IN FLYNN'S for July 25 you were offered two of the ingenious cipher systems invented by William Blair, the English surgeon. In this article you will find an expose of those ciphers, together with more products of Blair's cleverness. If you can puzzle these out, you may consider yourself in select company. They have been solved. But seldom by cryptographers who have not devoted years to the art. And whether you succeed or not, you are sure to find delight in working on them.
ILLIAM BLAIR, the inventor of the ciphers treated in this article, must have had an inordinate hankering after dots.
The stroke cipher of Charles I mentioned in last Solving Cipher Secrets, in FLYNN'S for July 25, consisted partly of dots. And you will remember that it was the accidental sight of this system of secret writing that led Blair to examine into the nature of ciphers.
During the course of this investigation Blair chanced upon an important find.
He discovered what turned out to be the key to a previously unexplained method of writing with dots by Edward Somerset, Marqui s of Worcester.
This nobleman, one of the most extraordinary personages of his time, devised a number of curious and ingenious systems of secret communication which will be dealt with later in more detail. Finally, when Blair decided to devise a cipher of his own, strangely enough he, too, hit upon dots as one of the vehicles of its expression.
Of course all this business about dots may be purely coincidental. At any rate, we are not so much concerned here with anything that may have suggested the form of Blair's ciphers as we are with their solutions.
And in this connection it must be borne in mind that according to the terms of Blair's challenge not only did he defy " all the scrutinizing powers of man" to decipher his cryptograms, but also to discover the principle on which his ciphers were constructed.
It is therefore with the special object in view of developing this principle that we must set about the analysis of his ciphers.
Blair's original challenge was accompanied with five different ciphers, all done with the same key. Two of these five, the dot-writing and the figure cipher, were printed in FLYNN'S for July 25. And other varieties are to be found in this issue.
It is well to begin, however, with an analysis of the dot-writing, as it has the appearance of being the simplest of all.
Here the first step toward solution is obviously the determination of the number of dots that act as a substitute for any character in the Alphabet and Key.
|Alphabet and Key|
|W. BLAIR inv. 1807|
This key consists of eighty-one characters. It is therefore reasonable to suppose that the number of dots used collectively as a substitute must be such as would provide in their various positions—above, upon, and under the line—eighty-one different combinations.
Two dots taken in three positions produce only nine combinations; three dots, but twenty-seven; while four dots varied through three places provide exactly eightyone permutations.
The smallest number of dots that could possibly act as a substitute for any character is thus four. An d before proceeding with the solution in any other direction it is well first to exhaust this possibility.
Now, narrowly observing,the Alphabet and Key, the dot (.) in the lower left square immediately arrests the attention. And some speculation as to its purpose might not be amiss.
A character like this might be a special indicator of some sort. Or it could be a punctuation mark. But the most reasonable assumption of all is that it has been intended as a space between words.
If this dot (.) has actually been used as a word space, then here is a weak point in Blair's cipher. And by taking advantage of this weakness it will be seen that the cipher can be solved with a minimum expenditure of time and effort.
Appended is a table of alphabetical frequencies, including that of the space between words. Thi s table is based on a count of twenty-five thousand letters and spaces of average English text, and shows die frequency per ten thousand of each character.
By pointing off two places the percentage of any character may be found without calculation. But it is well to note that all percentages so obtained will be somewhat lower than those in a table which takes no account of the space.
The average length of words in straight English text can readily be determined from this table by dividing 1856 (the frequency of the space) into 8144 (10000—1856). The quotient 4.39 results from this division, showing that in ordinary English the average length of words is, in round numbers, five letters.
Times found in
To return to the cipher, it will be observed from the above table that Blair's key, while apportioning the letters of the alphabet roughly according to their frequencies, has allowed but one substitute for the space.
In his dot writing we may therefore expect to find the particular combination of four dots that act as the substitute for this (.) occurring more frequently than any other, and at average intervals of twentyfour dots, or six characters.
It is easy to see, then, that a tabulation of the various dot combinations in the cipher, taken by fours, would at once reveal this particular arrangement. But it can be detected by a process even more superficial than this.
