Page 13 : Beale Ciphers Analyses

C3 and the signatures of the Declaration of Independence

   Is it just an uncanny coincidence that the character count of the 56 signatures of the Declaration of Independence is 618, the same as the C3 code count? Or that one of the signers is "Robt Morris"? Is there a connection to the "Robert Morriss" of the The Beale Papers ?

    This page documents our attempt to solve C3 based on this theory.

    My thanks go to a contributor from Florida for this suggestion, and for sharing his extensive Beale experience, ideas, and the following DOI image.

The signatures of the Declaration of Independence

    In more legible format, these are the 56 names, in the same order. Next to each name is its character count. The underlined portions are superfluous and excluded from the count.

    Character count totals:

    Admittedly, some of the characters at the end of the first name abreviations are difficult to read, and could lead to count errors. The original coder however, had the same problem and consequently the intriguing count similarity remains valid.

    The challenge is to find a way to fit these names into C3 without code conflicts. Where do we begin?

    We could write a program to try all the permutations, but this is impractical due to the immense quantity of possibilities. In scientific notation, there are 7.10999E+74 possibilities. For the decimal equivalent, move the decimal point 74 positions to the right and fill in with zeros. This computer program would take several months to run.

    The easiest starting points are usually the beginning or the end. C3 however, is coded in a manner to make this also impractical. At the beginning, there are 43 codes with no repetitions. Code 96 occurs at position 10 and again at position 44. It is the first repetition. With an average name length of 11 characters, we would have to enter five names before encountering the first repeat character as a test. Again, there are too many possibilities (458,377,920). Starting at the end and working back, there are 47 codes before the first repetition. These two starting points, beginning and end, are the two longest strings of non-repetitive codes in C3. It suggests that the coder was aware of this possible weakness.

    We then looked for short strings of non-repetitive codes, and discovered an interesting anomaly.

12-character string in C3 starting at position 530, with three overlapping substrings:

    This is our front door for this attack.

    The 6 and 7-character strings could be within a single name, but they probably span the end of one name and the beginning of the next. As the shortest name (WmPaca) is 6 characters long, they cannot span three names. Therefore, we generated a list of all the two-name combinations of the 56 names. There are 3080 (56X55) of them.

N.B: This list and all the others mentioned below are included in the EXCEL spreadsheet Signatures.xls which you can download at the end of this webpage.

    Note that the 7-character string overlaps the 6-character string by three codes, namely, 343, 264, and 119. Now we need to find the following:

1. Which 2-name combinations contain the same character 7 positions apart? There are 1628. Of these, some contain more than 1 such string, so the total number of 7-character strings is 2567.
2. Which 2-name combinations contain the same character 6 positions apart? There are 1851. Of these, some contain more than 1 such string, so the total number of 6-character strings is 3177.
3. Which of the 7-character strings found above end with the same three characters as the first three characters of the 6-character strings? Combine and overlap the matching 7 and 6 character strings into 10-character strings. There now remains 187.
4. Which of the 3080 2-name combinations contain these 10 character strings? There are only 56. These are possible candidates for insertion into C3 at that position.
5. But in creating the 10-character strings, we allowed the possibility that it could completely embed one of the short names, of 8 characters or less, thereby requiring a 3-name string for that code position. There are 21 such embedded names. We add these to the 56 above, for a total of 77 possibilities.

    Now, with reference to the three overlapping code strings in the graphic image above, we move on to the third string, bounded by "186". Note that the first 186 is two characters before our 10-character strings, and the second 186 is three characters before the end of our 10 characters. So we must find name matches for this pattern.

    With regard to the 21 embedded names there are four matches:

abraclARKWMPACAM
samuelchASEWMPACAM
phillivingstONGEOROSSOliverwolcott
geotaylORWMFLOYDF   

The first capitalized character is the beginning of the 10-character string, and fits in code 119 at position 532 of C3. Each of these has a terminating character which is the first letter of the following name. Note that there is only one name beginning with "O", and I have filled in OliverWolcott above.

    With regard to the previous 56 possiblities from step 4 above, we again look at the 3rd overlapping string (details in Signatures.xls) and reduce the possibilities to the following:

thoheywardABRACLARKCaesarrodney
johnhartABRACLARKCaesarrodney
elbridgegerryABRACLARKCaesarrodney
williamelleryABRACLARKCaesarrodney
wmhoopergEOCLYMERLYmanhall
geotaylorgEOCLYMERLYmanhall
thoheywardgEOREADEDWArdrutledge
wmfloydgEOREADEDWArdrutledge

    We now have a final total of 12 possibilities and are ready to begin inserting text in C3. For this purpose we use the Excel program explained in and downloadable from Page 12 of this website. In this program, the point of reference to begin entering is cell 53X, just above code 119. Enter the above possibilities with the first capitalized letter in that cell. As you enter, the same letter will appear in the other cells with the same code. It is then a matter of experimenting with the other names with the clues given by the new letters. Note the fifth code from the beginning of C3 is filled in and the letter can be matched against the fifth letter of the signatures.

Download the detailed files here: Signatures.xls 256Kb Note: This program is written in Excel 97 which is no longer supported or compatible with Windows Vista and Windows 7.

Comments

   I have tried all the possibilities and encountered code conflicts after the first few entries.

    This is the most intriguing idea I have yet seen on the Beale codes. The attempt above may have failed due to some overlooked detail, for example, my choice of spelling for some of the difficult-to-read signatures.

    It also has an aura of Edgar Allan Poe... as in his 'The Purloined Letter'... hidden in plain sight.

    The notion of overlapping code strings may also be useful in other attacks. There are four other overlaps of two each short strings, but the above is the only one I have found of three strings.

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