In 1998, my colleague Mr. Jerry Watt observed that
when Beale Cipher No. 1 (B1) is decoded with a key constructed from a correctly numbered Declaration of Independence
(DOI), the last two letters in the decoded text are the letters "TB." From his study of the
Beale Papers, Watt knew that Beale always signed his name using only his initials "TJB." While
Mr. Morriss knew Beale's full name, Beale himself never gave his name in any of the papers addressed to Mr. Morriss.
Watt believed it unlikely that Beale's initials "TB" would occur at the end of
the decoded cipher No. 1 by mere chance. To him, it seemed more likely that Beale had signed cipher No.
1 using his initials.
Recently, Mr. Watt brought this
matter to my attention. I recall hearing about it several years ago, but I never dug into it until now.
Here are my findings, you be the judge.
There seem to be three possibilities: (1) the letters "TB" were intentionally put
there by Beale and represent Beale's signature, (2) the letters "TB" were put
there by a hoaxer and represent a false signature, or (3) the letters "TB" are spurious, and resulted from
a chance event.
To repeat myself, we know that Beale signed his letters to Mr. Morriss using his
three initials "TJB." Thus, if Beale did sign cipher B1, we would expect him to sign using his initials
"TJB." But, for Beale, signing B1 was not a straightforward matter, as it must be accomplished using a
double encipherment technique. Nor did Beale have an option to juggle the signature left or right; it must fit in one
place only. As a consequence, Beale likely discovered that the uncommon letter "J" could not be encoded
using double encipherment, although the more common letters "T" and "B" presented no difficulty.
That would seem to make sense. But it doesn't explain why a hoaxer would choose to falsely sign B1 with only two letters
"TB" when no difficulty should be encountered in signing with three letters. The hoaxer had
only to select words in his DOI beginning with letters "TJB"; the more difficult step of double encipherment
was not involved. Therefore, if it can be shown that the
letters "TB" at the end of the decoded text are unlikely to be spurious—resulting from a chance event—then
we have the basis for arguing that these letters constitute a genuine signature placed there by Beale.
By way of review, James Gillogly observed
that when Beale Cipher No. 1 is decoded with a key constructed from a correctly numbered DOI (a.k.a. the key to Beale
Cipher No. 2), an unusually long monotonic increasing letter string ABFDEFGHIIJKLMMNOHPP occurred in the decoded text,
see Gillogly "The Beale Cipher: A Dissenting Opinion" (1980) [1]. More particularly, the letter string
corresponds to cipher numbers 147 436 195 320 37 122 113 6 140 8 120 305 42 58 461 44 106 301 13 408 at locations
188 through 207 in cipher B1. Gillogly points out that numbers 195 and 301, which do not decode properly, may
have been the result of simple clerical errors, as word 194 (one off from 195=F) begins with letter "C"
and word 302 (one off from 301=H) begins with letter "O." Gillogly notes that correcting these errors is not
critical to the argument, and therefore says "We will henceforth consider only the 14-letter monotonically increasing
string DEFGHIIJKLMMNO." Gillogly argues that it is extremely unlikely for a string of this length to occur by accident in a random text. He
says that the probability of a sequence of at least 14 letters is about 10-14. He says "In a random
text of 495 [sic 520] characters, the odds against getting a sequence this long would be about 1012 to
1." But instead of arguing that the strings were intentionally placed there by Beale, for an intended purpose,
he does an about face and argues that Cipher No. 1 is a hoax. Gillogly says: "I visualize the encryptor selecting
numbers more or less at random, but occasionally growing bored and picking entries from the numbered Declaration of Independence
in front of him, in several cases choosing numbers with an alphabetic sequence."
If you look closely at Gillogly's decoded text,
you will notice a few additional imperfect letter strings, or what looks to be imperfect letter strings. You
will also notice that the decoded text ends with the letters "TB," which could be Beale's signature, although
Gillogly makes no mention of this.
Altogether, there are three occurrences of letters "TB" in Gillogly's decoded
text. The probability that one of these "TB" will occur at the end of the decoded text (by accident) can be
approximated by breaking the problem into three steps and at each step approximating the number of available locations in
the decoded text in which a "TB" could occur. We first subtract out the locations in the decoded text that correspond
to the monotonic letter strings. The reader may wish to look ahead at Table 1, which shows that there are five letter
strings. Together these strings occupy 52 locations, resulting in six fragmented strings of cipher numbers. Thus, in
the fragmented text that remains, there are 520-52-6 = 462 locations in which a pair "TB" could occur at the first
step. At the second step, there are 460 or 459 locations available, depending on whether the first "TB" blocks out
two or three locations. For our purpose, we assume that three additional locations are blocked at each subsequent step. Thus,
the probability that at least one of the three "TB" will occur at the end of the decoded text is calculated
as one minus the probability that none of the "TB" will occur at the end of the decoded text. Hence, the
desired probability can be approximated as follows:
Prob. = 1 - ( (461/462) × (458/459) × (455/456) ) = 0.00579
The calculated probability (0.00579) appears small
enough so that one may reasonably conclude the following: The chance of one of three "TB" occurring in the
last position in a random text is roughly six tenths of one percent. Thus, it would appear that the "TB" which
occurs at the end of Gillogly's decoded text was put there intentionally.