Dividing the dots into groups of four, and examining them carefully for repetitions, the combination. (or 3313, as we shall speak of it) immediately attracts attention because of its frequent recurrence at average intervals of six groups. From all of this it is thus safe to assume that 3313 is the substitute in cipher for this (.) or space between words.
Now the dots are placed in three positions, and the key consists of eighty-one characters (3x3x3x3—81). And it is clear that the horizontal and vertical cross lines of the latter are meant as an artificial aid in rapidly dividing and subdividing the diagram into thirds.
Having tentatively decided on the equivalent in cipher for one of the characters of the key, in order to discover Blair's principle, it is therefore only required to find what manipulations of the key by these four dots (3313) will produce the (.) as a result.
Comparatively few schemes will effect this. And of course the only correct one is that which will also produce sense in the cipher.
The true principle, thus determined, may be expressed by the following rules:
(1) the first dot of any group of four acting as a cipher substitute, selects the top, middle, or bottom rectangle of twenty-seven letters of the key, accordingly as that dot i s over, upon, or under the line;
(2) the second dot, in a similar manner, selects the top, middle, or bottom line of nine letters of that rectangle indicated by the first dot;
(3) the third dot, similarly, selects the left. middle, or right triplet of characters (as subdivided by the verticals) of that line indicated b y the first two dots; and,
(4) the fourth dot selects the left, middle, or right character of that triplet indicated b y the first three dots.
The application of this principle may be aptly illustrated by the following diagram in which it is shown how 3313 selects the (.) or space:
The principle upon which Blair laid so much stress is thus one of geometrical subdivision of the key, each group of four dots acting upon the diagram as a geometrical selector, dividing and subdividing it by thirds, until at the fourth division there only remains that single character for which the four dots are the cipher substitute. Here follows a partial translation of the dot writing, in which the figures 1, 2, and 3 have been substituted respectively for dots over, upon, and under the line:
Completely deciphered, the dot writing stands thus:
"THE ART OF WRITING IN CIPHER HAS BEEN STUDIED BY MEN OF THE GREATEST TALENTS AND RANK IN EVERY CIVILIZED COUNTRY."
A cipher like this is said to be multisubstitutional. For in this type a given substitute is used fixedly for the same letter of the alphabet, but one or more of the letters of the alphabet have more than one substitute in cipher.
A consideration of this definition will enable the reader to appreciate the difference between the e multisubstitutional and the unisubstitutional alphabets. The Augustus cipher in FLYNN'S for February 21 is an example of the latter.
Multisubstitutional ciphers were well known in Blair's time. And for this reason, notwithstanding his claim that his cipher "exhibits an entirely new plan of secret writing" in an alphabet "wholly unlike any other," he cannot be credited with the invention of a new kind of cipher. Hi s device is an ingenious method of accomplishing a cipher of an already known type, but no more.
Further, this kind of cipher had already been proved unsafe. He thus had no reason for supposing that his own cipher should be indecipherable.
Of course, this cipher could have been solved in any case, either if Blair had included more than one space, or none at all. Nevertheless, the fact remains that this oversight provided a speedier means of arriving at the principle involved.
Blair's error is even more serious than this, however, for his cipher as it stands is practically one in a multisubstitutional alphabet with normal word divisions. And, as you will discover later on, a multisubstitutional cipher is easier to solve without the key when the normal word divisions are retained than otherwise.
Having now summarily disposed of the dot writing, let's have a try next at the figure cipher. This was the second of the two Blair ciphers in FLYNN'S for July 25 beginning thus:
The first peculiarity discovered upon inspection of this cipher is that while the zeros (0) always divide the figures into groups evenly divisible by 2, these groups are not always evenly divisible by 4, or other even numbers.
The correct inference here is that the zeros are used to separate words, and that two figures in the cryptogram represent one letter of the message. From this it follows that two figures of the figure cipher are equivalent to four dots of the dot writing.
Now there are just nine combinations possible with two dots in three positions, and these taken in their numerical order and placed under the nine digits, arrange themselves as follows:
If these new values be now substituted for the figures of the cryptogram, it may be read exactly in the same manner as the dot writing:
While this specimen may thus be treated as a double cipher, it may also be deciphered more directly by an entirely different manipulation of the key.
