Chapter 11

Analysis

                
Make me to see't: or (at the least) so proue it, That the probation beare no Hindge, nor Loope To hang a doubt on: Or woe vpon thy life. --Othello, Act iii, Scene 3.

Is this a genuine cipher?

The epigraph above faces the title-page of the Friedman's book. At the end of their first chapter they say:

"To be convinced that the authenticity of a literary idol could never be impugned even by a genuine cipher is an 
arbitrary attitude, and we do not share it. The question is: has a genuine cipher been found?" [@]

If a claim is made for a "genuine" cipher discovery, how must it be demonstrated?

The Friedmans were not sympathetic toward any Shakespearean cipher that they had examined but they did, most 
charitably and carefully, explain how to prove one to be authentic. In their second chapter, entitled "Cryptology as a 
Science," they defined the rules for a substitution cipher. The rules must be followed "even where a cipher message 
is written for posterity. . .there must be a direct and rigid relationship between the plain message and the cryptic 
version. . .the procedure must admit no doubts."

We can be convinced of the validity of a substitution cipher only by discovering such rules and applying them. One 
rule will concern the general system; another will follow the general system, but in specific ways: there may be 
specific keys to deal with such variable elements. As the Friedmans say:

"Usually the rules are of two kinds. The first lays down a basic general procedure (e.g. each cipher unit is formed of 
one letter of the English alphabet, and each such letter corresponds to one and only one unit in the plain text); 
technically, these rules are said to belong to the general system . . ." The second kind is more specific. It operates 
within the general system, and deals with its application in a particular cryptogram (e.g. in this cipher, Z 
corresponds to the letter A in plain text; N to the letter B, etc.) In technical jargon it constitutes the specific key  
which deals with the variable elements . This is quite a familiar distinction: bridge players, for example, are well 
aware of the difference between the laws of the game (which lay down the general procedure) and the rules 
governing a particular convention of bidding (which sets out one specific way of acting in accordance with the laws.)"

With this in mind, we should read again the twenty-five letters of the ciphertext contained in the title-page and the 
Dedication page of the Sonnets .

S S R D T N Y G D T T M Y A F I O E E R F E G S R

They are still meaningless because the letters of this cryptogram have previously been concealed as an acrostic 
steganogram and then doubly enciphered. First, the primarily significant letters  are scattered through the open text 
according to a general rule: these are the terminal, the very last letters of each capitalized word, and a capitalized 
letter standing alone is counted as a word; the numbers are treated separately. Such acrostics have been called "null 
ciphers" because ordinarily all of the letters in each word, except one, are nulls.
The second encipherment is accomplished by the use of a key alphabet having twenty-one letters in normal order 
but ending in "STVY."

A B C D E F G H I K L M N O P Q R S T V Y

The third encipherment is done in Caesar's fashion by displacing the key alphabet four letters, so that a ciphertext 
"E" equals a plaintext "a", a ciphertext "F" equals a plaintext "b", and so on, without exception. The cryptographer, 
within his unique alphabet, has substituted the fourth letter back from each ciphertext letter -- we must move 
backward four characters. However the numbers have undergone an additional encipherment before being 
submitted to this rule; they have been assigned to the alphabet in the most elementary fashion: 1 = "A", 2 = "B", 3 = 
"C" and so on. The numbers "1609" must be converted to "AFI", which correspond to the numbers "169". Since there 
is no letter corresponding to zero, it may be excluded. These rules apply from the beginning ("SHAKE-SPEARES") to 
the putative end, the lower-case superscripted "r" in "Mr."

The additional step in deciphering the numbers should not be criticized. Bacon himself stated that to use "changes," 
"nulls," "doubles" and "non-significant" letters was an acceptable procedure within his own apprehension of 
sophisticated 17th century cryptography. The Friedmans say (@ p. 62), "To change the alphabet on a given signal is a 
perfectly normal practice in cipher messages."

