ABCDEFGHaaaaaaaaabaaabaaaabbaabaaaababaabbaaabbbIKLMNOPQabaaaabaabababaababbabbaaabbababbbaabbbbRSTVWXYZbaaaabaaabbaababaabbbabaabababbabbababbb
“Nor is it a slight thing which is thus by the way effected. For heare we see how thoughts may be communicated at any distance of place by means of any objects perceptible either to the eye or ear, provided only that those objects are capable of two differences; as bybells, trumpets, torches, gunshots, and the like. But to proceed with our business. When you prepare to write, you must reduce the interior epistle to this bi-literal alphabet. Let the interior epistle be:
Fly.Example of reduction.FLYaababababababba
“Have by you at the same time another alphabet in two forms; I mean in which each of the letters of the common alphabet, both capitals and small, are exhibited in two different forms,—any forms that you find convenient.”
[For instance, Roman and Italic letters; “a” representing Roman and “b” representing Italic.]
“Then take your interior epistle, reduced to the bi-literal shape, and adapt it, letter by letter, to your exterior epistle in the biform character; and then write it out. Let the exterior epistle be:
“Do not go till I come.”Example of reductionFLYaababababababbaDONOTGOTILLICOM—Edo notgo tillI come
From the above given dates it would almost seem as if Bacon had treated the matter in a purely academic manner, and had drawn out of his remembrance of his younger days a method of secret communication which had not seen any practical service. Spedding mentions in his book “Francis Bacon and his Times” that Bacon may have got the hint of the ‘bi-literal cypher’ from the work of John Baptist Porta, “De occultis literarum notis,” reprintedin Strasburg in 1606, but the first edition of which was published when Porta was a young man. It is however manifest from certain evidence, that Bacon practised his special cipher and used it for many years. Lady Bacon, mother of the philosopher, writing in 1593, to her son Anthony, elder brother of Francis, speaking of him, Francis, says, “I do not understand his enigmatical folded writing.” Indeed it is possible that many years before he had tried to have his invention made use of for public service. His was an age of secret writing. Every Ambassador had to send his despatches in cipher, for thus—and even then not always—could they be safe from hostile eyes. The thousands of pages of reports to King Philip made by Don Bernardino de Mendoza, the Spanish Ambassador at the Court of Queen Elizabeth, before the time of the Armada, were all written in this form; the groaning shelves of the records at Simancas bear evidence of the industry of such political officials and of their spies and secretaries. An ambitious youth like Francis Bacon, son of the Lord Keeper, and so traditionally and familiarly in touch with Court and Council, who in his baby days was addressed by Elizabeth as her “young Lord Keeper,” and who spent the time between his sixteenth and eighteenth years in the suite of the English Ambassador in Paris, Sir Amyas Paulet, must have had constant experience of the need of a cipher which would fulfill the conditions which he laid down as essential in 1605—facility of execution, impossibility of discovery, and lack of suspiciousness. When, in a letter of 16 Sept. 1580, to his uncle Lord Burghley, he made suit to the Queen for some special employment, it is possible that the post he sought was that of secret writer to Her Majesty. His letter, though followed up with a more pressing one on 18th October of the same year, remained unanswered. Whatever the motive or purpose of these last two letters may have been, it remained on his mind; for eleven years laterwe find him again writing to his uncle the Lord Keeper: “I ever have a mind to serve Her Majesty,” and again, “the meanness of my estate doth somewhat move me.” In the interval, on 25th August, 1585, he wrote to the Right Hon. Sir Francis Walsingham, Principal Secretary to the Queen: “In default of getting it, will go back to course of practice (at Bar) I must and will follow, not for my necessity of estate but for my credit’s sake, which I fear by being out of action will wear.” His brother Anthony spent the best part of his life abroad, presumably on some secret missions; and as Francis was the recipient of his letters it was doubtless that “folded writing” which so puzzled their mother which was used for the safety and secrecy of their correspondence. Indeed to what a fine point the biliteral method must have been brought by Bacon and his correspondents is shown by the extraordinarily minute differences given in his own setting forth of the symbols for “a” and “b” etc., in the “De Augmentis” of 1623 and later. In the edition printed in Latin in Paris the next year, 1624, by Peter Mettayer, the differences, possibly through some imperfection of printing, are so minute that even the reader studying the characters set before him, with the extra elucidation of their being placed under their proper headings, finds it almost impossible to understand them. The cutting for instance of the “n” which represents “a” and that which represents “b” seems, even after prolonged study, to be the same.