Each pair of figures will indicate its letter directly from the key diagram if the first figure be made to refer to the row of letters—from 1 to 9—in the key, and the second figure to the particular letter—also from 1 to 9—in that row.
Thus 53 above, indicates 5th row, 3rd letter=A; 22 indicates 2nd row, 2nd letter=M; and so on with the rest. The results are exactly similar, even though the methods are different.
All of this demonstrates that Blair's ciphers were not as reliable as he thought. That he had implicit faith in his system, however, is shown by the following statement that accompanied his challenge.
"The inventor presumes to think," writes Blair, "that this contrivance is deserving the attention of ingenious men; and might be a very advantageous acquisition in the foreign Secretary of State's office; but, it would be incompatible with his—Blair's — feelings to submit any such proposal to the judgment of inferior clerks, who perhaps know nothing beyond the mechanical uses of ciphers, and are totally unqualified to appreciate the merits of a scientific invention. At present he has, therefore, not chosen to divulge the principle of this cipher to any person living. "
Blair supplied only five examples of secret writing with his challenge, but he said that he could have easily included "several hundred more varieties" to be likewise deciphered by the same key.
As one of these he suggested a triformed alphabet. And we have used this idea in constructing Cipher No. 1, below.
Possibly you can think of some ingenious variation of this cipher yourself.
If so, submit your idea. I t will be passed on to the fans if it is thought to be of general interest.
Here are two more Blair ciphers.
They illustrate still further applications of the same key.
CIPHER No. 1. Remember the bijormed alphabet in Sir Francis Bacon's biliteral cipher in Solving Cipher Secrets for April 25? Blair endeavors here to out-Bacon Bacon with a triformed alphabet.
The bearer of this message is a brave and courageous man, and a staunch friend of our common cause. He has highly important knowledge of certain secret enemy plans that he wishes to inform you of. Treat him with every considera tion.
When you have deciphered the above you will learn of the big surprise in store for the bearer early in the morning of that day following his delivery of the message.
CIPHER No. 2. If you decipher this one you will probably be willing to admit that it is nothing if not clever; yet not clever enough.
The solutions to these ciphers will be found in next Solving Cipher Secrets.
The selection of a few ciphers for this, section from the many excellent ones submitted by fans is no easy task.
The number of ciphers that can be included here is, of course, limited. That the one you may have submitted has not yet been published does not indicate that it will not be used.
Many of these ciphers involve principles which have not yet been explained in the main articles. And they are thus being held over until that time when they can be used to the best advantage of all concerned.
In the meantime, if another good idea should occur to you, don't hesitate to send it right along. It will be used at the earliest opportunity.
CIPHER No. 3.
Several neat specimens have been received from J. Levine, Long Beach, California. This one is easy if you know the secret.
3- 127 103 201 157, 22 69 172 213 49, 276 261 295, 248 163 14 56 203 3, 5 52 11 86 293 201 7 112, 13 32 78, 171 481 277 122 524 85 168, 432 289, 13 243 18, 104 508 265, 31 344 115 48 61 302 262 85 211 292, 452 378, 14 25 22, 44 11, 7 13 52, 41 32 5 18 37, 27 35 82 151 112 57 97 438, 14 71, 36 74 95 171 53, 537 335 296 33 502 445 481 922.
CIPHER No. 4.
Recall the Gronsfeld cipher in Solving Cipher Secrets for June 6?
The following example from Austin Minette, Clear Lake, Iowa, is of the same type, with the exception that Mr. Minette's is based on a forward count of any number up to 26, instead of but 9, as in the original Gronsfeld.
To illustrate, 17-3-25-11 could be the key to one of his ciphers. But not to this one.
ZAQYVWJXQYMIQXVLKWSMPKLBUKG, ZAMMBITMZGYB.CKQZMMTUGPNTKL DKKVK.MPOLIAMPUKEXHBKAQYUWU DAUOMXYQLMGEXIXLIMHENXVZAMS TRUKQZRWLMPKMPOGOYAMCKWZXI HHCZPMXXCTWZKTUKWWL.YZUFIYV QKGBOYQITVJBVZXZKLBOGOXXIJBV MIWOGBOVWTLQJXZNBUGGMDVMRE MTMIAMPUK.
