Motivation:
I had now given up hope that Mr. Sanborn was going to make this easy (as if!). And I had learned a lesson too. Whereas in earlier times, I had considered the Morse Code snippets in the various Strata to be unnecessary for the solution (but perhaps helpful for confirmation, like “Dig Tale Interpretation” was) now I had an example (“(Wha)T is your Position”) that seemed to indicate otherwise. So it was with great chagrin that I noticed three Morse Code sections that I still had not either used or reconciled:
• Lucid Memory
• RQ
• SOS
That meant that the decryption game was most likely still a few layers deeper. Time to step it up a notch.
Pre-Step Observations:
I was intrigued by the number of “T”s and “O”s in the “information” that I had extracted from the original matrix, and I noticed a popular periodicity of 6 between some of them. So I wrote out this information in rows of 6 and computed the index of coincidence (IC) for each row along with an average. (See the Excel file, “PathofKryptos.xls”, which contains an IC calculator that you can play with.) For rows of 6, the average IC is 0.083, as shown in the figure below, which is pretty darned impressive even for such a short sequence of characters.
Based on this observation, I took as a premise that I may be seeking a poly-alphabetic solution with a period of 6. The correspondence of a period of 6 with the length of the word MEMORY was too nice for me too ignore. And if I were to assign some significance to “MEMORY”, then I should do something with “LUCID” as well. So following the examples of K1 and K2, I postulated that I might use the word “LUCID” to make a Vigenère table, shown in the next figure, and the word “MEMORY” as the periodic key. (This is known as A “Quagmire III” encryption/decryption process.)
Step Process:
Using the keyword “MEMORY” along with the table in Figure 14, you can decrypt the character string
“TMHTIPRKYAFDTQSOWSTXTKOCHWFXONRZVNFAVKOTUNTJIEOK”.
The result of the decryption process is
“EBXAJRAAJPPBEHBLDVEPEXXDXOVFXPARFZPEFACAGPEDPRXN”.
Post-Step Observations:
This result is simply amazing. Here is the histogram:
Note that four of the possible 26 letters (A, E, P, and X) represent 25 of the 48 entries. Over half! By pure chance, an arbitrary set of four letters should sum to 7.38 counts (on average), and for any set of 48 characters, the four most common should sum to 16.1 (on average) with a standard deviation of 1.8. Even English doesn’t typically yield this kind of regularity for its most frequent letters (although for character strings of such short length, it certainly can).
It is possible that there is an “Easter Egg” here. Note that these four prominent letters can be used to spell the word “APEX” (as observed by two members of the Yahoo Kryptos group, Larry McElhiney and Donna “Piranha” Byczkiewicz). Consider also the following quote:
• “The final part is obviously the, you know, the apex of the pyramid there.”
-Jim Sanborn, excerpt from interview in Wired Magazine
Now, I could go off and compute the odds that those specific four letters would account for 25 out of the 48 entries instead of the expected value of 7.38. If you do that, you find that the odds against are about 317 Million to one. Those kinds of odds just haul off and punch you in the face... but I may be falling into a trap: Jim Sanborn has probably said a lot of four letter words in interviews, not to mention 3 letter words or n-letter words, any of which I could attempt to find some kind of coincidence with. Instead, I am going to rely on the anonymous peaks and troughs of the histogram. By “anonymous”, I mean that I strip away all correspondence between the peaks and the particular letters that they belong to, and I consider what fraction of the entire sample space of 48 characters is occupied by sequences that have such dominant peaks (for any letters at all). The jury is still out with me over whether the correspondence to the word “apex” is significant in any way, but I have nevertheless decided to call this sequence of characters “the APEX Sequence” for future reference. Lets move on to the analysis of the histogram.
The APEX sequence has a remarkable amount of structure. Of note:
• The index of coincidence is .071
• The 4 most common letters account for 25 out of 48 characters in the sequence. On average, the top 4 letter counts in a random set of 48 characters sum to about 16.1, with a standard deviation of about 1.8
• There are 9 nulls. On average, a random set of 48 characters has about 3.95 nulls with a standard deviation of about 1.5
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•Computer simulations have shown that the odds of random strings with 48 characters having at least 9 nulls and whose top four peaks sum to at least 25 counts are about 138,000 to 1
According to these statistics, the APEX sequence possesses the type of structure that is typical for “lightly encoded” text but atypical for random text. Therefore I believe that I remain on the correct path. Unfortunately, the APEX sequence is still not plaintext. But at this point, I am not surprised. Here is another relevant quote:
“WN: Jim said that he took your techniques and then he deliberately masked them even more so that even you wouldn't know what was in the puzzle.
Scheidt: Ah hah. I can't respond to that one. I haven't heard him say that before. It's possible I guess. I haven't talked to Jim on what he did, but I do know ... there was some masking techniques that were used and that's about it.”
-Jim Sanborn, excerpt from interview in Wired Magazine
Much ado has been made about the mentioned “masking” techniques, but the examples provided by Scheidt suggest that he is referring to a very broad spectrum of techniques that completely conceal letter frequencies such that standard cryptanalyst techniques are no avail. My assertion that K4 is simply a (transposed) set of coordinates into a custom-designed array (the original matrix) is a particular example. Such a process would completely obscure the English frequencies. Whether Mr. Sanborn truly applied more “masking” techniques is unknown.
What remains, then, is for me to invert at least one more step. I believe that I am on the cusp, for there are few clues left unreconciled and distinct frequencies have emerged.