It is normal because it is not uncommon for the cryptographer to try to defeat cryptanalysis. In our own cipher 
problem, after the first twelve ciphertext letters are decrypted, we run into four numbers which represent the date of 
publication of the Sonnets -- "1609". What is to be done with them? Omitting them as nulls, which is permissible in 
cryptanalysis, there remains in the plaintext the two zeros and the words "nypir" and "cypphr," but deleting the 
converted numbers (169=AFI) leaves "kaanbacon" dangling. Including them in the ciphertext, of course, completes 
the plaintext message and matches "bekaan" to the adjoining "bacon," our "probable word" crib. We need not change 
the general rule, the twenty-one letter keyed alphabet, to incorporate these digits in their proper order and they are 
submitted to the same Caesar, fourth letter back, system as are the ciphertext letters. The "given signal," to which the 
Friedmans refer, is obvious enough; after twelve ciphertext letters the numbers are encountered. To omit them 
would create a gap in the serial regularity of the general system.

On at least one occasion Francis Bacon openly used a number to substitute for some of the letters in a word. The 
Folger Shakespeare Library has on file (x.d.158) a letter of his written on October 18, 1623. Here is how he dates it: 
"18. of 8 bre 1623". "Octo" (as in "8") is the Latin word for the Roman numeral VIII. (See photo illustration).

[Graies Jnne this / 18. of 8bre 1623]

So, after the numbers "1609" are admitted to the chain, the general and specific cipher structure continues as before. 
We will recall that the first twenty-five ciphertext letters were:

S S R D T N Y G D T T M Y A F I O E E R F E G S R

A view of the critical letters of the title-page and Dedication will, perhaps, be welcome (see photo illustration). The 
ciphertext letters are bold:

                                                                            SHAKE-SPEARES

                                                                                  SONNETS.

                                                                       Neuer before Imprinted.
                                                                         ___________________
                                                                         ___________________

                                                                               AT LONDON
                                                                      By G. Eld for T.T. and are
                                                                  to be solde by William Aspley .
                                                                                       1609.

                                                                  TO.THE.ONLIE.BEGETTER.OF.
                                                                    THESE.INSVING.SONNETS.
                                                                     Mr.W.H. ALL.HAPPINESSE.

The deciphered plaintext is:

o o n y p i r c y p p h r s b e k a a n b a c o n

According to William F. and Elizebeth S. Friedman:

"The cryptogram must be keyed and of a reasonable length before it is safe to assume that it has a unique solution. . .
about twenty-five letters are needed before the cryptanalyst can be sure that his solution of a mono-alphabetic 
substitution cipher is the only possible solution [citing Shannon]."

We have our twenty-five letters in this solution to a mono-alphabetic substitution cipher.
The Friedmans then apply the principles of probability and chance:

"The point must be reached where he (the cryptologist) begins to feel that the whole thing did not and could not 
happen by accident. . .If the cryptanalyst finds a certain key and (on the basis of the way it is built up) he calculates 
that the chances of its appearing by accident are one in one thousand million, his confidence in the solution will be 
more than justified. . ."

What are the odds against finding these twenty-five particular  letters in this exact  order? The elementary 
probabilities are against it by twenty-one (being the number of letters in the abbreviated alphabet) to the 25th power 
(being the number of letters in the message). This is a very large number. The odds are unfavorable to the extent of 
1.136 billion trillion trillion to one. I am aware that in the science of probability and statistics, this basic figure must 
be reduced, depending upon what other postulates and variables may reasonably be chosen to represent some 
particular form and vocabulary of Elizabethan philology; but not to such a degree that these twenty-five letters may 
be regarded as an ordinary phenomenon. This series is not a solitary prototype; the pattern will be found to repeat 
itself in many other empirical examples, and each of them must be looked upon as a pragmatic confirmation of the 
others. (For serious students of probability and statistics, see Elementary Course in Probability for the Cryptanalyst , 
Andrew M. Gleason, Aegean Park Press, revised 1985).

Two cryptanalysts, the Friedmans say, while working independently must always be able to find a nearly identical 
solution. If the rules defined here are followed, there can be no other solution. They also say that some concession 
may be made for the encipherer's  mistakes:

"In practice, one has to make allowances for a few mistakes here and there; and certainly, occasional errors may lead 
to minor differences in the solutions offered by different cryptanalysts working independently. . .each case must be 
treated on its merits, but in practice the allowable error is seldom more than five to ten percent at the outside."

However, we need not here make such an allowance; it does not appear that any mistakes have been made in the 
planning and composition of this particular twenty-five letter cryptogram.