However, this conclusion is puzzling in light of additional uncovered facts, which are discussed next.
As the reader will appreciate, the matter of Beale's signature is closely related to the monotonically increasing
letter strings in cipher B1, as in both cases, the strings and the signature are produced as a consequence of decoding cipher
B1 with the key to cipher B2. And, while it is tempting to argue that the letters "TB" occurring at the
end of Gillogly's decoded text are Beale's signature, there is a problem! The DOI and key to cipher B2 used by Gillogly in
his analysis are not those used by the creator of cipher B1, although fortunately a near correct letter string was recovered
in Gilogly's decoded text, and thus his conclusion with respect to the discovered letter string is correct.
I suspect that the key to cipher B2 used by Gillogly was derived from or taken from a presumed-to-be-correct copy
of the Beale Papers, reprinted in George L. Hart's set
of private papers, commonly referred to as the Hart Papers [2]. Later, it was discovered that the copy
of the Beale Papers reprinted in the Hart Papers was not a correct and true copy of the Beale Papers, after a copy of Ward's pamphlet was recovered by a fellow researcher and member of the Beale
Cipher Association.
In fact, it shall be shown that the intentionally misnumbered DOI (or key to cipher B2) given
in Ward's pamphlet closely approximates Beale's key, whereas the key to B2 in Gillogly's paper does not. This
is easily shown to be the case by decoding cipher B1 with the key to B2 given in Gillogly's paper and with
the key to B2 given in Ward's pamphlet, respectively, and comparing the recovered letter strings in both cases (five
in number). The recovered letter strings are given in Table 1 below:
|
|
|
Letter String Decoded with Gillogly's Key and Version of DOI |
Letter String Decoded with Ward's Key and Version of DOI
|
|
37
|
758 485 604 230 436
|
T A A B B
|
|
|
44
|
150 251 284 308 231 124 211 486 225 401
|
|
A A A B B C D E F F
|
|
84
|
25 485 18 436 65 84 200 283 118 320 138
|
A A B B C C A C D D E
|
|
|
111
|
24 283 134 92 63 246 486
|
A C B C D D L
|
A C B C D D E
|
|
188
|
147 436 195 320 37
122 113 6 140 8 120 305 42 58 461 44 106 301 13 408
|
A
B F D E F G H I
I J K L M M N O H P P
|
A
B C D E F G H I I J K L M M N O H P P
|
Table 1. A comparison of the monotonically increasing letter strings
in cipher B1.
Referring now to Table 1, there are eight instances (highlighted in gray) in which cipher numbers
in the strings decoded with Gillogly's key and version of the DOI (also Hart's key and version of the DOI) do not
match the correctly decoded counterpart letters recovered with Ward's key and version of the DOI. Thus, it
is evident, on the basis of this simple side-by-side comparison, that the letter strings in the decoded B1 were created
using a DOI (or key) equivalent to or closely approximating the misnumbered DOI (or key) given in
Ward's pamphlet. The letter strings were not created using the DOI (or key) given Gillogy's paper or in
the Hart Papers.
In any case, when cipher B1 is decoded with the misnumbered DOI (or key) in Ward's pamphlet, the final
two letters in the decoded text are "TF," not "TB." Thus, the results are puzzling. Gillogy
recovered a "TB" at the end of his decoded text when cipher B1 is decoded with a proven-to-be-incorrect DOI
(or key), yet the "TB" occurring at the end of the decoded text is unlikely to be a chance event, whereas letters
"TF" are recovered at the end of the decoded text when cipher B1 is decrypted with the superior or near
perfect DOI (or key) given in Ward's pamphlet. Frankly, I am unable to explain this.
However, it is possible for Beale to have signed cipher
B1 provided that he did so using a different key. Although, I believe it is unlikely that Beale would go to such lengths.
