureau fetcher
smatterer bureau practical loosish cubless
taurine cellarets

CODE MESSAGE No. 3.

MUYENGLUHO CUZANUTUJU
KIDIYOPESE DEWUJIYEMA
MUKATEFUKE

To afford every one a fair chance at the code problems, their solutions will not be published for three or four weeks. In the meanwhile, fans, do your level best and send in as many answers as you can get.

The key phrase ciphers of January 22 aroused more than the usual interest and enthusiasm. Did any of our readers succeed in duplicating the classic feats of Poe and Berryer?

Well! Just look over this list and judge!

• K. Davidson, Montreal, Quebec, Canada.
• Dr. G. A. Ferrell, Bessemer, Alabama.
• Charles E. Roe, Hudson, Massachusetts.
• M. Walker, Akron, Ghio.
• F. M. Sutton, Beaumont, Texas.
• Mrs. A. J. Hyatt, Jackson Heights, Long Island, New York.
• Eric G. Haden, Louisville, Kentucky.
• Paul A. Napier, Louisville, Kentucky.
• Arthur Bellamy, Boston, Massachusetts.
• George P. Wood, M. D., Detroit, Michigan.

Every solver in this list submitted answers to both ciphers, and in almost every instance the solutions were accompanied by the correct and completed key phrases. The most prevalent error in this respect was the use of the Modern French "foi" in place of the Old French "foy," in key phrase No. 1. Messrs. Roe, Walker, and Haden, however, were correct even in this detail.