Category Archives: Beale Ciphers

Given that I’ve paid my findmypast subscription (and that money’s not coming back any time soon), I thought it might be interesting to look at the records it holds for Thomas Beale Jr‘s mother Chloe Delancy / Delancey. We know a fair bit about Thomas Beale Sr, so why not find out more about his mother?

Chloe Delancy / Delancey

As far as I can see, “Cloe Delancy” only appears in Botetourt County in the 1810 and 1820 US census records. This would seem to imply that she married, moved, or died before the 1830 census – given that there are plenty of holes in the census records, it’s sensible to be at least a bit defensive.

In the 1810 census records, she is apparently living alone (“Number of free white females age 26-44” = 1) – every other column is blank. (Hence it would seem that Thomas Beale Jr may not have been living with her then.) Other than being in Botetourt County VA, no location is given.

In the 1820 census records, there is one “free white female age 45 and up” (presumably her), one “free white female age 10-16”, and one “free white female under age 10”. The location is noted in the margin as “Fin.”, which is without any doubt Fincastle.

There’s no obvious sign of her in the 1830 Census, yet that was the year that the case Delancey vs Beale was in the Supreme Court in Louisiana, so she was presumably still alive then (unless you know better?).

(Note that there is an online genealogy mentioning a Chloe Emaline Delancy b. 1834 Rockingham NC to William D. Delancey (1785-1860) and Catherine [nee Roach] (1799-1860): but this person seems entirely unconnected.)

Virginia Cloes / Chloes?

The 1830 Census has a Chloe Switcher living in Botentourt County, but she is a F 30-40 living with a M 15-20. Similarly, the 1840 Census has a Cloe Switzer, but she is a F 40-50 living with a M 20-30: I think it’s a pretty safe bet that the two entries refer to the same person, and that this probably isn’t Chloe Delancy.

Broadening the search a little, there are eight women called Cloe in Virginia listed in the 1830 Census: Cooper, Masters, Myho, Powelson, Simmons, Whichard, and Withers (though note that these are all the head of their household).

• Cloe Cooper: 1 x F under 5, 1 x F 20-30, 1 x F 50-60
• Cloe Masters: 1 x M under 5, 1 x M 5-10, 2 x M 15-20, 1 x M 20-30, 1 x F 2-30, 3 x F 30-40, 1 x F 60-70
• Cloe Myho (actually Mayho): no details of household supplied
• Cloe Powelson: 1 x M 10-15, 1 x M 15-20, 1 x M 20-30, 1 x F 10-15, 1 x F 15-20, 1 x F 40-50 [also in 1840 and 1850 censuses]
• Cloe Simmons: 1 x F 5-10, 1 x F 50-60
• Cloe Whichard: 1 x M 30-40, 1 x F 20-30, 1x F 50-60
• Cloe Withers: 1 x M 30-40, 1 x F 15-20, 1 x F 70-80

Similarly, there are sixteen women called Chloe in Virginia listed in the 1830 Census: Atkins, Buske, Cheshire, Coleman, Ellison, Gaskins, Goodrich, James, Lunsford, Mifflin, Mills, Pitman, Powell, Sitcher, Thomas, and Vanlandingham.

• Chloe Atkins: 1 x M 20-30, 1 x F 15-20, 2 x F 50-60 [also in the 1840 census]
• Chloe Buske: 1 x M 20-30, 3 x F 20-30, 1 x F 50-60
• Chloe Cheshire: 1 x M under 5, 1 x M 15-20, 1 x F under 5, 1 x F 10-15, 1 x F 20-30, 1 x F 50-60 [also in the 1810 census]
• Chloe Coleman: 1 x M under 5, 1 x M 20-30, 2 x F 5-10, 2 x F 30-40, 1 x F 60-70
• Chloe Ellison: 1 x F 50-60 [also in the 1810, 1820 and 1840 censuses]
• Chloe Gaskins: 1 x M under 5, 1 x M 5-10, 1 x M 10-15, 1 x F 30-40 [also in the 1850 census]
• Chloe Goodrich: 1 x F 60-70
• Chloe James: 1 x F 20-30, 1 x F 70-80
• Chloe Lunsford: 2 x F 15-20, 1 x F 50-60
• Chloe Mifflin: no details given
• Chloe Mills: 1 x M 10-15, 1 x M 15-20, 1 x M 20-30, 2 x F 5-10, 1 x F 15-20, 1 x F 20-30
• Chloe Pitman: 1 x F 50-60 [also in the 1840 census]
• Chloe Powell: 1 x M 5-10, 1 x F 5-10, 1 x F 30-40
• Chloe Sitcher/Switcher/Switzer: 1 x M 15-20, 1 x F 30-40
• Chloe Thomas: 1 x F 20-30, 1 x F 60-70 [also in the 1820 census]
• Chloe Vanlandingham: 1 x M 10-15, 1 x F under 5, 1 x F 10-15, 1 x F 15-20, 1 x F 40-50

Note that Cloe Cooper is also in the 1840 Census, but listed as F 80-90.

Any Other Mentions?

There is one possible mention I found, which is in the Annals of Southwest Virginia 1769-1800 (Lewis Preston Summers, 1929), p.465. There, the entry for 10th February 1796 in the minutes of the County Court mentions that the grand jury presented “Isaac Dawson and Chloe Delaney for living in an unlawful way”.

Thoughts on the US Census

I have to say I was expecting to find a little more than I did. It may be that we now have a weak indication that Chloe Delancey had two younger daughters we were (or, at the very least, I was) previously unaware of: but the limitations of the census data mean that we have (I think) no obvious paths to go down to find their names.

Has anyone got any better information on Chloe Delancey and/or her possible two daughters than this?

In many ways, Beale Cipher B1 is a lot like the Zodiac Killer’s Z340 cipher, insofar as they both have what seem to be direct predecessor homophonic ciphertexts (B2 and Z408) that are very publicly solved: yet we seem unable to exploit both ciphertexts’ apparent similarities in both system and presentation to their respective parent.

At the same time, it’s easy to list plenty of good reasons why Beale Cipher B1 has proved hard to crack (even relative to B2), e.g. its very large proportion of homophones, the high likelihood of transcription errors, etc. Combining just these two would seem to be enough to push B1 out of the reach of current automatic homophone crackers, even (sorry Jarlve) the very capable AZdecrypt.