However,
if I were forced to speculate as to how Beale might have signed cipher B1, I could put a storyline to it. Although,
as the reader will see, the explanation is complicated and predicated on several assumptions that seem too
much of a stretch. If you read on, I suggest that you have at your disposal a copy of the misnumbered
DOI given the Ward's pamphlet.
Beale's DOI contains the variant wording "institute a new government" at word location 154 and the
more common wording "mean time" at word location 520. (The pamphlet's DOI uses the word "meantime" (one
word), and this should be changed to "mean time" (two words) so that ten words occur between numbered
words 500 and 510 instead of the present nine words. The printer of Ward's pamphlet may have unwittingly combined the two
words.) In any case, in the period from 1776 to 1822, inclusive, the text of
the Declaration of Independence (in English) was printed in 327 different works (books, pamphlets, and periodicals).
The Declarations in 26 of the 327 works are consistent with Beale's reconstructed Declaration, meaning that Beale could
have chosen his Declaration from any one of these 26 works, but not from one of the remaining 301 works. The
analysis supporting this conclusion is given in chapter 6 of Beale Treasure Story: The Hoax Theory Deflated
[3].
After selecting his Declaration
from one of the 26 identified works, it is supposed that Beale copied the words in the DOI to work sheets.
He then carefully counted off groups of ten words, placing a vertical mark at the end of each group of 10 words.
Finally, he constructed a key by extracting the initial letters from the words on his work sheets, and arranged them
in a table with 10 letters per line and 101 lines. However, while copying the words to his work sheets, Beale made
three clerical errors, as follows: (1) a word was accidentally omitted after word 241 and before word 246, (2) a word
was accidentally omitted after word 630 and before word 654, and (3) a word was accidentally omitted after word 677
and before word 819. It is not important that you have the exact numbers in mind; focus more on the fact that three
errors were made, and that each error consisted of accidentally dropping or omitting a word while attempting to
copy the words to his work sheets. These three clerical errors were actually made, and they were corrected or compensated
for in the pamphlet's misnumbered DOI by the anonymous author. However, the anonymous author had no way to know for certain
the exact words that had been accidentally omitted or skipped over, and so he handled the situation, in each
case, by counting 11 words instead of 10 words. If the anonymous author had known the exact words that Beale had
skipped or missed, he would have omitted these words in the DOI printed in Ward's pamphlet, thus ensuring that
each interval would contain exactly 10 words. In any case, in the pamphlet's DOI there are 11 words that come between
numbered words 240 and 250, also 11 words that come between numbered words 630 and 640, and also 11 words that come between
numbered words 670 and 680. In the latter two cases, the locations selected by the anonymous author are arbitrary, as
other locations could have been selected without any effect on the decoded cipher B2. Although, the selected locations
could potentially effect the decoded B1, i.e., when cipher B1 is decoded with the key to cipher B2.
While creating his key from his work
sheets, Beale made one additional clerical error; he accidently skipped over 10 words in the work sheets immediately
following word 480, thus omitting an entire line of 10 letters in the key. The anonymous author dealt with this
problem by misnumbering word 490 as word 480 (i.e., repeating number 480), misnumbering word 500 as word 490, 510
as 500, and so forth.
The misnumbered DOI in Ward's pamphlet is the result of the anonymous author's best attempt to
simulate Beale's key. He did a pretty good job of it, although some might disagree.
We do know one important fact: If Beale did sign cipher B1, it wasn't signed using the same exact key that was
used to encipher Paper No. 2. or to create the letter strings in cipher B1. That means that a second key would
have to be used to sign B1. Recall that I said earlier that the anonymous author's choice to have 11 words come
between numbered words 670 and 680 in the pamphlet's DOI was arbitrary. The 11 words could have instead come between
numbered words 680 and 690, or 690 and 700, or 700 and 710, or 710 and 720, or 720 and 730, or 730 and 740, or 740 and 750,
or 750 and 760, or 760 and 770, or 770 and 780. The selection of 670 and 680 was strictly an arbitrary choice on the part
of the anonymous author, and none of the choices would have had an effect on the decoded cipher B2, although it
could affect the decoded cipher B1. In fact, note that if 11 words were made to occur between words 750 and
760, or 760 and 770, or 770 and 780, then the word "beyond" that now is numbered 749 would instead be numbered 750.
The anonymous author could have selected one of these latter three choices, and if so, the misnumbered DOI in Ward's pamphlet
would instead show numbered word 750 to be the word "beyond," rather than the word "seas." In
fact, it wouldn't matter where Beale's clerical error actually occurred between words 670 and 780, it matters only
where the anonymous author chose to include the mentioned 11 words to compensate for the clerical
error. So let us suppose that the anonymous author had chosen to include the 11 words between words 750 and 760,
or words 760 and 770, or words 770 and 780, in which case the word "beyond" would be numbered 750.