There is an interesting requirement that the Friedmans do not  impose. "Nor is it reasonable to expect," they declare, 
"that, if cryptic messages actually were inserted in the text, they would be clearly signaled in some way. . .We shall 
not therefore demand any external guide to the presence of the secret texts. . ." If the decryption is shown to be 
unique and reached "by valid means we shall accept it, however much we shock the learned world by doing so."
The Friedmans do not offer any extra credibility points if there might be found, in the open text, a signal (a "beacon" 
we might call it) pointing to the existence of a concealed cipher. Neither do they offer any reward for the discovery 
of instructions for its solution. Yet in the Dedication to the Sonnets  there are such signals and there are such 
instructions.

The obvious signals are thirty: thirty (I shall call them) decimal points. Where else are such points, periods, full 
stops, or whatever to be found in the printing of literature in 17th century England or in any age? They are 
uncommon to the point of distinction. They arrest the attention; they have, historically, caused curious comment. 
Their insertion follows no known rule of punctuation. And why is the whole Dedication set in capitals (except for 
that lonely, superscripted "r")? And why are the lines so unevenly filled, with five words standing alone? And how 
did the bad grammar get past the proofreader?

The structure of the language of the Dedication has the same aspect: nobody really knows what it means in spite of 
the many opinions that have been offered. It just doesn't make much sense. Having come this far, we can now 
understand that the first nine words of the Dedication had to be chosen so that their terminal letters would fit the 
ciphertext. The last letter of each word had to be a particular letter. With this exacting constraint, it is not surprising 
that the Dedication verges upon nonsense. The very incoherence of the text is a weathercock pointing to a secret.

By contrast, the title-page of the Sonnets is a model of conformity to Elizabethan typographic form. Though it seems 
above suspicion, it masks a prodigious example of the steganographer's art. Its very antithesis highlights the 
strangeness of the next page, the nearly impenetrable Dedication.

As I have exemplified them, these are the signals  which have for so long been the subject of scholarly discussion, yet 
their latent significance has been overlooked. And there is more; there are instructions  for the decipherer set forth in 
the Dedication.

As has been mentioned, a short ciphertext presents great difficulty in cryptanalysis. Ordinary methods, such as 
determining letter frequency, are of no use. In brief modern cipher messages the key, also encrypted, must be 
inserted somewhere. It may be entered at the beginning or at the end and such messages are kept short so as to 
defeat cryptanalysis. Bacon understood this principle, yet he did not intend to forever silence some whisper from his 
grave. He included a few words of advice in his cryptograms.

As previously narrated, before beginning my recent work I had stumbled upon the enciphered name of Bacon in the 
last letter of the last five of the first nine words of the Dedication. It was extracted by means of the Caesar cipher 
system, even while using the conventional twenty-four letter, 17th Century English alphabet. I suspected that this 
name might be a crib which could be employed to extend my search. I could not bear to abandon this "general 
system," even though the results were meager, so I began to think about a different alphabet. I have described the 
kinds of abbreviated alphabets that I tried and, while in the midst of this seemingly endless job, I looked at the 
Dedication again.

Simple arithmetic and difficult cryptography are still brothers, and each must depend upon the other. At the very 
beginning  of this devious Dedication are the words "TO.THE.ONLIE." At the very end  is the word "FORTH." These 
are words related to numbers . "TO." obviously may refer to "two"; at least it is a homonym. "ONLIE." may refer to 
"one." And "FORTH." is a homonym of "fourth."

We have seen that in the Sixteenth Century spelling was in its infancy; spelling was more of a habit with the writer 
than an object of criticism for his reader or editor. There were no standards; sounding out the letters was sufficient 
for the contemporary reader to communicate with the writer. But for Shakespeare, his 1609 spelling of "ONLIE." was 
a singular one. Formerly he had spelled it "onely." For example, in 1596, in "The Merchant of Venice," (iv,1) we read, 
"I will have nothing else but onely  this." In the 1598 version of "The Merry Wives of Windsor" (iii, 2) a character 
says, "Spend all I have onely  give me so much of your time in exchange. . ." In the 1602 "Hamlet" (iv, 2) appeared 
this phrase: "Your onely  ligge-maker." In the Sonnets  themselves (141, line 13) the author uses "Onely" and again (1, 
line 10) "only." But, in the Sonnet Dedication, the inconvenient last letter, "y", would not do. It had to be an "E" to 
enfold the ciphertext properly. Therefore he spelled it "ONLIE."