But in many ways, that’s the easy side of the whole challenge: arguably the difficult side is working out why B1’s ciphertext is so darned improbable. This is what I’ve been scratching my head about for the last few months.

Incremental Series

I posted a few days ago about the incremental sequences in B1 and B3 pointed out by Jarlve, i.e. where the index values increased (or indeed decrease) in runs. Jarlve calculated the (im)probability of this in B1 as 4.61 sigma (pretty unlikely), B2 = 2.72 sigma (unlikely, but not crazily so) and B3 = 9.86 sigma (hugely unlikely).

Why should this be the case? On the one hand, I can broadly imagine the scenario loosely described by Jim Gillogly where an encipherer is pulling random index values from the same table of homophones used to construct B2, but where the randomness sometimes degenerates into sweeping across or down the table (depending on which way round it was written out), and that this might (somehow) translate into a broadly positive incrementality (in the case of B1).

But this kind of asks more questions than it asks, unfortunately.

Gillogly / Hammer Sequences

Surely anyone who has read more than just the mere surface details of the Beale Ciphers will know of the mysterious Gillogly strings in Beale Cipher B1 (that were in fact discussed at length by both him and Carl Hammer).

On the one hand, finding strings in broadly alphabetic sequence within the resulting plaintext (if you apply B2’s codebook to B1’s index numbers) would seem to be a very improbable occurrence.

And yet the direct corollary of this is that the amount of information stored in those alphabetic sequences is very small indeed: indeed, it’s close to zero.

One possible explanation is that those alphabet sequences are nothing more than nulls: and in fact this essentially the starting point for Gillogly’s dissenting opinion, i.e. that the whole B1 ciphertext is a great big null / hoax.

Alternatively, I’ve previously speculated that we might be looking here at some kind of keyword ‘peeking’ through the layers of crypto, i.e. where “abcdefghiijklmmnohp” would effectively be flagging us the keyword used to reorder the base alphabet. For all that, B1 would still be no more than a “pure” homophonic cipher, DoI notwithstanding. As a sidenote, I’ve tried a number of experiments to use parts (e.g. reliable parts, and only some letters) of the B2 codebook to ‘reduce’ the number of homophones used by the B1 ciphertext to try to finesse it to within reach of AZdecrypt-style automatic cracking, but with no luck so far. Just so you know!

I’ve also wondered recently whether the abcd part might simply be a distraction, while the homophone index of each letter (e.g. 1st A -> 1, 2nd A -> 2, 3rd A -> 3, etc) might instead be where the actual cipher information is. This led me to today’s last piece of improbability…

The Problem With jklm…

Here’a final thing about the famous alphabetic Gillogly string that’s more than a bit odd. If you take…

• the B1 index (first column)
• map it to the slightly adjusted DOI numbering used in the B2 ciphertext (second column, hence 195 -> 194)
• read off the adjusted letter from the DoI (third column, i.e. “abcdefghiijklmmnohp”)
• print out the 0-based index of that homophone (fourth column, i.e. “0” means “the first word beginning with this specific letter in the DoI”)
• and print out how many times that letter appears in the DoI

…you get the following table:

  147 ->  147 -> a -> 16 /166
  436 ->  436 -> b -> 12 / 48
  195 ->  194 -> c ->  7 / 53
  320 ->  320 -> d -> 10 / 36
   37 ->   37 -> e ->  2 / 37
  122 ->  122 -> f ->  1 / 64
  113 ->  113 -> g ->  1 / 19
    6 ->    6 -> h ->  0 / 78
  140 ->  140 -> i ->  5 / 68
    8 ->    8 -> i ->  1 / 68
  120 ->  120 -> j ->  0 / 10
  305 ->  305 -> k ->  0 /  4
   42 ->   42 -> l ->  0 / 34
   58 ->   58 -> m ->  0 / 28
  461 ->  461 -> m ->  7 / 28
   44 ->   44 -> n ->  1 / 19
  106 ->  106 -> o ->  7 /144
  301 ->  301 -> h ->  7 / 78  [everyone thinks this one is wrong!]
   13 ->   13 -> p ->  0 / 60

What I find strange about this is not only that the “jklm” sequence is in perfect alphabetic order, but also that its letters are all the 0th instance of “jklm” in the DoI. To me, this seems improbable in quite a different way. (Perhaps Dave Oranchak and Jarlve will now both jump in to tell me there’s actually a 1 in 12 chance of this happening, and I shouldn’t get so excited.)

The reason I find this extremely interesting is that it specifically means that the jklm sequence contains essentially zero information: the B2-codebook-derived letters themselves are in a pure alphabetic sequence (and so can be perfectly predicted from letter to adjacent letter), while each letter is referred to the index of the very first word-initial occurrence in the DoI.

This means (I think) that there isn’t enough information encoded inside the jklm sequence to encipher anything at all: which I suspect may actually prove to be a very important cryptologic lemma, in terms of helping us eliminate certain classes of (or attempts at) solutions.

I’ve recently been trawling through lots of sources of information on the Beale Ciphers, and thought it might be nice to dump a whole load of thoughts in a single place, rather than sprawl these out over 4-5 posts. So here goes…

Clayton Hart

The suggestion that the Beale Ciphers might be three genuine ciphertexts but that the Beale Papers could simultaneously just be fantastical meanderings woven around those ciphertexts is not original to me (and I never claimed it was). However, what I didn’t realise until the last few days was that Clayton Hart also wondered that this might have been true, possibly as far back as 1903:

Clayton Hart actually met with James Ward and his son, who both, in 1903, confirmed the content of his pamphlet. In particular he states: “I have wondered if Ward might have written his manuscript based upon some figures he found, or made up; and yet, we have the word of Ward, his son, and friends to the contrary. Inquiry among some aged neighbors of Ward showed the high respect they had for him, and brought forth the statement that Ward would never practice deception.”

Interesting, hmmm?

C3 and high numbers

Another Beale page on the same angelfire.com site (though watch out for those pesky pop-unders there, *sigh*) demonstrates that the high numbers in B3 are concentrated very strongly in the second half of the ciphertext:

The image is credited to researcher Simon Ayrinhac, who has a picture from 2006 or earlier here:

Ayrinhac’s French discussion on the Beale Ciphers is also online, though as it doesn’t include the above diagram, there may well be further Beale analyses of his elsewhere online (which I haven’t yet found).