I shall address the issue of why Beale might have felt the need to sign
B1 in a moment. But for now, suppose that after encrypting cipher B2 and after creating his letter
strings in cipher B1, Beale destroyed his key in accordance with good security practices. But later he determined
that it would be beneficial if he signed cipher B1. Naturally, he would want to sign using the key to cipher B2.
However, the key had already been destroyed. However, the assumption is made here that the work sheets containing
the copied DOI, numbered in groups of 10 words per group, were still available. (This assumption may be too
much of a stretch.) Of course, Beale didn't know that he had accidentally omitted a line of 10 letters while
constructing the original key to B2. So naturally, he thought that the work sheets could be used as a pseudo-key, not
requiring him to create a completely new key. After all, he had only two sets of letters to be double enciphered. The
words on the work sheets were marked off in groups of 10 words, and so Beale only had to number the groups to form a
workable pseudo-key. The work sheets contained the same three clerical errors that had occurred when the words were copied
to the work sheets (a good thing), and differed only from the original key by a line of 10 words that had been skipped
over when the original key had been created. Thus, the pseudo-key would permit Beale's signature ("TB") to be signed
with numbers 60 and 760. The initial letters of words in the pseudo-key from 1 to 480 would be the same as letters 1
to 480 in Beale's original key. Only the initial letters of words
numbered beyond word 480 would be different from the letters in the original key. More importantly, the word "beyond"
would now be numbered 760 instead of 750. Therefore, Beale's choice of numbers 60
and 760 was fortunate, as word 60 was unaffected, thus ensuring that its initial letter remained letter
"T," while word 760 (shifted by +10) was now the word "beyond" with initial letter "B."
By luck, number 760 was not used in cipher B2 nor was it used in the creation of the letter strings in cipher B1.
Naturally, Beale would have thought that if Mr. Morriss followed his instructions to create the key to cipher B2, that this
key could also be used to decode B1 and recover the letter strings as well as the signature at the end of the decoded text.
He wouldn't have known that a simple clerical error of accidentally omitting a line of 10 letters in the original key would
screw up things.
Did Beale go to these lengths? I don't
know, but it does seem like quite a stretch. Although, I do believe that if Beale had
wanted to sign B1 under the conditions specified (his key had been destroyed but the work sheets containing
his copy of the DOI were still available), then he may well have handled the
situation in the manner described.
The reader may wonder the
following: Instead of using the pseudo-key to sign only cipher B1, could the pseudo-key have been used also to create
the letter strings in B1? I considered this possibility; but it doesn't appear to work. If cipher B1 is decoded
using the pseudo-key, the recovered letters contain a total of four errors, as follows: letter string AAAAB is recovered
as TATAB. letter string AAABBCDEFF
is recovered as AAABBCDLFF, and letter string ACBCDDE is recovered as ACBCDDL. Therefore, the best recovery of letters in the letter strings occurs when cipher
B1 is decoded using the key to cipher B2 given in Ward's pamphlet.
In any case, if the treasure story is true and Beale did sign cipher B1, then
he must have had a purpose for doing so. And, it seems likely that signing B1 would have been part of a
plan for handling some contingency. Beale had a predilection for handling contingencies. Most likely, the
signature "TB" would be part of a plan for reclaiming the locked iron box from Mr. Morriss or
from a person with Mr. Morriss' delegated authority. Moreover, the person reclaiming the box could be a
person other than Beale himself, e.g., one of his associates or possibly an agent engaged by Beale for
this purpose alone. As mentioned earlier, we know from the Beale Papers that Beale
had been careful to avoid including his name or the names of his associates in the letters provided to Mr. Morriss.
He signed his communications only with his initials TJB. Thus, it is possible (although I doubt it) that Beale could have
developed a plan for the recovery of the locked box and it contents, sophisticated enough, so that it could be accomplished
anonymously without the need to explain the nature of his enterprise or to describe the contents of the locked
box to be recovered.
Such a plan might have worked like this: Beale
had two keys to the lock placed on the iron box given to Mr. Morriss. Beale would keep one of the keys while the
other key would be wrapped together with a short note, in a small package given to the agent, along with a
set of verbal instructions. The agent would be directed to visit Mr. Morriss in Lynchburg, or the person whom Mr.