CIPHER No. 5.
This cryptogram, in its form reminiscent of the cipher in Poe's Gold Bug—see FLYNN'S for May 16—is from Fred G. Knaus, 941 North Rendon Street, New Orleans, Louisiana.
,. ‡86:] ([ 96,.[ * .*†; .8 ,-5☞82[ ‖:4xx† (6. ‡£4 x8. ?[. ),5£[☞ ‖*x† .8 )8☞☞[†58x] ‡,.£ [*)£ 8.£[☞ 6†,x? ),5£[☞† 8‖ 2*☞,86† ;,x]†
CIPHER No. 6.
R. Hamilton, of New York, N. Y., fights with a two-edged blade. He heartily agrees with Poe's proposition that "human ingenuity cannot concoct a cipher which human ingenuity cannot resolve," but at the same time he submits the following cryptogram, together with its solution, and defies us to discover the method. How is it done?
EIEEOSNOAWTRTGTUDMMNODENLOL TYINPEIICUILHNIHMMSPTETACPESE ECSOCAURNAVNINNYSAAHTOKSAOEF MRAAAEMRHOIYRHCIHTTTUTCTEMCS SSNNOORNH.
"Socrates could not have put it more concisely. Man makes nothing which man cannot destroy. A cypher is the supreme test of a man's ingenuity. R. Hamilton."
How did he do it?
CIPHER No. 7.
The message hidden in this cryptogram from John O'Bryan, Baltimore, Maryland, came as a pleasant surprise.
We need not mention the type of this cipher. It's well known to you.
74-46-96-86-48-86-77-58-86-76-30-55-68-58- 86-67-30-87-68-28-86-77-66-58-96-59-76-95- 69-75-64-37-53-108-39-76-68-49-75-97-38- 58-85-26-84-78-30-87-64-59-86-76-30-78-95- 30-85-68-48-87-97-39-74-68.
How did you make out with the Nihilist ciphers in last Solving Cipher Secrets? Did the double ciphers baffle you?
These latter are especially interesting, demonstrating as they do, that it is perfectly feasible to determine the key to the unmodified Nihilist cipher even when both the key and enciphered text are but mere jumbles of letters.
Here are the solutions to the several specimens in FLYNN'S for July 25:
CIPHER No. 3.
Submitted by Paul M. Conroe, San Diego, California. Key; CONROE. Message: " I have been a FLYNN fan since last December, and, believe me, FLYNN'S can't be beaten. You have invited readers to send in a Nihilist cryptogram, and say that you will decipher it without the key word. I've taken the liberty of combining it with a very simple code previously published in FLYNN'S."
In other words, Mr. Conroe first enciphered his message in Augustus cipher, described in FLYNN'S for February 21, and then enciphered the result in Nihilist cipher using his own surname as the key word.
CIPHER No. 4.
Submitted by Harry Roberts, New York City. Key: XNYHPS. Message: "It took me an hour to solve your cryptogram. How long did it take you to solve mine? "
Mr. Roberts first took the letters of his message in reverse order, and then alternated the true letters with nulls. He then enciphered the result in Nihilist cipher using the key XNYHPS, which you will note is nothing but SPHYNX written backward.
CIPHER No. 5.
Submitted by C. M. Eddy, Jr., Providence, Rhode Island. Key: EXTEMPORANEOUS, Message: "I chose a long key word on the theory that it made solution more difficult. Am I correct?"
Mr. Eddy's cipher used the longest key word of any of its type submitted. His supposition that the difficulty in solving this kind of cipher increases with the length of the key word is in the main correct.
In general almost any cipher of this type becomes more difficult to solve as the length of the key increases, and as that of the message decreases.
It had been intended to include with this article the answers to a number of interesting inquiries from cipher enthusiasts. On account of lack of space, however, we regret that these will have to be held over until the next installment of this department.