Declaration of Independence

One of Stephen M. Matyas Jr.’s major contributions to Beale Cipher research is his extensive collection of printed versions of the Declaration of Independence from 1776-1825, which is available both in printed form and online on his website, e.g. his checklist and addenda PDFs (both highly recommended).

This has led him to build up what I think is a really solid reasoning chain about the Declaration of Independence used in the (solved) Beale Cipher B2. For example, as far as the word “unalienable” goes, Matyas writes:

Many, in fact, most Declarations printed before 1823 contain the word “unalienable.” Thus, it may be surmised that Beale’s Declaration contained the word “unalienable,” not “inalienable,” and therefore that the two Declarations are different and taken from two different source works (probably books).

In Chapter 6 of his book “Beale Treasure Story: The Hoax Theory Deflated” (according to this page, but more about Matyas’ books another day), Matyas further writes about the word “meantime”:

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.)

So, the first big takeaway from Matyas’ careful analysis of all the pre-1826 printed copies of the Declaration of Independence is that the DoI that was used to create B2 was, he asserts, not an obscure and wonky variatn, but instead a genuine mainstream copy of the DoI. Matyas says that of the 327 printed versions he was aware of, 26 were entirely consistent with the cipher: and he believes that the one used to encipher B2 was from a book (rather than, say, from a newspaper).

His second big point is that some of the errors that affected the DoI numbering in the pamphlet seem to have arisen because the author of the pamphlet included a version of the DoI that he had adapted / reconstructed to better fit the one used to turn B2’s decrypted plaintext into its ciphertext. As Matyas puts it, “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.”

From all this, I think it is clear that anyone genuinely trying to decrypt B1 and B3 should very probably be working forward from one of Matyas’ 26 remaining compatible DoI texts rather than backwards from the DoI version given in the pamphlet. This is a tricky point with code-breaking ramifications I’ll return to in a follow-up post.

Matyas’s Reconstruction

With the above in mind, Matyas moves on to show the sequence of steps that he believes was taken to construct Beale Cipher B2, which I reduce to bullet-point format here:

1. “[I]t is supposed that [the encipherer] copied the words in the DOI to work sheets.”
2. “He then carefully counted off groups of ten words, placing a vertical mark at the end of each group of 10 words.”
3. “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.”
4. The encipherer “made three clerical errors”:
(a) “a word was accidentally omitted after word 241 and before word 246,”
(b) “a word was accidentally omitted after word 630 and before word 654, and”
(c) “a word was accidentally omitted after word 677 and before word 819.”
5. The encipherer “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.”

Matyas believes that because of these errors, when the anonymous author of the Beale Papers pamphlet came to reconstruct and number his own Declaration of Independence, he adapted the numbering and wording to better fit the plaintext he had worked out.

Even though Beale Ciphers B1, B2, and B3 each consist of similar-looking strings of numbers, it’s far from obvious that they have been generated in the same way (i.e. that they all result from using the same cipher system).

Usage Patterns

We can quickly map the usage of the first 1000 index values (I remain a bit suspicious of higher numbers), with the following bitwise key:
* ‘.’ => unused
* ‘1’ => used in B1
* ‘2’ => used in B2
* ‘3’ => used in B1 + B2
* ‘4’ => used in B3
* ‘5’ => used in B1 + B3
* ‘6’ => used in B2 + B3
* ‘7’ => used in B1 + B2 + B3

77773777777757777776775777777376777777777777676777
7766576377737777755577754577317777755555.75777575.
77516774525774757757774525554135276747531.6.143147
42.3..4227.5.4..4..1454.4564.45.4124..1.7.171624.7
515.65574175554565525..51454.7111745.42421.44752.2
52...4...414154...46..247....1..132522.34..1.46.4.
73457..3.444474644475.11.5.5........4..11.46.1.4..
4.2..1...31..55.1..32..44....444.....2.....2..4..2
1.1.22.12.144..541.2..1..1....1..4.1..43......1...
.........55.11.2....1..1..........33........4....1
1...2.....2..................1.......1.3..1....3..
...2..2..........1......2.....33.................2
1131..3...41.1..54.2..11......4...........24..2...
...1.........1.21.......41...1.1.4................
...............14..........1.......1..............
.......1.....................1....................
......2...21.14.41554.11....1..........1....4.....
.....4.1..11.4.......1..1..............5....141...
...........1....411.14.4......1..4.5..............
44.......111..1.........5.........1..............1

From this, we can see that even though the numbers that are used in all three ciphers are biased towards low numbers (e.g. look at all the ‘7’ values at the top), B1 numbers (and to a slightly lesser extent B3 numbers) appear throughout the number range. Furthermore, apart from the numbers near the top, there seems to be no systematic relationship between the usage map of any two pair of ciphers (not even B1 and B3).

And yet we have quite strong evidence that the same enciphering tables derived from the DoI were used for both B2 (which has been solved) and B1 (which remains unsolved). I think this alone is strong evidence that for all their underlying “causal similarities” (for want of a better phrase), B1 and B2 were not generated by the same ciphering system.

Note also that the map shows runs of adjacent indices that appear in only one of the three ciphertexts (e.g. “4444” in B3) or that appear in both B1 and B3 but not in B2 (e.g. “55555”). However, these look broadly within the range of normal randomness, so I doubt these are highlighting anything unusual.

Jarlve’s Incremental Series

In a comment here a few days ago, Jarlve observed that all three Beale ciphers have stretches of numbers that were numerically ordered to a degree that was somewhat unusual. And furthermore:

Testing the significance of these incremental series versus randomizations, then B1 = 4.61 sigma, B2 = 2.72 sigma and B3 = 9.86 sigma.

If we map B1’s “incrementality” (i.e. where ‘.’ => decrement, and ‘*’ => increment), we can indeed see a six-long increment sequence about 60% of the way through, plus a couple of five-long increment sequences. What is just as striking is that the long decrement sequence in B1 is four-long (twice), which points to some kind of subtle asymmetry.