It is to be noticed that Bacon in setting forth the cipher in its completeness directs attention to its infinite possibilities and variations. The organised repetition of any two symbols in combinations of not more than five for one or both symbols may convey ideas. Not letters only but colours, bells, cannon, or other sounds may be used with effect. All the senses may be employed, or any or some of them, in endless combinations.
Again it is to be noted that even in his first allusion to the system in 1605, he says, “to write Omnia per Omnia, which is undoubtedly possible, with a proportionQuintuple at most, of the writing infoulding, to the writing infoulded.”
“Quintuple at most!” But in the instances of his system which he gives eighteen years later, when probably his time for secret writing as a matter of business had ceased, and when from the lofty altitude of the Woolsack he could behold unmoved any who had concealments to make—provided of course that they were not connected with bribes—there is only one method given, that of five infolding letters for each one infolded. In the later and fuller period he speaks also of the one necessary condition “that the infoulding writing shall containat least five times as many lettersas the writing infoulded”—
Even in the example which he gives “Do not go till I come,” there is a superfluous letter,—the final “e;” as though he wished to mislead the reader by inference as well as by direct statement.
Is it possible that he stopped short in his completion of this marvellous cipher? Can we believe that he who openly spoke from the first of symbols “quintuple at most,” was content to use so large a number of infolding letters when he could possibly do with less? Why, the last condition of excellence in a cipher which he himself laid down, namely, that it should “bee without suspicion,” would be endangered by a larger number than was actually necessary. It is by repetition of symbols that the discovery of secret writing is made; and in a cipher where, manifestly, the eye or the ear or the touch or the taste must be guided by such, and so marked and prolonged, symbols, the chances of discovery are enormously increased. Doubtless, then, he did not rest in his investigation and invention until he had brought his cipher to its least dimensions; and it was forsome other reason or purpose that he thus tried to divert the mind of the student from his earlier suggestion. It will probably be proved hereafter that more than one variant and reduction to lower dimensions of his biliteral cipher was used between himself and his friends. When the secrets of that “Scrivenry” which, according to Mr. W. G. Thorpe in his interesting volume, “The Hidden Lives of Shakespeare and Bacon,” Bacon kept at work in Twickenham Park, are made known, we shall doubtless know more on the subject. Of one point, however, we may rest assured, that Bacon did not go back in his pursuance of an interesting study; and the change from “Quintuple at most” of the infolding writing of 1605, to “Quintuple at least,” of 1623, was meant for some purpose of misleading or obscuration, rather than as a limitation of his original setting forth of the powers and possibilities of his great invention. It will some day be an interesting theme of speculation and study what use of his biliteral cipher had been made between 1605 and 1623; and what it was that he wished to conceal.
That the original cipher, as given, can be so reduced is manifest. Of the Quintuple biliteral there are thirty-two combinations. As in the Elizabethan alphabet, as Bacon himself points out, there were but twenty-four letters, certain possibilities of reduction at once unfold themselves, since at the very outset one entire fourth of the symbols are unused.
ON THE REDUCTION OF THE NUMBER OF SYMBOLS IN BACON’S BILITERAL CIPHER
WhenI examined the scripts together, both that of the numbers and those of the dots, I found distinct repetitions of groups of symbols; but no combinations sufficiently recurrent to allow me to deal with them as entities. In the number cipher the class of repetitions seemed more marked. This may have been, however, that as the symbols were simpler and of a kind with which I was more familiar, the traces or surmises were easier to follow. It gave me hope to find that there was something in common between the two methods. It might be, indeed, that both writings were but variants of the same system. Unconsciously I gave my attention to the simpler form—the numbers—and for a long weary time went over them forward, backward, up and down, adding, subtracting, multiplying, dividing; but without any favorable result. The only encouragement which I got was that I got additions of eight and nine, each of these many times repeated. Try how I would, however, I could not scheme out of them any coherent result.
When in desperation I returned to the dotted papers I found that this method was still more exasperating, for on a close study of them I could not fail to see that there was a cipher manifest; though what it was, or how it could be read, seemed impossible to me. Most of the letters had marks in or about them; indeed there werevery few which had not. Examining more closely still I found that the dots were disposed in three different ways: (a) in the body of the letter itself: (b) above the letter: (c) below it. There was never more than one mark in the body of the letter; but those above or below were sometimes single and sometimes double. Some letters had only the dot in the body; and others, whether marked on the body or not, had no dots either above or below. Thus there was every form and circumstance of marking within these three categories. The only thing which my instinct seemed to impress upon me continually was that very few of the letters had marks both above and below. In such cases two were above and one below, orvice versa; but in no case were there marks in the body and above and below also. At last I came to the conclusion that I had better, for the time, abandon attempting to decipher; and try to construct a cipher on the lines of Bacon’s Biliteral—one which would ultimately accord in some way with the external conditions of either, or both, of those before me.
