This paper reports a
statistical anomaly in B1 which suggests that it my be a hoax.
Keywords: Beale Cipher, homophonic cipher, book cipher, treasure cipher.
In 1885 James B. Ward of Virginia published a pamphlet describing a fabulous
treasure buried by an explorer named Thomas Jefferson Beale in Bedford County,
Virginia, over 60 years earlier. The location, contents, and intended
beneficiaries of the treasure were concealed in three separate ciphers. Ward
claimed to have broken the second cipher (B2), describing the contents, and
found it to be a book cipher based on the Declaration of Independence (DOI). The
words of the DOI were numbered consecutively, and each plaintext letter was
replaced with the number of a word in the DOI beginning with that letter. The
details of the encryption are discussed exhaustively by Dr. Carl Hammer [1], The
initials of words in the DOI are given in Table 1.
The first of the Beale Cipher papers (Bl) contains 495 numbers from 1 to 2906
(Table II). This would seem to preclude the DOI, with only 1322 words, from
being the key text. This impression is supported if the first few characters of
B1 are decrypted with the DOI, yielding SCS?E TFA?G CDOTT .... where ? stands
for the plaintext of a ciphertext number greater than 1322. This much gibberish
was probably adequate to dissuade early cryptanalysts from pursuing this line.
But it is difficult to bore a computer. I wrote a very simple program which
accepts as input a cryptogram in "Beale cipher" and the initial letters of any
document, and attempts the decryption. Table III shows the result of applying
the DOI to B1. If the DOI is the wrong key, the resultant text should be a
random sequence of letters drawn from the distribution of DOI initials.
There are a number of oddities in this "decryption," but the most striking is
the sequence ABFDE FGHII JKLMM NOHPP. Note in passing that the first F is
encrypted as 195 and that letter 194 of the DOI is a C. Similarly, the last H is
301, and letter 302 of the DOI is an O. Hammer [1] noted 23 examples where the
person who encrypted B2 made errors of this type, or about one every 33 letters.
But correcting these errors is not critical to the argument. We will henceforth
consider only the 14letter monotonically increasing string DEFGH IIJKL MMNO.
This is obviously an unlikely occurrence to tied in an assumed random text.
To establish just how unlikely, consider the following simple model: assume 26
letters of equal frequency and find the expected number of monotonic runs of
each length. For a sequence of length 3, say, the probability that the second
letter is equal to or one greater than the first is 2/26 or 1/13, assuming for
the sake of neatness that A is the successor of Z. Similarly, the probability
that the third letter continues the sequence is 1/13, so that the probability of
a sequence at least 3 letters long is 1/(13^2), or about 10^4. Thus one would
expect to find about three 495/(13^2) sequences of at least 3 characters in a
random text of 495 equally likely letters.
Continuing the argument, the probability of a sequence of at least 14 letters
is 1/(13^13), or about 10^14. In a random text of 495 characters, the odds
against getting a sequence this long would be about 10^12 to 1.
Those figures are only approximate because the frequencies of initial letters
in the DOI are assuredly not evenly distributed across the alphabet. The
prevalence of T (the, that, etc.) suggests that strings of T's would be
considerably more frequent. Hammer [l] shows 19% for T, which would give the
sequence TTTTT (which occurs at position 135) an expected value of 0.6
occurrences in a text this long, which is acceptably high. On the other hand, J
and K are very much less common. In order to construct the sequence DEFGH IIJKL
MMNO, the hypothetical random selection had to choose one of the 10 J's in the
DOI, followed by one of the 4 K's. The effects of the unevenness of the
distribution tend to offset one another.
How could this kind of sequence occur? Among the possibilities is that it is
a random event, and "just happened" in a cryptogram enciphered using another
document. This is quite unlikely, as the previous arguments show. Another
possibility is that the DOI is in fact the key, but that another level of
encryption (e.g. elimination of nulls) must be stripped away. My investigations
do not preclude this possibility, although I have been unable to extract any
intelligible plaintext from it. Also, Hammer [3] is convinced that the same
method was used to encrypt B1 and B2, and B2 did not use a second level of
encryption.
My inclination is to a third possibility: that at least the first document,
B1, is a hoax. 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.
The view of the Beale ciphers as a hoax is supported to some extent by the
decrypted message of B2 [2], which ends "Paper number one describes the exact
locality of the vault, so that no difficulty will be had in finding it." Hammer
has shown [1] that encryption was, for the author of B2, extremely laborious and
fraught with error. Why would he waste the effort of encrypting another 87
characters of a message which would be redundant when the first paper, B1, was
deciphered? When viewed as a hoax it makes perfect sense: the author wanted to
sell the idea that the first document was worth reading.