B1:

*.*...**.*.*.*..**.**.***.**.*.**.**.*.**..***..**
.*..**.*.***...*.**..**..**.*..*.*.*.***.*..*..***
..*.*.*.***...***.*.**.***.*..*..**.****.*.**.*.**
..*.*..*..*.**.*.***....***.**..***.**.*.*..*.**.*
*.**.**..**.*.*.*..***..***.*.*.*****.**.*.**.*...
***.*..****.*.**.***..*..****..****.*.*.***..***..
*.******.*..**.***.*..*..**...**.*..**.*.*.*.*.**.
*..*.*..*.**.****..*.*..**..*.*.*.*..****..*..**..
**.*..**..***.*.***..**.*..**.**.****.****.*..*.*.
.***....*.***..*..*****.*..*.**..*.*.**...***.*.*.
**.***...*.****..**

Compare this with B2, which has a six-long decrement sequence (about 30% of the way through), and a pair of five-long increment sequences.

B2:

..*.*..***..**..*.*.*.**.**..*..*..***....*.*.**..
*.*..**.**.*.*.**..***.**.*..***.**.*.*.*.**.*.*.*
*.*.**...*...**..**.**.***.*.**..**..***.*..*.**.*
.***.*.*.*.*..*..**..*.***.*.***..**..***.*..**..*
.*.**......*.**.*....*..*.*.***.***..**.*..***..**
.*.*.*..**..*.*.*...*.***.*.**.*.*.**.*.*.**.*.*.*
.***.***.*..**..*.****...*..*.*.**..***.**.*.**.**
.*.*.**.*.*.*..*.*....***.*..*..*..**..**...**.*..
*.*.**.****..**.*..*.**.***...*.*...**.*..*..*.*.*
*.***.**..**.**.*.**.*...*.**..*.*.****.*****..**.
***..*.*..**.*.**.*.*.**..***..**...***.*....*.*..
*.**...***.*.****..*.*.*.*.*..**..**.**..*.*.*.*..
**.**...*..*.*.*.*..***.*.****..*.**..*.*.*..*.*.*
*.**.*..***..*..**...**.*.*..**....*.**.*..*****.*
***.*.*..**.**.*.***.**.*..**.*...**..*..*.****.*.
***..***.***

But all of this in B1 and B2 is almost as nothing to B3’s extremely unbalanced set of increment series, firstly in a patch in the middle (two seven-long increments and two six-long increments) and then in a long patch at the end (where the positive increment sequences are 9, 9, 7, 6, 7, 9, and 6 long). By way of contrast, the longest decrement sequences in B3 are a single 6-long set, and a single 5-long set).

B3:

.*.*..*.**.*.**..***..*.*..*.***..*.*.*..*.*.**.*.
**.*.*.*.*..*..**.***..*.**.****.***.**.*.*.**.***
*.*.*.*...*...**.*.*.**.**..*.**..*.***.*.***..*..
*.***.**.**..*****...*.*.*..****..*....***..*.****
.*****..***...*.*.****.*******..**.*.*.*..**..**.*
***.**...**..*..**.*.*.***.**.**.****.****.******.
***..****.**...*.*.**..*.***.*******..*...**.*****
*.**..*.*.**.*.***.*.**..*.*.**..*****..***.**..*.
***.**.****.****.*.***.*...**...**.*......*.*..**.
**..*.*****.****.*****.*.*.*.*.**.*.*....*.*.*****
****.*********..**.**.*******..**.*..******.*.****
..*.**.****.*****.....*.**..*******.****..*.*.***.
.*********.******

Putting All This Together

I think Jarlve’s incrementing series perhaps offer a quite different dimension to what Jim Gillogly (perhaps better known for breaking parts of the Kryptos ciphers) mused in his “Dissenting Opinion” on the Beale Ciphers, where he opined:

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.

Whereas this loosely seems to fit B1 (where mysterious alphabet-like strings do indeed appear, but which require the cipher table used in B2 to have been used in a different manner), the immediate problem is that it doesn’t really capture what happens in B3 (where no mysterious alphabet-like strings appear if you apply B3’s index values to the DoI) at all. There, (thanks to Jarlve) we can say that the same encryptor seems to have instead chosen numbers with a strong bias towards incrementing numeric series.

But why would that be?

By now, everyone and his/her crypto-dog must surely know that the second Beale Cipher (“B2”) was enciphered using a lookup table created from the first letters of the words of the Declaration of Independence: that is, a number N in the B2 ciphertext corresponds to the first letter of the Nth word in the DoI.

Even working out that this was the case was far from trivial, because the version of the DoI used was non-standard, and there were also annoying numerical shifts (which strongly suggest that the encipherer’s word numbering messed up along the way). There were also a few places where the numbers in the B2 ciphertext appear to have been miscopied or misprinted.

Yet I don’t share the view put forward by some researchers that this would have made it nigh-on-impossible for anyone to figure out that the DoI had been used, simply because most of the number instances are low numbers, i.e. they are concentrated near the front end of the DoI where there are fewer differences with normal DoI’s, and before the numbering slips started to creep in. This means that even if you used nearly the right DoI, a very large part of the ciphertext would become readable: and from there a persistent investigator should be able to reconstruct what happened with the (not-so-straightforward) high-numbered indices to eventually fill in the rest of the gaps. Which is basically where Beale research had reached by the time Ward’s pamphlet was printed.

So far, so “National Treasure”. But this isn’t quite the whole story, because…

B1 Used The Same Table!

Even if we have so far failed to work out precisely how B1 was enciphered, we do also know something rather surprising, courtesy of Carl Hammer and Jim Gillogly: that the process used to construct B1 used almost exactly the same DoI used to encipher B2. Jim Gillogly, in his famous article “The Beale Cipher: A Dissenting Opinion” [April 1980, Cryptologia, Volume 4, Number 2, pp.116-119, a copy of which can be found in the Wayback Machine here] concluded that the ‘plaintext’ patterns that emerged from this were artificial nonsense, and so B1 (and by implication B3) were empty hoax texts, i.e. designed to infuriate rather than to communicate.