But Bacon’s Biliteral as set forth in theNovum Organumhad five symbols in every case. As there were here no repetitions of five, I set myself to the task of reducing Bacon’s system to a lower number of symbols—a task which in my original memorandum I had held capable of accomplishment.
For hours I tried various means of reduction, each time getting a little nearer to the ultimate simplicity; till at last I felt that I had mastered the principle.
Take the Baconian biliteral cipher as he himself gives it and knock out repetitions of four or five aaaaa: aaaab: abbbb: baaaa: bbbba: and bbbbb. This would leave a complete alphabet with two extra symbols for use as stops, repeats, capitals, etc. This method of deletion, however, would not allow of the reduction of the number of symbolsused; there would still be required five for each letter to be infolded. We have therefore to try another process of reduction, that affecting the variety of symbols without reference to the number of times, up to five, which each one is repeated.
Take therefore the Baconian Biliteral and place opposite to each item the number of symbols required. The first, (aaaaa) requires but one symbol “a,” the second, (aaaab) two, “a” and “b;” the third (aaaba) three, “a” “b” and “a;” and so on. We shall thus find that the 11th (ababa) and the 22nd (babab) require five each, and that the 6th, 10th, 12th, 14th, 19th, 21st, 23rd and 27th require four each. If, therefore, we delete all these biliteral combinations which require four or five symbols each—ten in all—we have still left twenty-two combinations, necessitating at most not more than two changes of symbol in addition to the initial letter of each, requiring up to five quantities of the same symbol. Fit these to the alphabet; and the scheme of cipher is complete.
If, therefore, we can devise any means of expressing, in conjunction with each symbol, a certain number of repeats up to five; and if we can, for practical purposes, reduce our alphabet to twenty-two letters, we can at once reduce the biliteral cipher to three instead of five symbols.
The latter is easy enough, for certain letters are so infrequently used that they may well be grouped in twos. Take “X” and “Z” for instance. In modern printing in English where the letter “e” is employed seventy times, “x” is only used three times, and “z” twice. Again, “k” is only used six times, and “q” only three times. Therefore we may very well group together “k” and “q,” and “x” and “z.” The lessening of the Elizabethan alphabet thus effected would leave but twenty-two letters, the same number as the combinations of the biliteral remaining after the elision. And further, as “W”is but “V” repeated, we could keep a special symbol to represent the repetition of this or any other letter, whether the same be in the body of a word, or if it be the last of one word and the first of that which follows. Thus we give a greater elasticity to the cipher and so minimise the chance of discovery.
As to the expression of numerical values applied to each of the symbols “a” and “b” of the biliteral cipher as above modified, such is simplicity itself in a number cipher. As there are two symbols to be represented and five values to each—four in addition to the initial—take the numerals, one to ten—which latter, of course, could be represented by 0. Let the odd numbers according to their values stand for “a”:
a=1aa=3aaa=5aaaa=7aaaaa=9
a=1aa=3aaa=5aaaa=7aaaaa=9
and the even numbers according to their values stand for “b”:
b=2bb=4bbb=6bbbb=8bbbbb=0
b=2bb=4bbb=6bbbb=8bbbbb=0
and then? Eureka! We have a Biliteral Cipher in which each letter is represented by one, two, or three, numbers; and so the five symbols of the Baconian Biliteral is reduced to three at maximum.
Variants of this scheme can of course, with a little ingenuity, be easily reconstructed.
THE RESOLVING OF BACON’S BILITERAL REDUCED TO THREE SYMBOLS IN A NUMBER CIPHER
Placein their relative order as appearing in the original arrangement the selected symbols of the Biliteral:
a a a a aa a a a b&c
Then place opposite each the number arrived at by the application of odd and even figures to represent the numerical values of the symbols “a” and “b.”
Thus aaaaawill be as shown9aaaabwill be as shown72aaabawill be as shown521
and so on. Then put in sequence of numerical value. We shall then have: 0. 9. 18. 27. 36. 45. 54. 63. 72. 81. 125. 143. 161. 216. 234. 252. 323. 341. 414. 432. 521. 612. An analysis shows that of these there are two of one figure; eight of two figures; and twelve of three figures. Now as regards the latter series—the symbols composed of three figures—we will find that if we add together the component figures of each of those which begins and ends with an even number they will tot up to nine; but that the total of each of those commencingand ending with an odd number only total up to eight. There are no two of these symbols which clash with one another so as to cause confusion.