So I had found a 2 and a 1 and a 4th. 2 + 1 = 3 or, perhaps a little less obviously, twenty-one. What if this was a 
lesson -- to knock three letters off the twenty-four letter alphabet? As it turned out, it was such an instruction and 
that saved me much labor.

After this possibility appeared, I concentrated on twenty-one letter alphabets, testing by omitting three likely letters 
at a time. Eliminating the need for trying alphabets having more, or perhaps fewer, letters probably saved me from 
giving up, even with my speedy, time-and-paper-saving computer program.

Since I had been inspecting all possible solutions of the Caesar cipher, using a variable twenty-one letter alphabet, 
the last instruction, "FORTH.", was not really necessary. Yet it proved to be a confirmation. When the plaintext 
solution appeared on the screen, it was on the fourth line. It was where it should have been. It was where Francis 
Bacon had put it, after counting backward four places to the fourth letter of his keyed alphabet.

The numbers, then, are  instructions. They were inserted in the doggerel of the Dedication as helpful tools, tools 
without which I might have failed. I have indicated that the periods after each word were signals. Without using 
those periods and those numbers as hints and as instructions I might also have failed. Those curious "points" had 
previously suggested to me that I should try using,in a Caesar, either the first or the last letter of each word beside 
which they stood. I had tried both ways. On the Dedication page itself it worked; those periods were primary 
lessons and they guided me directly to what has been presented.

I know of no way to calculate the additional probative value of these signals or of these instructions. I know that 
they were useful to me, and led me to what I offer here as a successful solution and as proof of that solution.
Basically these are acrostic methods; the critical letters have been enciphered and re-enciphered and then hidden in 
an acrostic steganogram. The name of Bacon is thus to be found twice in a book almost unanimously, though 
erroneously, attributed to William Shakespeare. Bear with me; we shall see it enciphered and deciphered again and 
again.

I will call upon the Friedmans for another example:

". . .acrostics have unquestionably been used to establish claims to authorship. . .in a Spanish treatise on the history 
of New Mexico the author was ostensibly a Count of Torene, Don Pedro Baptist Pino; but his ghost writer was not to 
be denied all credit for his work. The first letters of successive sentences, beginning on p. 43 with paragraphs for 
breaks between words, reveal the name Juan Lopez Cancelada, a surreptitious but none the less certain 
manifestation of the ghostly hand which held the pen. . .there is no room to doubt that they were put there by the 
deliberate intent of the author; the length of the hidden text, [in this case only 18 letters] and the absolutely rigid 
order in which the letters appear, combine to make it enormously improbable that they just happened to be there by 
accident. . ."

At another place, the Friedmans declare:

"Acrostic devices have the advantage that, unlike ciphers which depend on accidents of page-numbering or 
particular kinds of type, they leave no doubt that the author of the open text must also have been responsible for any 
hidden message. . .any message found must have been inserted by the man who wrote the open text. . .If, therefore, 
any genuine messages of this kind exist, they must be taken as conclusive ." (Emphasis added).

Here it must be noticed that the Friedmans and others have accepted as convincing the cryptanalysis of the names of 
several concealed authors. The minimum number of plaintext letters for proof of a monoalphabetic acrostic plaintext 
name seems not to apply to such examples.

The form  of Bacon's cipher is not one unknown to his era. At the end of Chapter 9, I have described a cipher system 
invented by Johannes Trithemius before 1526. His manuscripts were collected and in 1606 were published in Latin, 
the universal language of scholarship. In that timely book a remarkably similar device for superencipherment was 
explained. The keys of Trithemius were included in the opentext; the keys referred to the first letters of words; an 
abbreviated alphabet was required for decryption; and the ancient Caesar system was employed to read the 
plaintext. Bacon published his keys to a variation of this cipher three years later. It is apparent, considering his 
known interest in cryptography, that he adapted Trithemius to his own use. The precedent is manifest.