Morriss had delegated authority to in the matter. Upon meeting, the agent was directed to say that he was here to
recover the locked iron box left in Mr. Morriss' charge in the spring of 1822, whereupon he was directed to hand the
small wrapped package to the recipient (Mr. Morriss or the person with his delegated authority) , asking the person to
open the package and follow the instructions contained therein. Upon opening the package, the recipient would
find the key and short note. This is the first time that the agent would learn the contents of the package. The
note would state the following: "Use this key to open the locked box, follow the agent's instructions, and if he
is able to demonstrate to your satisfaction that he knows some particular facts about the unintelligible papers contained
therein, and if you satisfied that he is my true and trusted agent, with my authority, then place all the
papers, including my letter of May 9, 1822, to Mr. Morriss, in the box, lock it with the key, and provide the locked
box to the agent. Keep the key and destroy it after the agent departs. The agent was instructed to return
the locked box to Beale, who could open it with his copy of the key. Under the plan, the agent had no opportunity
to view the contents of the box or to make a duplicate key. If the agent were to break the lock and replace it with another,
Beale's key would not fit the lock. The plan was not perfect, but it left no easy or obvious way for the agent to learn the
details of Beale's enterprise.
The additional instructions provided by the agent to Mr. Morriss or to the person with his delegated authority
were these: First secure a copy of the Declaration of Independence and consecutively number the words from 1 to 1000.
The locked box contains unintelligible papers, the shortest of which begins with number 71. Locate this paper
and copy the 20 numbers at locations 188 through 207 to a work sheet. Replace each number with the initial
letter of that numbered word in your copy of the Declaration, whereupon you will recover an alphabetic string
of letters beginning with letter "A" and ending with letter "P." Only a person with authority
to recover the box and its contents would know this secret. If Beale didn't want the agent to know that the DOI was the
document to be used, he could instead provide the name of the document in the short note in the wrapped
package.
Beale
recognized that at some point in the conversation, most likely early on, Mr. Morriss or the person with his delegated
authority would likely ask "Who sent you?" The agent was instructed to respond saying "The
name of my benefactor is unknown to me, but I will answer the question at a later point." This would be
a signal to Mr. Morriss or the person with his delegated authority to refrain from disclosing Beale's name, although
the scheme was not a perfect one. After the letter string was decoded, the agent would respond to the earlier question
by saying "My benefactor has instructed me to say that if the last two numbers in the same unintelligible paper
are decoded, in like manner, you will recover the initials of his first and last name." Morriss would
know this to be correct upon decoding the letters. A person with Morriss' delegated authority could easily verify this by comparing
the letters "TB" with the signature "TJB" on the May 9, 1822 letter from Beale to Morriss. Recall
that Beale requested that the May 9, 1822, letter be given to the person with delegated authority. Chances are that Beale's
name would already be known to this person. In any case, the signature "TB" would add another layer of
security to an already intricate plan.
Of course, Beale would have no way of knowing that such a plan was fraught
with error. From his perspective, every copy of the Declaration of Independence was the same, and all numberings of the document
were perfect. He probably had no idea how easy it was to make clerical errors. How wrong could he be? Beale would have
thought that his scheme involved just one Declaration. It is supposed that under Beale's initial plan, the DOI was used
to encrypt B2 and to create the letter strings in B1. Thus, after these objectives had been met, the key was destroyed in
accordance with good security practices. Later, after thinking about the whole matter in greater detail, Beale may have
realized that his agent would likely be asked "Who sent you?" Without some kind of ready response, the agent
might appear to be "fishing" for information without actual authority from Beale. To handle the contingency, Beale
decided to sign cipher B1. This required him to at least create the equivalent of another enciphering key. Although, it
is conjectured that Beale instead used his work sheets of words copied from the DOI and numbered in groups
of 10 words as a pseudo-key, which he naturally thought was the same as his original key.
Did Beale sign cipher B1?
Maybe, maybe not. But, I don't think at present there is sufficient evidence to support such a conclusion.
References
[1] James J. Gillogly. "The
Beale Papers: A dissenting opinion." Cryptologia, volume 4, number 2, 116-119, April 1980.
[2] George L. Hart. The Beale
Papers (Presenting details of an alleged burial of gold, silver and jewels near Goose Creek, Bedford, County, Virginia, by
Thomas Jefferson Beale and associates in November 1819 and December 1821.) ... In an attempt to bring up-to-date all that
is known and surmised about the subject. A photocopy, from the Roanoke Public Library, Roanoke, Virginia, dated 1964.
Made from an original typescript [written January 1, 1952] presented to the Roanoke Public Library, by George L. Hart, Sr.
[3] Stephen M. Matyas, Jr. Beale
Treasure Story: The Hoax Theory Deflated, Haymarket, Virginia / Stephen M. Matyas, Jr. 2011.