To fit the alphabet to this cipher the simplest plan is to reserve one symbol (the first—“0”) to represent the repetition of a foregoing letter. This would not only enlarge possibilities of writing, but would help to baffle inquiry. There is a distinct purpose in choosing “0” as the symbol of repetition for it can best be spared; it would invite curiosity to begin a number cipher with “0,” were it in use in any combination of figures representing a letter.
Keep all the other numbers and combinations of numbers for purely alphabetical use. Then take the next five—9 to 45 to represent the vowels. The rest of the alphabet can follow in regular sequence, using up of the triple combinations, first those beginning and ending with even numbers and which tot up to nine, and when these have been exhausted, the others, those beginning and ending with odd numbers and which tot up to eight, in their own sequence.
If this plan be adopted, any letter of a word can be translated into numbers which are easily distinguishable, and whose sequence can be seemingly altered, so as to baffle inquisitive eyes, by the addition of any other numbers placed anywhere throughout the cipher. All of these added numbers can easily be discovered and eliminated by the scribe who undertakes the work of decipheration, by means of the additions of odd or even numbers, or by reference to his key. The whole cipher is so rationally exact that any one who knows the principle can make a key in a few minutes.
As I had gone on with my work I was much cheered by certain resemblances or coincidences which presented themselves, linking my new construction with the existingcipher. When I hit upon the values of additions of eight and nine as the component elements of some of the symbols, I felt sure that I was now on the right track. At the completion of my work I was exultant for I felt satisfied in believing that the game was now in my own hands.
ON THE APPLICATION OF THE NUMBER CIPHER TO THE DOTTED PRINTING
Theproblem which I now put before myself was to make dots in a printed book in which I could repeat accurately and simply the setting forth of the biliteral cipher. I had, of course, a clue or guiding principle in the combinations of numbers with the symbols of “a” and “b” as representing the Alphabetical symbols. Thus it was easy to arrange that “a” should be represented by a letter untouched and “b” by one with a mark. This mark might be made at any point of the letter. Here I referred to the cipher itself and found that though some letters were marked with a dot in the centre or body of the letter, those both above and below wherever they occurred showed some kind of organised use. “Why not,” said I to myself, “use the body for the difference between “a” and “b;” and the top and bottom for numbers?”
No sooner said than done. I began at once to devise various ways of representing numbers by marks or dots at top and bottom. Finally I fixed, as being the most simple, on the following:
Only four numbers—2, 3, 4, 5—are required to make the number of times each letter of the symbol is repeated, there being in the original Baconian cipher, after the elimination of the ten variations already made, only three changes of symbol to represent any letter. Marks at the top might therefore represent the even numbers“2” and “4”—one mark standing for “two” and two marks for “four”; marks at the bottom would represent the odd numbers “3” and “5”—one mark standing for “three” and two marks for “five.”
Thus “a a a a a” would be represented by “̤a” or any other letter with two dots below: “a a a a b” by ä b, or any other letters similarly treated. As any letter left plain would represent “a” and any letter dotted in the body would represent “b” the cipher is complete for application to any printed or written matter. As in the number cipher, the repetition of a letter could be represented by a symbol which in this variant would be the same as the symbol for ten or “0.” It would be any letter with one dot in the body and two under it, thus—̤t.
For the purpose of adding to the difficulty of discovery, where two marks were given either above or below the letter, the body mark (representing the letter as “b” in the Biliteral) might be placed at the opposite end. This would create no confusion in the mind of an advised decipherer, but would puzzle the curious.
On the above basis I completed my key and set to my work of deciphering with a jubilant heart; for I felt that so soon as I should have adjusted any variations between the systems of the old writer and my own, work only was required to ultimately master the secret.