"Shakespeare had a word for it" -- we have all heard that tired cliche. I shall call on him for two quotations that fit 
our entrancing puzzle: "Who is so grosse, that cannot see this palpable device? Yet who so bold, but sayes he sees it 
not?" ("Richard the Third," iii, 6, 12). And again: "Our very eyes, Are sometimes like our Iudgements, blinde." 
("Cymbeline," iv, 2, 302).

What explanation can be offered, what meaning can be read into this brief awakening message, this whisper that we 
have heard from an old grave?

For a while we shall move away from the science of cryptography, away from the abode of rules, of precise 
reckonings, of mathematical certainties. We may take with us the name of the author of the cryptogram, Bacon; the 
name of the author of the Sonnets , Bacon; two letters or numbers which are either "O"s or zeros; Bacon's inclusion of 
Napier's name; and Bacon's use of the word "ciphers," a surprising and most uncommon term to be found within 
one passage of a cipher message.

In deriving this cipher solution we have used the scientific methods of induction, the ways that Francis Bacon taught 
us. By experimenting with the first words of his book of Sonnets we have arrived at our premises and we have 
found the concealed message. The very exercise reminds us that Bacon implored the scientists of his time to abandon 
their Aristotelian routines, of passing quickly from unproven, subjectively established theories and then hurrying 
onward to false and scientifically unprofitable conclusions. Now that our postulates are settled we may turn to the 
inferences to be drawn from them, to apply both inductive and deductive means, and to marshal the internal 
evidence to be found in these and other pages of the Sonnets. Let us begin with the name of John Napier. In 1608, a 
year before the Sonnets , there was published a book with this title-page:

 

DISME:
The Art of Tenths,
OR
Decimall Arithmetike ,
Teaching how to performe all Computations
whatsoever, by whole Numbers without
Fractions, by the foure Principles of
Common Arithmeticke: namely, Ad-
dition, Subtraction, Multiplication,
and Division.
Invented by the excellent Mathematician,
Simon Stevin.
Published in English with some additions
by Robert Norton , Gent.
 ________________________________

 ________________________________

Imprinted at London by S.S. for Hugh
Aspley , and are to be sold at his shop at
Saint Magnus corner. 1608.


Stevin had, in 1582, imprinted a work called La Practique d' Arithmetique , and then, in 1585, both in Flemish and in 
French, La Thiende . An earlier, less facile, notation for expressing fractions in tenths was shown in both. In 1608, in 
DISME , Stevin's proposal for the adoption of the decimal system was first translated and printed in London, 
although Stevin still did not employ decimal points. Here is how he recommended his novel way of computing by 
decimal fractions:

"We will speak freely of the great utility of this invention; I say great, much greater than I judge any of you will 
suspect, and this without at all exalting my own opinion. . .For the astronomer knows the difficult multiplications 
and divisions which proceed from the progression with degrees, minutes, seconds and thirds. . .the surveyor, he will 
recognize the great benefit which the world would receive from this science, to avoid. . .the tiresome multiplications 
in Verges, feet and often inches, which are notably awkward, and often the cause of error. The same of the masters 
of the mint, merchants and others. . .But the more that these things mentioned are worth while, and the ways to 
achieve them more laborious, the greater still is this discovery disme , which removes all these difficulties. But how? 
It teaches (to tell much in one word) to compute easily, without fractions, all computations which are encountered in 
the affairs of human beings, in such a way that the four principles of arithmetic which are called addition, 
subtraction, multiplication and division, are able to achieve this end, causing also similar facility to those who use 
the casting-board (jetons ). Now if by this means will be gained precious time. . .if by this means labor, annoyance, 
error, damage, and other accidents commonly joined with these computations be avoided, then I submit this plan 
voluntarily to your judgment."

