In my last post from November 24, 2010 I attempted to identify the "row-columns" and "column-columns" that exist from using a polybius square for the substitution phase of the encryption.
I did do some due diligence and check the frequency counts for each digit of a 7x28 matrix, but saw no compelling evidence to suggest this shape was used.
My focus then remains on the 14x14 transposition matrix. Once the columns are paired (un-fractionated?) there will be a 7x14 (98 character) simple substitution cipher remaining. The trick is first solving the the transposition encryption independently of the substitution.
Tiago Rodrigues does a great job summarizing this strategy on his D'Agapeyeff.com website.
Back to the 14 columns, and the transposition space:
| C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | C11 | C12 | C13 | C14 |
| 5 | 4 | 4 | 3 | 5 | 4 | 3 | 4 | 2 | 5 | 5 | 3 | 2 | 2 |
| 2 | 4 | 5 | 5 | 4 | 5 | 5 | 1 | 2 | 3 | 2 | 3 | 3 | 4 |
| 2 | 4 | 3 | 5 | 3 | 5 | 2 | 1 | 5 | 2 | 4 | 5 | 2 | 2 |
| 5 | 2 | 2 | 1 | 2 | 3 | 1 | 1 | 1 | 4 | 4 | 2 | 2 | 2 |
| 1 | 4 | 4 | 3 | 5 | 2 | 4 | 4 | 5 | 4 | 4 | 3 | 2 | 3 |
| 2 | 3 | 1 | 1 | 4 | 2 | 3 | 3 | 1 | 1 | 1 | 4 | 2 | 5 |
| 1 | 1 | 5 | 5 | 3 | 2 | 3 | 5 | 4 | 2 | 3 | 2 | 3 | 1 |
| 4 | 3 | 4 | 5 | 1 | 3 | 2 | 4 | 1 | 4 | 5 | 2 | 2 | 4 |
| 1 | 1 | 5 | 5 | 5 | 2 | 5 | 5 | 2 | 2 | 4 | 2 | 5 | 5 |
| 4 | 1 | 3 | 5 | 1 | 1 | 1 | 4 | 5 | 2 | 1 | 5 | 4 | 4 |
| 1 | 4 | 5 | 4 | 4 | 1 | 3 | 5 | 4 | 4 | 1 | 2 | 5 | 5 |
| 4 | 4 | 5 | 2 | 5 | 2 | 3 | 5 | 5 | 1 | 5 | 3 | 2 | 1 |
| 5 | 2 | 5 | 2 | 4 | 1 | 3 | 2 | 5 | 1 | 2 | 5 | 1 | 2 |
| 4 | 2 | 3 | 2 | 5 | 4 | 4 | 4 | 1 | 3 | 4 | 2 | 3 | 2 |
I surmised that columns C3, C7, C12, and C13 were likely to be "row-columns" while C1, C8, C11, and C14 were likely to be "column-columns" based on differing frequency counts for each of the 5 ciphertext characters. The remaining six columns were sorted into row-columns or column-columns based on their frequency distribution.
Another member of the D'Agapeyeff cipher Yahoo! forum continued with some analysis of his own based on my assumptions to date. That analysis is located here. The outcome is similar to my findings with the caveat that C4 and C10 don't seem to favor being a row or a column.
Additionally this analysis output the largest Phi values possible - where 584 is the maximum value and is attained when the pairs are:
C1 - C6
C2 - C12
C5 - C7
C8 - C14
C9 - C13
C10 - C4
C11 - C3
If you recall, 634 is the expected Phi value for English text where N=98. 584, as well as several other sets of column pairings fall within an acceptable range, however no value of Phi(o) exceeds 634.
Assume for a moment that these are the correct column pairings, what remains is a 7! transposition which when in the correct order will leave a very simple substitution cipher.
Perhaps we're making headway against this as yet unsolved cipher.
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