From the same evidence, Carl Hammer concluded (quite differently) that B1 and B2 were encrypted in the same way using the same tables, though he didn’t have a good explanation for the mysterious patterns. For what it’s worth, my own conclusion is that B1 and B2 were encrypted slightly differently but using the same tables, which is kind of a halfway house between Gillogly’s coglie and Hammer’s clamour. 😉

All three agree on this: that if you plug the DoI’s first letters into the B1 ciphertext, mysterious patterns do appear (more on those shortly). But for many years, my view has been that Gillogly’s end conclusion, though clear-headed and sincere, was both premature (because I don’t believe he had eliminated all possible explanations) and unhelpful (because it had the possibly unintentional effect of stifling nearly all subsequent cryptological research into the Beale ciphers).

Regardless, it seems highly likely that almost exactly the same DoI was used to construct B1 as was used to encipher B2. This is because the statistically improbable mysterious patterns only emerge in the B1 plaintext if you use the DoI.

Furthermore, what I think is quite striking is, as I pointed out some years ago, that if you use the corrected cipher table (i.e. the cipher table generated from the same DoI and using the same numerical mistakes as were used in the cipher table used to construct the B2 cipher text), the mysterious patterns not only remain, but become even more statistically improbable than before.

What this implies, I believe, is that not only was the same non-standard DoI used in both, but also the same enciphering tables derived from it, numerical errors and all.

Here’s what B1 looks like when combined with the raw DoI (numbers above 1000 map to ‘?’)

s c s ? e t f a ? g c d o t t u c w o t w t a a i w d b i i d t t ? w t t a a b b p l a a a b w c t
l t f i f l k i l p e a a b p w c h o t o a p p p m o r a l a n h a a b b c c a c d d e a o s d s f
h n t f t a t p o c a c b c d d l b e r i f e b t h i f o e h u u b t t t t t i h p a o a a s a t a
a t t o m t a p o a a a r o m p j d r a ? ? t s b c o b d a a a c p n r b a b f d e f g h i i j k l
m m n o h p p a w t a c m o b l s o e s s o a v i s p f t a o t b t f t h f o a o g h w t e n a l c
a a s a a t t a r d s l t a w g f e s a u w a o l t t a h h t t a s o t t e a f a a s c s t a i f r
c a b t o t l h h d t n h w t s t e a i e o a a s t w t t s o i t s s t a a o p i w c p c w s o t t
i o i e s i t t d a t t p i u f s f r f a b p t c c o a i t n a t t o s t s t f ? ? a t d a t w t a
t t o c w t o m p a t s o t e c a t t o t b s o g c w c d r o l i t i b h p w a a e ? b t s t a f a
e w c a ? c b o w l t p o a c t e w t a f o a i t h t t t t o s h r i s t e o o e c u s c ? r a i h
r l w s t r a s n i t p c b f a e f t t

Of the many artificial-looking sequences here, the one that caught Hammer’s and Gillogly’s eyes was:

a b f d e f g h i i j k l m m n o h p p

If we instead plug the same set of B1 numbers into the corrected DoI cipher table, this is what you get:

s b s ? e t f a ? g c d o t t u c w o t w t a a i s d b t i d t t ? w t f b a a b a d a a a b b c d
e f f i f l k i g p e a m n p w c h o c o a l l p m o t a m a n h a b b b c c c c d d e a o s d s t
b n t f t a t p o c a c b c d d e p e t p f a b t h i f f e h u u b t j t t t i h p a o a o s a t a
b t t ? m n m p a a a a r b o p j d t f ? ? t s b c o h d a f a c p n r b a b c d e f g h i i j k l
m m n o h p p a w t a o m b b l s o e s a t o f i s p c t a o l b t f l h d o a h g b w t e n c l c
a s s a a s t a t d t g t a w g f e a a o c a a a t t w h t t t a a o e t s a f a a s b s t c i h r
c a b t o t s c t d c n h w t s t e h i o o a t s t w t t s o f a a s t a a m s i w c p c w s o t l
i n i e e i t t d a t t p i u f a e r f a b p t c t a o i d n a t t o a t s t a ? ? a t m a t w n w
t t o c w t o t p a t s o t e b a t r c h b t o g a w c d r o l i t i a h l w a a s ? b c s t a f a
e w c m ? f t o w l t s o c c t e w t a f o a o w t t t t t o t h r i s u e o h a c u a f ? p o i h
r m s s t r a s n i t p c t u o w f t t

This yields even more mysteriously ordered patterns than before:
* a a b a d a a a b b c d e f f i f
* a b b b c c c c d d e
* a b c d e f g h i i j k l m m n o h p p

Sorry, Jim, but something is going on there to cause feeding B1’s numbers into the refined DoI to produce these patterns: and even if I agree that the rest of the Beale pamphlet is a steaming heap of make-believe Boy’s Own backfill, I still don’t think the B1 ciphertext is a hoax. There’s just too much order.

Filling In The Gaps

Now, if it is true that exactly the same cipher table was used to construct both B1 and B2 (and though I believe this is highly likely, I have to point out that this remains speculative), these mysterious patterns may offer us the ability to advance our understanding of the cipher table yet further. This is because we can look at those places where the mysterious patterns break down in mid-sequence, and use those places to suggest corrections either to the table or to the B1 ciphertext itself. That is, even if we can neither decrypt nor understand B1, we can still use its mysterious plaintext patterns to refine our reconstruction of the enciphering table used to construct it and/or our understanding of the B1 ciphertext itself.

150=a 251=a 284=a 308=b 231=b 124=c 211=d 486=e 225=f 401=f 370=i 11=f

370=importance BUT 360=forbidden, so I suspect that 370 may have been a copying slip for 360.

24=a 283=c 134=b 92=c 63=d 246=d 486=e

283=colonies BUT 284=and, so I suspect that 283 may have been a copying slip for 284.

890=a 346=a 36=a 150=a 59=r 568=b

59=requires, but I’m not sure what happened here.

147=a 436=b 195=c 320=d 37=e 122=f 113=g 6=h 140=i 8=i 120=j 305=k 42=l 58=m 461=m 44=n 106=o 301=h 13=p 408=p

301=history BUT 302=of, so I suspect that 301 may have been a copying slip for 302.