The following tables will illustrate the making and working—both in ciphering and de-ciphering—of the amended Biliteral Cipher of Francis Bacon:
P (Plain) means letter left untouchedD (Dot) means letter with dot in bodyOne Dot—(.) at Top (t) = 2One Dot—(.) at Bottom (b) = 3Two Dots—(..) at Top (t) = 4Two Dots—(..) at Bottom (b) = 5
Bacon Cipher.No. of Symbols RequiredNumber Cipher.Alphabet to be arranged in order.Dot CipherNo. Values of Symbols reported.A — 1— a a a a a— 1 —9— A— P..bB — 2— a a a a b— 2 —7.2— D— P..t — DC — 3— a a a b a— 3 —5.2.1— Y— P .b — D — PD — 4— a a a b b— 2 —5.4— B— P .b — D.tE — 5— a a b a a— 3 —3.2.3— T— P .t — D — P.tF — 6— a a b a b— 4 —3.2.1.2G — 7— a a b b a— 3 —3.4.1— X.Z.— P .t — D.t — PH — 8— a a b b b— 2 —3.6— O— P .t — D.bI — 9— a b a a a— 3 —1.2.5— P— P — D — P.bK — 10— a b a a b— 4 —1.3.3.2L — 11— a b a b a— 5 —1.2.1.2.1M — 12— a b a b b— 4 —1.2.1.4N — 13— a b b a a— 3 —1.4.3— R— P — D .t — P.tO — 14— a b b a b— 4 —1.4.1.2P — 15— a b b b a— 3 —1.6.1— S— P — D .b — PQ — 16— a b b b b— 2 —1.8— E— P — D..tR — 17— b a a a a— 2 —2.7— I— D — P..tS — 18— b a a a b— 3 —2.5.2— K.Q.— D — P .b — DT — 19— b a a b a— 4 —2.3.2.1V — 20— b a a b b— 3 —2.3.4— H— D — P .t — D.tW — 21— b a b a a— 4 —2.1.2.3X — 22— b a b a b— 5 —2.1.2.1.2Y — 23— b a b b a— 4 —2.1.4.1Z — 24— b a b b b— 3 —2.1.6— G— D — P — D.b25— b b a a a— 2 —4.5— U.V.— D .t — P.b26— b b a a b— 3 —4.3.2— M— D .t — P.t — D27— b b a b a— 4 —4.1.2.128— b b a b b— 3 —4.1.4— L— D .t — P — D.t29— b b b a a— 2 —6.3— C— D .b — P.t30— b b b a b— 3 —6.1.2— N— D .b — P — D31— b b b b a— 2 —8.1— F— D..t — P32— b b b b b— 1 —9— Repeat— D..b
Note.—When there are to be two dots at either top or bottom of a letter, the dot usually put in the body of a letter which is to indicate “b” can be placed at the opposite end of the letter to the double dotting. This will help to baffle investigation without puzzling the skilled interpreter.
Divide off into additions of nine or eight. Thus if extraneous figures have been inserted, they can be detected and deleted.
Cipher.De-Cipher.A=9O=Repeat LetterB=54125=PC=63143=RD=72161=SE=1818=EF=81216=GG=216234=HH=234252=K or QI=2727=IK.Q=252323=TL=414341=X or ZM=43236=ON=612414=LO=36432=MP=12545=U or VR=143521=YS=16154=BT=323612=NU.V=4563=CX.Z=34172=DY=52181=FRepeat=O9=A
Finger Cipher.Values the same as Number Cipher.TheRIGHThand, beginning at the thumb, represent theODDnumbers,TheLEFThand, beginning at the thumb, represent theEVENnumbers.
Values the same as Number Cipher.
TheRIGHThand, beginning at the thumb, represent theODDnumbers,
TheLEFThand, beginning at the thumb, represent theEVENnumbers.
Hands
P—Letter left plain..—Dot.D—Dot in centre or where are two dots t or b in other end (b or t).t—top of letter.b—bottom of letter.
Cipher.De-Cipher.A=P.. bP——D——P. b=PB=P. b—D. tP——D. t—P. t=RC=D. b—P. tP——D.. t——=ED=P.. t—DP——D. b—P—=SE=P—D.. tP. t—D——P. t=TF=D.. t—PP. t—D. t—P—=X or ZG=D—P—D. bP. t—D. b——=OH=D—P. t—D. tP.. t—D———=DI=D—P.. tP. b—D——P=YK.Q=D—P. b—DP. b—D. t——=BL=D. t—P—D. tP.. b—————=AM=D. t—P. t—DD——P——D. b=GN=D. b—P—DD——P. t—D. t=HO=P. t—D. bD——P.. t——=IP=P—D—P. bD——P. b—D—=K or QR=P—D. t—P. tD. t—P——D. t=LS=P—D. b—PD. t—P. t—D—=MT=P. t—D—P. tD. t—P. b——=U or VU.V=D. t—P. bD.. t—P———=FX.Z=P. t—D. t—PD. b—P——D—=NY=P. b—D—PD. b—P. t——=CRepeat=D.. b(W=U repeated)D.. b——=Repeat (W)