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.