It is often much more difficult, if not impossible, to prove that a document
is meaningless than to extract the sense from a meaningful one. The observations
in this paper do not constitute an unequivocal proof that the Beale treasure
cipher, Bl, is a hoax, but they do constitute strong evidence that the
Declaration of Independence was used to encipher at least the long alphabetic
string. This fact should be taken into account in any theory of the authorship
and intent of the Beale Ciphers.
REFERENCES
1. Hammer, Carl. 1979. "How Did TJB Encode B2?" Cryptologia. 3: 915.
2. Innis, P. B. 1964. "The Beale Fortune." Argosy. August: 7071,
8284.
3. Kahn, David. 1967. The Codebreakers. New York: Macmillan. 771772.
1 WITCOHEIBN 101 LLATPOHTTS 201 AAEHSTMAMD 301 HOTPKOGBIA
11 FOPTDTPBWH 111 TRGAIAMDTJ 211 TSWEASTTRT 311 HORIAUAHID
21 CTWAATAATP 121 PFTCOTGTWA 221 BATFTWTAAB 321 OTEOAATOTS
31 OTETSAESTW 131 FOGBDOTEII 231 WALTOAAUPI 331 TPTLFBSTAC
41 TLONAONGET 141 TROTPTAOTA 241 TSOEADTRTU 341 WHHRHATLTM
51 ADRTTOOMRT 151 IATINGLIFO 251 ADIITRIITD 351 WANFTPGHHF
61 TSDTCWITTT 161 SPAOIPISFA 261 TTOSGATPNG 361 HGTPLOIAPI
71 SWHTTTBSET 171 TTSSMLTETS 271 FTFSSHBTPS 371 USITOTHASB
81 AMACETTAEB 181 AHPIWDTGLE 281 OTCASINTNW 381 OAWSSHHUNT
91 TCWCURTATA 191 SNBCFLATCA 291 CTTATFSOGT 391 ATTHHRTPOL
401 FTAOLDOPUT 501 IOAHRTTPAL 601 OATAAPOTSH 701 AUFPTBAMTT
41l PWRTRORITL 511 FTETSRITME 611 HEAMONOASH 711 PFAMWTSCOT
421 ARITTAFTTO 521 TATDOTFWAC 621 SOOTHOPAEO 721 IOTSFCOOTW
431 HHCTLBAPUU 531 WHHETPTPOT 631 TSHHKAUITO 731 APOTWFITOU
441 ADFTDOTPRF 541 SFTPOTLFNO 641 PSAWTCOOLH 741 WOCFDUIMCO
451 TSPOFTICWH 551 FRTPOTETMH 651 HATRTMIOAS 751 TBOTBJFTUB
461 MHHDRHRFOW 561 ARTCONAOLH 661 TTCPHHCWOT 761 STBTFPOFAT
471 MFHIOTROTP 571 HOTAOJBRHA 671 SUTAJFTOCA 771 FSOELIANPE
481 HHRFALTASD 581 TLFEJPHHMJ 681 UBOLGHATTA 781 TAAGAEIBSA
491 TCOTBEWTLP 591 DOHWAFTTOT 691 OPLFQLBOAT 791 TRIAOAEAFI
801 FITSARITCF 901 TABWCOCAPS 1001 TOWHPFRITM 1101 AWHCTBTTOO
811 TAOCAOMVLA 911 PITMBAATUI 1011 HTORPHBAOB 1111 CKTDTUWWII
821 AYTFOOGFSO 921 HOACNHHCOF 1021 RIAPWCITMB 1121 OCACTTHBDT
831 OLADTIWPTL 931 CTCOTHSTBA 1031 EAWMDATIUT 1131 TVOJAOCWMT
841 FUIACWHHAG 941 ATCTBTEOTF 1041 BTROAFPNHW 1141 AITNWDOSAH
851 HBDUOOHPAW 951 ABOTFTBTHH 1051 BWIATOBBWH 1151 TAWHTROMEI
861 WAUHHPOSRO 961 HEDIAUAHET 1061 WTFTTTOABT 1161 WIPFWTTROT
871 CBOTADTLOO 971 BOTIOOFTMI 1071 LTEAUJOUWH 1171 USOAIGCAAT
881 PHIATTTLAO 981 SWKROWIAUD 1081 RTOTCOOEAS 1181 TSJOTWFTRO
891 FMTCTWODDA 991 OAAXACIESO 1091 HWHATTNJAM 1191 OIDITNABAO
1201 TGPOTCSPAD 1301 FROTPODMWM
1211 TTUCAAOROT 1311 PTEOOLOFAO
1221 BFAISTTAAF 1321 SH
1231 AATTBCATAP
1241 CBTATSOGBI
1251 AOTBTDATAF
1261 AISTHFPTLW
1271 CPCAECATDA
1281 OAATWISMOR
1291 DAFTSOTDWI
Table I. Initial letters of words in the
Declaration of Independence.