OK, I’d agree this isn’t a huge step forward: but given that the printed version of (the solved!) B2 has seven similar copying slips…

* B2 index #223 is ’84’, but should be ’85’
* B2 index #531 is ’53’, but should be ’54’
* B2 index #571 is ‘108’, but should be ‘10,8’
* B2 index #590 [#591] is ‘188’, but should be ‘138’
* B2 index #666 [#667] is ‘440’, but should be ’40’
* B2 index #701 [#702] is ’84’, but should be ’85’
* B2 index #722 [#723] is ’96’, but should be ’95’

…I’d expect that we’re likely to have between 10 and 20 copying slips in B1’s series of numbers. That, combined with the larger ratio of homophones (i.e. as compared with the size of the ciphertext), keeps pushing B1 out of the range of automated homophonic ciphertext solvers. So all we can do to try to correct for those may well be a help!

To decipher the sequence of numbers that make up the second Beale Cipher (‘B2’), you use them to index into the words a slightly-mucked-around version of the Declaration of Independence (A.K.A. a “book cipher” / “dictionary cipher”): the sequence of initial letters this produces yields the decrypted plaintext. Errm… except that this isn’t the whole story: thanks to the Committee of Five’s inexplicable omission of a right to bear xylophones, yoyos, or zebras, the B2 cipher maker also had to improvise a second “rare letter cipher” to encipher rare word-initial letters such as x- and y-. (But that’s a post for another day.)

For book ciphers that literally use dictionaries as their code book, this wouldn’t be a problem (because they necessarily go all the way from aardvarks to zymurgy). Of course, given that the letters of the alphabet appear there in strictly ascending order, using an actual dictionary would probably be a bit dumb. Hence people use book ciphers instead, preferably ones with zebras playing xylophones. 😉

So: strictly speaking, then, Beale Cipher B2 doesn’t employ a pure book cipher, but instead uses a slightly hybridized one, where letters absent from the DoI get enciphered by some (currently) unknown means. So here are some numbers to introduce how the book cipher part of the B2 cipher system works.

B2’s Mapping Statistics

I haven’t seen B2’s letter mapping statistics anywhere on the Internet, so I thought this would be a good place to start (note q and z are not used in B2, so do not appear):

* a [43/15,av=2.9,34.9%]: 24[4] 36[2] 28[5] 147[2] 45[1] 81[4] 98[3] 51[4] 284[1] 150[6] 27[2] 230[4] 83[2] 25[2] 152[1]
* b [11/7,av=1.6,63.6%]: 308[1] 9[1] 77[4] 18[2] 134[1] 485[1] 194[1]
* c [19/7,av=2.7,36.8%]: 84[7] 65[2] 92[2] 4[3] 94[1] 200[2] 21[2]
* d [49/11,av=4.5,22.4%]: 52[10] 15[8] 211[3] 118[4] 63[11] 252[1] 135[2] 246[3] 320[5] 406[1] 582[1]
* e [103/14,av=7.4,13.6%]: 37[13] 49[6] 7[15] 79[4] 85[11] 138[15] 191[7] 620[2] 486[3] 511[6] 548[2] 603[4] 575[2] 33[13]
* f [21/8,av=2.6,38.1%]: 196[4] 160[4] 122[6] 273[1] 131[3] 360[1] 666[1] 11[1]
* g [15/4,av=3.8,26.7%]: 270[3] 48[6] 113[5] 133[1]
* h [37/8,av=4.6,21.6%]: 73[8] 107[5] 394[1] 6[4] 20[9] 301[2] 205[7] 466[1]
* i [55/12,av=4.6,21.8%]: 115[5] 647[1] 140[15] 2[7] 8[12] 154[4] 314[2] 159[1] 67[4] 185[1] 241[2] 370[1]
* j [2/2,av=1.0,100.0%]: 120[1] 581[1]
* k [1/1,av=1.0,100.0%]: 305[1]
* l [32/10,av=3.2,31.3%]: 42[5] 101[6] 102[7] 234[1] 400[4] 158[3] 197[1] 420[3] 177[1] 405[1]
* m [6/4,av=1.5,66.7%]: 58[1] 82[1] 117[2] 208[2]
* n [69/8,av=8.6,11.6%]: 47[13] 10[13] 287[8] 353[8] 607[2] 540[10] 44[13] 557[2]
* o [63/12,av=5.3,19.0%]: 31[7] 56[4] 5[4] 136[3] 46[4] 106[15] 12[6] 43[6] 57[2] 125[9] 143[1] 302[2]
* p [12/4,av=3.0,33.3%]: 17[1] 105[4] 30[5] 121[2]
* r [40/7,av=5.7,17.5%]: 59[5] 53[9] 96[8] 220[8] 248[2] 344[2] 112[6]
* s [48/12,av=4.0,25.0%]: 62[5] 35[6] 71[4] 78[2] 110[11] 38[9] 217[2] 505[3] 600[2] 297[1] 275[2] 285[1]
* t [69/17,av=4.1,24.6%]: 22[4] 29[5] 26[6] 554[1] 3[5] 41[6] 16[9] 34[5] 60[2] 61[3] 14[7] 50[6] 32[4] 64[2] 39[1] 643[2] 288[1]
* u [24/8,av=3.0,33.3%]: 239[3] 316[5] 95[3] 250[6] 371[3] 388[2] 409[1] 440[1]
* v [18/1,av=18.0,5.6%]: 807[18]
* w [13/6,av=2.2,46.2%]: 72[2] 290[1] 19[2] 66[2] 40[5] 1[1]
* x [4/1,av=4.0,25.0%]: 1005[4] (though note that the DOI has no word beginning with x-.)
* y [9/1,av=9.0,11.1%]: 811[9] (though note that #811 = FUNDAMENTALLY, i.e. the DOI has no word beginning with y-.)

That is, ‘a’ appears 43 times in B2 and has 15 homophones, which means that the average number of instances per individual ‘a’ homophone is 2.9, and the proportion of ‘a’ homophones to ‘a’ instances is 34.9%: specifically, index #24 appears 4 times, index 36 appears 2 times, index #28 appears 5 times, and so on.