Stevin's ideas caused a revolution in ordinary arithmetic. He recommended converting all of the odd and varying 
fractions to be found, then and still in the measurement of weights, volume, length, angles and coinage, into tenths 
or hundredths or thousandths. Such new ways of measuring did not become universal in France until the metric 
system was adopted, but the concept has since spread over the world, especially for scientific uses, and has led to 
far greater efficiency and accuracy in the handling of numbers. Stevin's tools multiplied the skills of astronomers 
who were then trying to work from circles to ellipses in their studies of the orbits of the planets. Even some 
gamblers, at "the casting-board," benefited. Meanwhile, John Napier had already been practicing those methods.
What did Shakespeare know about Disme and his contribution to technology? Read a few lines from "Troylus and 
Cressida" (ii, 2, 15):

 

Surety secure: but modest Doubt is cal'd
The Beacon of the wise: the tent that searches
To'th'bottome of the worst. Let Helen  go,
Since the first sword was drawne about this question
Every tythe soule 'mongst many thousand dismes,
Hath bin as deere as Helen : I meane of ours:
To guard a thing not ours, nor worth to vs
(Had it our name) the valew of one ten;


The author continues and mentions "a Scale of common Ounces" and "spannes and inches." He had read Stevin and 
understood the application of Disme to awkward English inch-pound-gallon measurements, and the need for 
reform. (See chapter 14 for the decryption of this passage.)

We may note, in passing, that Hugh Aspley published Stevin's book in 1608, William Aspley did the same for the 
Sonnets  in 1609, and W. Aspley was a co-publisher of the 1623 Folio.

About this time (1609) Napier was finishing his Herculean task of the calculation of the logarithmic tables. He had 
been working on them since 1590, or thereabouts. These tables, when they were published, showed that he had 
himself made use of decimals and of the period as a separatrix -- the decimal point.

The real and worthy object of Francis Bacon's Dedication to the Sonnets was John Napier. The mathematician from 
Edinburgh had hugely simplified ordinary calculation (ciphering) by the invention of natural logarithms; he had then 
redefined for his special purpose the value of unity (the number one) as equal to zero. He had suggested that 
principle to Henry Briggs (a co-founder with Francis Bacon of the Virginia Company on Roanoke Island) who then 
chose an equation for the foundation of logarithms to the base 10. So also had he embraced Stevin's decimal system. 
The efficiency of mathematics had thereby been improved by many orders of magnitude. The thirty superfluous 
decimal points of the Sonnet Dedication are Francis Bacon's tribute to Napier's accomplishments.

The man who wrote Sonnet 136 was also well aware of the basis for logarithms; he knew of it before  1609 when the 
Sonnets were registered and printed, and knew of it before  the books of Napier and Briggs were published. Here 
are a few lines from that verse:

 

In things of great receit with ease we prooue,
Among a number one is reckon'd none.
Then in the number let me passe vntold,
Though in thy stores account I one must be,


Only in a table of logarithms does 1 = 0. The log of 1 is zero, the log of 10 is one, the log of 100 is two, etc. 
Logarithms are used mostly "in things of great receipt," that is, with large numbers to simplify multiplication and 
division and in calculating powers and roots. But in "thy stores account" (a simple inventory) one still equals one and 
must be counted in the conventional manner.

The message "Zero zero Napier ciphers" becomes, with this understanding, an honor paid to John Napier's great 
industry, genius and contribution to ciphering (calculating). And the zeros are used in Bacon's additional amusing, 
ambiguous ways -- a zero may be defined as a number, a cipher; we see that Bacon's bold use of that word is 
concealed within a cipher, a secret writing. With what exactitude and brevity and skill has the encipherer composed 
and signed and hidden his cryptogram.

The first part of the message may be understood to say, "Zero, zero [is how] Napier calculates." "b e k a a n" is 
another word well chosen for its equivocation. We have seen a list of other odd ways that "beacon" has been spelled. 
The word was used in the 17th century as a verb, meaning "to signal," or "to give light and guidance to." It was then 
pronounced almost as "Bacon." The sense of the message is thus extended and, without contradiction, changes; now 
we may read, "Zero, zero, Napier's ciphers give light and guidance to Bacon." And, of course, "b e k a a n" must be 
recognized as a variant Elizabethan spelling of, and a homonym for, "Bacon."

o o n y p i r c y p p h r s b e k a a n b a c o n

These are our twenty-five cipher letters, occult upon first reading but significant upon reflection. We must consider, 
with some sympathy, the severe restraints upon the encipherer; the necessity to arrange the title-page in a proper 
and innocent-appearing form; the need to light veiled beacons within the Dedication; and all the while to enfold the 
plaintext within a steganographic ciphertext.
This concludes our exercise in elementary Baconian cryptography. We shall continue, but no longer shall there be 
any easy solutions.