71 194 38 1701 89 76 11 83 1629 48 94 63 132 16 111 95 84 341 975
14 40 64 27 81 139 213 63 90 1120 8 15 3 126 2018 40 74 758 485
604 230 436 664 582 150 251 284 308 231 124 211 486 225 401 370
11 101 305 139 189 17 33 88 208 193 145 1 94 73 416 918 263 28
500 538 356 117 136 219 27 176 130 10 460 25 485 18 436 65 84 200
283 118 320 138 36 416 280 15 71 224 961 44 16 401 39 88 61 304
12 21 24 283 134 92 63 246 486 682 7 219 184 360 780 18 64 463
474 131 160 79 73 440 95 18 64 581 34 69 128 367 460 17 81 12 103
820 62 116 97 103 862 70 60 1317 471 540 208 121 890 346 36 150
59 568 614 13 120 63 219 812 2160 1780 99 35 18 21 136 872 15 28
170 88 4 30 44 112 18 147 436 195 320 37 122 113 6 140 8 120 305
42 58 461 44 106 301 13 408 680 93 86 116 530 82 568 9 102 38 416
89 71 216 728 965 818 2 38 121 195 14 326 148 234 18 55 131 234
361 824 5 81 623 48 961 19 26 33 10 1101 365 92 88 181 275 346
20l 206 86 36 219 320 829 840 68 326 19 48 122 85 216 284 919 861
326 985 233 64 68 232 431 960 50 29 81 216 321 603 14 612 81 360
36 51 62 194 78 60 200 314 676 112 4 28 18 61 136 247 819 921
1060 464 895 10 6 66 119 38 41 49 602 423 962 302 294 875 78 14
23 111 109 62 31 501 823 216 280 34 24 150 1000 162 286 19 21 17
340 19 242 31 86 234 140 607 115 33 191 67 104 86 52 88 16 80 121
67 95 122 216 548 96 11 201 77 364 218 65 667 890 236 154 211 10
98 34 119 56 216 119 71 218 1164 1496 1817 51 39 210 36 3 19 540
232 22 141 617 84 290 80 46 207 411 150 29 38 46 172 85 194 36
261 543 897 624 18 212 416 127 931 19 4 63 96 12 l01 418 16 140
230 460 538 19 27 88 612 1431 90 716 275 74 83 11 426 89 72 84
1300 1706 814 221 132 40 102 34 858 975 1101 84 16 79 23 16 81
122 324 403 912 227 936 447 55 86 34 43 212 107 96 314 264 1065
323 328 601 203 124 95 216 814 2906 654 820 2 301 112 176 213 71
87 96 202 35 10 2 41 17 84 221 736 820 214 11 60 760
Table II. The Beale Treasure Cipher
(B1).
SCS?E TFA?G CDOTT UCWOT WTAAI WDBII DTT?W TTAAB BPLAA ABWCT
LTFIF LKILP EAABP WCHOT OAPPP MORAL ANHAA BBCCA CDDEA OSDSF
HNTFT ATPOC ACBCD DLBER IFEBT HIFOE HUUBT TTTTI HPAOA ASATA
ATTOM TAPOA AAROM PJDRA ??TSB COBDA AACPN RBABF DEFGH IIJKL
MMNOH PPAWT ACMOB LSOES SOAVI SPFTA OTBTF THFOA OGHWT ENALC
AASAA TTARD SLTAW GFESA UWAOL TTAHH TTASO TTEAF AASCS TAIFR
CABTO TLHHD TNHWT STEAI EOAAS TWTTS OITSS TAAOP IWCPC WSOTT
IOIES ITTDA TTPIU FSFRF ABPTC COAIT NATTO STSTF ??ATD ATWTA
TTOCW TOMPA TSOTE CATTO TBSOG CWCDR OLITI BHPWA AE?BT STAFA
EWCI? CBOWL TPOAC TEWTA FOAIT HTTTT OSHRI STEOO ECUSC ?RAIH
RLWST RASNI TPCBF AEFTB
Table III. "Decryption" of B1 using the
DOI.