We can also list these results in order of the well-known ETAOINSHRDLU decreasing frequency mnemonic:
* E [103/14,av=7.4,13.6%]
* T [69/17,av=4.1,24.6%]
* A [43/15,av=2.9,34.9%]
* O [63/12,av=5.3,19.0%]
* I [55/12,av=4.6,21.8%]
* N [69/8,av=8.6,11.6%]
* S [48/12,av=4.0,25.0%]
* H [37/8,av=4.6,21.6%]
* R [40/7,av=5.7,17.5%]
* D [49/11,av=4.5,22.4%]
* L [32/10,av=3.2,31.3%]
* U [24/8,av=3.0,33.3%]

Hence the actual implicit frequency ordering (i.e. in terms of decreasing number of homophones used in B2) was more like:

* 17 T
* 15 A
* 14 E
* 12 O/I/S
* 11 D
* 10 L
* 8 F/H/N/U
etc

DOI letter statistics

We can also look at the letter statistics for the DOI (numbers corrected as per B2), and at how many times each index is used in the B2 ciphertext (i.e. ‘.’ = “index not used”):

* a occurs 166 times: (4)(2)(2)(5)(2)(1)(4)(4)(2).(3)…..(2)(6)(1)………..(4)……(1)………………………………………………………………………………………………………………..
* b occurs 48 times: (1)(2)(4).(1)(1)…(1)…(1)…………………………….
* c occurs 53 times: (3)(2)(2)(5)(2)(1)..(2)……………………………………..
* d occurs 36 times: (8)(10)(11)(4)(2).(3)(3)(1).(5)(1)….(1)……………….
* e occurs 37 times: (15)(13)(13)(6)(4)(13).(15).(7)….(3)..(6).(2)(2)(4)(2)…………..
* f occurs 64 times: (1)(6)(3)(4).(4)..(1)…(1)…………..(1)………………………………
* g occurs 19 times: (6)(5).(1)…(3)………..
* h occurs 78 times: (4)(9)(8)(5).(7).(2)………..(1)……(1)……………………………………………
* i occurs 68 times: (7)(12)(4)(5).(15).(4)(1)..(1)(2)……(2)..(1)………(1)……………………………..
* j occurs 10 times: (1)..(1)……
* k occurs 4 times: (1)…
* l occurs 34 times: (5)(6)(7).(3)(1).(1)(1)…(4)(1)(3)……………….
* m occurs 28 times: (1)(1)(2).(2)…………………..
* n occurs 19 times: (13)(13)(13)…(8).(8).(10)(2)(2)……
* o occurs 144 times: (4)(6)(7)(6)(4)(4)(2)(15)(9).(3)(1)……..(2)……………………………………………………………………………………………………………
* p occurs 60 times: .(1)(5)(4)(2)……………………………………………….
* q occurs 1 times: .
* r occurs 40 times: (8)(5)(7)(6).(8)(2)..(2)…………………………
* s occurs 62 times: (6)(9)(5)(4)(2)(11)……..(2)…(2).(1)(1)…….(3).(2)…………………………
* t occurs 252 times: (5)(7)(9)(4)(6)(5)(4)(5)(1)(6)(6)(1).(2)(3)(2)……………………………………………(1)………………………………………………(1)………..(2)………………………………………………………………………………………………………
* u occurs 28 times: (4)(3)(6)(5)(3)(2)(1).(1)……………….
* v occurs 2 times: (18).
* w occurs 59 times: (1)(2).(5)(2)(2)……(1)……………………………………….

Of course, this clearly confirms the theory that the DOI contains no xylophones, no yoyos, and no zebras. 🙂

As has been pointed out many times, the way that the usage patterns are heavily biased towards low numbers implies that the homophones were mainly taken from the start of the DOI, though with scattered exceptions.

B2’s Homophone Patterns

Because the encipherer used so few of the possible homophones (i.e. because A appears 166 times in the DOI, all 43 instances of A in B2 could have used different symbols, but only 15 homophones for A were used in B2), the ciphertext B2 is solvable as a pure homophone cipher: and in fact some automated homophone solvers can solve Beale B2 unassisted (though not B1 or B3, sadly).

With that in mind, it is also interesting to look at B2’s homophone pattern, to see if this tells us more about how B2 was constructed:

* a homophone sequence: ABCDAEFFCGHHIJKLLMLCFKNLDHOCGBJAMJAGJJJNFCH
* b homophone sequence: ABCCCDCDEFG
* c homophone sequence: ABCCADEFDGABAGFDA
* d homophone sequence: ABACDEAEADECBFEAABGEEBHCIHAIBJIIAIEEKADBABBGDEHEE
* e homophone sequence: ABCDECAFGBEGHGGEACIJAFDJKLCMNEFDBDFCAABFEFNAEABCNGEJCNCILNJKANCNFANCNFEFCCGFEFCANJHFNAEFENACNGJLBCEFIEMLF
* f homophone sequence: ABCCACADCCEAFEGBHBEBC
* g homophone sequence: ABCBCDBCACBCBAB
* h homophone sequence: ABACDEFEBEDAGAGEDEDFBAEBEEGAGGAHBAGEG
* i homophone sequence: ABCDCEFGACDHCEFFEACAAIECDCDEDIECGDCCIDEEJFEKCLCEECIKECC
* j homophone sequence: AB
* k homophone sequence: A
* l homophone sequence: ABCDEFGHBFCCBCFEIACHCEBEHBAAJABC
* m homophone sequence: ABCCDD
* n homophone sequence: ABCDACABDECFGCFAFGDHFEGBBDCAAAGBGDBCGBHAGBFDFAGBGGAFFBBDFGAGBGCCADFBA
* o homophone sequence: ABCDEFABGHIFFHFEFJJCIHGBJKGGAFHFALAFAJHHFEJBJDGFFJFFEAFCJFGCJDL
* p homophone sequence: ABCBDCCDCBCB
* r homophone sequence: ABBCAADCEDFADEBGFDBBDAGCGGDDGCCBCCDBBG
* s homophone sequence: ABCDBEBEAEFGCHBAACIFJFBEFFBGEEFCEAKELFDEHFEFKEHI
* t homophone sequence: ABCDEFGHIECJBKGHFLJKBBEKCHGFMLNOAEJMBLGKACHFLPMCQKILGLHGNAEPFKGGMFKCGR
* u homophone sequence: ABCDBEFFAAEBCDDBDDECGBDCH
* v homophone sequence: AAAAAAAAAAAAAAAAAA
* w homophone sequence: ABCDEFEDCAEEE
* x homophone sequence: AAAA
* y homophone sequence: AAAAAAAAA

My Conclusions

One thing that stands out for me is that only a single homophone for V was used, (a) even though it appeared 18 times in B2, and (b) even though two were available (DOI #818 “VALUABLE” and DOI #1132 “VOICE”). To me, this seems a fairly clear indication that the search for homophones stopped earlier in the DOI. Combine this with the fact that X is #1005, and it seems likely that the highest genuine DOI index would have been (say) 1000: everything after that would be a special secondary code (e.g. for ‘X’).

I know, I know: this is the same Mental Floss that also publishes articles like 10 Things You Might Not Know About Jeff Goldblum (sample fact: “My first wife and I would bring our juicer on planes, and we’d do a carrot cleanse for a week, until I’d turn orange and all my poop would be orange”).

But bear with me on this, because the long-form article by Lucas Reilly on the Beale Ciphers / Papers / Treasure that just came out is really good. No, it’s really good.

And I’m not just saying that because Reilly quotes me a few times: he covers all the important ground at a nice even pace without getting overly technical. As part of his research, he even tried to walk the Beale walk a bit (though without actually hiring a backhoe), and even got the desk-full-of-documents Beale treatment when he visited the Bedford County Museum and Genealogical Library in Montvale. Which is nice.

Reilly also managed to dig up a couple of Beale decryptions I can’t remember seeing before, including this one mentioned in a Washington Post article from 1984, attributed to an “M.C.D.”:

ONE RAN TO COVER THE TOP / HIT THE
RAM NUB ON THE TOP OF THE NEST /
BEST I TRY HEAT / SEE CALL TO FIT
TOY SO HAT NOD IF FULL / I WILL BE
IN THE CUT FIND AND DIG IT … GO WIN
YOUR SLICE AND BE LONG IN LOVE

…as well as this one:

LEND AN EAR / I LEARNED A
TRADE TO READ FINE ART OF ROTE
… / I FEEL GREAT / I FIND TEN
TON ORE IT IS STORED ON NORA,
NORMAN, BROWN FARM / ROAD RUN
AROUND RED BARN.

Incidentally, the Washington Post article (“Legendary Treasure Quests” by Hank Burchard, 5th October 1984) also give this decryption:

CEMETERY OFF GAP / TOOK RIDGE / PINEWOOD 4 M /
NORTH TOP OF HOLCOMBS ROCK / RIGGED A BOOM OF LOGS /
GOLD ORE HID / BARGE HOLDING TUBS /
CABOCHONS FACE LIDS / BUFORD VA /
VAULT CACHE OF GOLD / TB.

Is there no end to the fun people can have staring at a blank wall? Apparently not, it would seem.

But all the same, you can now tell all your friends the important life lesson you learned from the Beale Ciphers: Go Win Your Slice And Be Long In Love. Enjoy! 😉

Here’s a link to a 24-minute Youtube video of Elonka Dunin making a presentation on the Beale Ciphers a few weeks ago (November 2015) at PhreakNIC 19, a hacker/tech convention held in Nashville every year.

[ Note that in the following, I try to actively distance the Beale Papers (i.e. the pamphlet, which is hugely problematic as a source of historical evidence) from the Beale Ciphers (i.e. the three dictionary ciphertexts). ]

Elonka starts by showing a brief (but poor quality) intro to the Beale Papers courtesy of the TV history documentary series “Myth Hunters”, which you can tell is full of crackpot theorists serious historians because my face appears straight away. 🙂

Elonka’s Opinion…

Ultimately, Elonka’s opinion is that despite the crypto, both the Beale Papers and the Beale Ciphers are literary fakes, even though she appreciates that the Gillogly strings (which we should probably actually call the Hammer strings, after Carl Hammer who first described them) can very clearly be taken either as evidence of the Beale Ciphers’ fakery or as evidence of its genuineness.

In some ways, it’s not often individual cipher mysteries break down to an either/or (my apologies, I just heard Simon Munnery on “Quote Unquote”, which brought back fond memories of being filmed in a draughty warehouse for Munnery’s Kierkegaardian TV show “Either/Or” as a sort-of-quiz participant many years ago), so this is quite an unusual aspect of the Beale Ciphers. By which I mean that unlike the Voynich Manuscript’s ten thousand stupid competing theories, the presence of the Gillogly strings implies that there are only really two workable explanations for the Beale Ciphers (note: not the Beale Papers): (a) that they’re completely genuine, or (b) that they’re completely fake.

Specifically: if there’s any evidence that suggests that the Beale Papers are themselves anything but a lurid fabrication, I have yet to see it. In fact, the only actual issue would seem to be whether the papier maché fleshing out was done on top of a thin (but genuine) wire skeleton, or whether the underlying skeleton was fake as well.

My Opinion…

For me, I think it is reasonably likely that there was indeed a Thomas Beale who left a box (containing the cryptograms) behind at the Washington Hotel for safe keeping. But given that the innkeeper Robert Morriss didn’t actually start working there until 1823, it should be possible for us to directly conclude that the letters (in the pamphlet) apparently addressed to Morriss at the Washington Hotel and supposedly written in 1822 are therefore completely fake. Basically, Beale couldn’t have written letters to someone who wasn’t working there yet.

And if those letters are fake, then the backbone of the entire pamphlet is fake. And so I find it easy to agree with people who think that the Beale Papers are fake. But what, then, of the Beale Ciphers?

My own suspicion is that what we’re looking at here is – much as seems to have happened with the “La Buse” cryptogram – a fake story elaborated around the hearsay bones of a real (but poorly-understood) cryptogram. But, as again so often happens, perhaps there were several layers to the storytelling going on here.

Firstly, I suspect that Morriss made the first level of elaboration in order to justify his having broken the locks of a sealed container some years after it had been left at the Washington Hotel (presumably for safekeeping with a previous innkeeper). And I would expect that there was a second level of elaboration added by the person who became the next owner of the object (though I doubt we will ever know more about this shadowy person). And whether the topmost level of elaboration (to turn it all into pamphlet form) was added by Ward or Sherman probably matters not a jot.

So in the Beale Papers, it would seem from all this that what we have been handed down is a fictional story wrapped around a retelling of a self-justificatory lie, which itself in turn was wrapped around a set of three ciphertexts that themselves may or may not be real. No wonder it has proved difficult for people to make sense of it all!

Ultimately, though I think the Beale Ciphers are real, Elonka concludes otherwise: hence we sit either side of that particular either/or fence – but feel free to choose whichever side seems to you to have the greener grass. 😉