Kryptos - The Cipher (Part 3)

This post is about is more or less a collection of several approaches and facts that has been said as well as some speculations.

▊ B-ary integer representation. According to [1] during a Question and Answer round, Jim Sanborn was asked again about the hint BERLIN. The question was if N decodes to B, Y decodes to E, etc, etc. and Jim confirmed it does. Emphatically. It is written, that Jim Sanborn rattled through the entire crib:
\begin{align}
  \texttt{N} &\stackrel{\text{decode}}{\rightarrow} \texttt{B} \\
  \texttt{Y} &\stackrel{\text{decode}}{\rightarrow}  \texttt{E} \\
  \texttt{P} &\stackrel{\text{decode}}{\rightarrow}  \texttt{R} \\
  \texttt{V} &\stackrel{\text{decode}}{\rightarrow}  \texttt{L} \\
  \texttt{T} &\stackrel{\text{decode}}{\rightarrow}  \texttt{I} \\
  \texttt{T} &\stackrel{\text{decode}}{\rightarrow}  \texttt{N}
\end{align} When the same question was asked to Ed, Jim cut in and said “I’m the only one who knows.” If we trust Sanborn, this neglects any form of Transpositional Cipher. So also the promising approach from Scott to use Quagmire3 with EMUFPHZLRFA (the first eleven letters from K1) and the linear congruence $77$+$38$x mod $97$, which yields BERLIN at the correct position, must be a dead end.

KRYPTOS - Unaligned letters; Source [1]

As i already wrote previously, Sanborn said that there are many interesting clocks in Berlin but we should delve into that particular clock. Hence many people tried to use the special way this clock works in order to get hints towards the used encryption system for K4. And the special way is, that the Berlin Clock uses a base 5 representation to illuminate the time.So lets stay with the idea that a different base representation of integers is the key to solve K4. Are the further hints towards such a usage? Yes, there are:

1. In the YouTube Video [4], Ed Scheidt mentions at least one time different base representation of information
2. The upperscript letters in row Y,A,R in row $15$. The also form the word ARY which is the typical term when talking about different base notations, e.g., $3$-ary numbers, binARY number, tenARY numbers or in general $b$-ary numbers. 
3. He created other sculptures using binary numbers (IRS Computing Center) [3].

The normal alphabet has $26$ characters and it is $26-1 = 5^2$ and $26+1 = 3^3$. So we have nearby perfect powers. For example, if we use the alphabet with 25 characters, where J equals I, we could use GF$(5^2)$ to represent the letters or GF$(3^3)$ if we add a further letter. However, K4 itself contains 26 different letters, which renders this approach a little bit less acceptable. So how to encrypt a plaintext using different base representations?

For example, if $A = 0, B = 1, \ldots,I/J = 9,\ldots, Z = 24$ then this translates into $0\cdot 5 + 0$, $0\cdot 5 + 1$ up to $4\cdot 5 + 4$.

Then one could e.g. use the Hill-Cipher method or any other form of transposition to mix up the coefficients. For example a simple swap of the tuple items would 'decrypt'
$$\texttt{O,B,K,R} \rightarrow (2,4),(0,1),(2,0),(3,2)$$
to
$$(4,2),(1,0),(0,2),(2,3) \rightarrow \texttt{X,F,L,S}$$
▊ Intentional vs. non-intentional errors. I will give arguments for both directions, intentional and non-intentional. Is there a plausible explanation for the error, is it a essential part to decrypt the cipher of did Sanborn just carved accidentally the wrong letter?

The first error is probably the wrong letter Q in IQLUSION. The picture below on the left shows Sanborn's original encryption chart for K1. In the first line, he wrote the keyword for K1. It can be seen, that he misspelled the word PALIMPSEST at two places. The first time already in the headline and the second time at the position where ILLUSION is encrypted. Because of the incorrect letter C in PALIMPCEST, the encryption results into erroneous cipherletter K. Albeit Sanborn said that this error is deliberate, for me it feels more like a human error and that it is non-intentional.

Sanborn's K1 encryption chart Source:
http://cryptocrap.blogspot.com/2011/07/kryptos.htm

The next error is the U in UNDERGRUUND. There is a picture of Sanborn's encryption chart for the K2 cipher, where he did not make this error. Of course, it is always possible that he just carved the wrong letter, but we neglect this case here. In [2] it is written that this error is not repeated on Antipodes, but after checking this i found that this mistake is still present (or am i being wrong?). So repeating this even a second time creates the impression that this error is intentional.

So notice, in both cases (IQLUSION, UNDERGRUUND) the plaintext was correct English. However, in the first time, he correctly carved the wrong cipher letter and in the second time he wrongly carved the correct cipher letter.

The left out S in K2 in line 14. According to [3], Sanborn said the following about this error:

He [Sanborn] also indicated that there was a missing character on the sculpture, probably something that would have resulted in a plaintext "X" before that section. He said that he had thought that with the missing character, the section in question would have come out to be an unintelligible scramble. Instead, he was astounded to see that by sheer chance, the resulting random text had turned out to be apparently intelligible English, "ID BY ROWS", although that was not what was intended.

There is a chance, that Sanborn accidentally skipped this letter during carving. But if not, he maybe tries to focus the attention to this particular two words. So the 'LAYER TWO' might have a deeper meaning?

The letters Y, A, R that are in upperscript in line 15. This is not a spelling error but can be classified as an alignment error. And there is no chance that this is non-intentional. These letters are so striking that they have to have a deeper meaning unless Sanborn inserted them as a trap to distract the people.
There are a lot of possible explanations for this:

1. As written above, a hint towards b-ARY integers, 
2. As Sanborn always says that the orientation is important, does this upperscript letters simply symbolize an exponent?
3. Or, as written in [7]: "does d Y A h R might mean that in each grouping of five letters (and many codes are written in groups of 5), that the 2nd 3rd and 5th letters need to be rotated/shifted up (or down) a notch".

Sanborn's K2 encryption chart Source:
http://cryptocrap.blogspot.com/2011/07/kryptos.htm

The additional L on the end of line 15 is the next error. Perhaps, since this is also on line 15, reading the errors from right to left yields L R A Y, which might be a short term for "Light Ray", A clue? As also mentioned at several places, the additional letter on the left side, the tableau side, of the sculpture leads to the same amount of letters on both sides.

The next intentional error is probably DESPARATLY.  In a short movie where Jim Sanborn talks about Kryptos, he holds the encryption chart for K3 in his hand. In the picture below on the right side you can see the beginning of the plaintext of K3: SLOWLY DESPARATLY SLOWLY... So unlike in the case of the first two errors (IQLUSION, UNDERGRUUND) he already made the error in the plaintext. So is
 it reasonable, that a made a spelling error while writing up a english text for a CIA sculpture? I think this is very doubtful and since he would have proofread the text carefully.

Sanborn's K3 encryption chart.
Source: https://www.dailymotion.com/video/x35x1vc [4:16]

The missing E in DESPARATLY from K3. You can not see it directly on the screenshot from the movie [6] and also not in the movie itself. But based on the fact, that you can see the beginning characters of the next lines and assuming that each line has the same amount of characters, the E can not be part of the plaintext, i.e., the E is already missing in the original plaintext. Below you can see the two cases. The first without the letter E which results into the correct starting letters for the following lines and second with the letter E. This results into into a wrong starting letter line 3.
\begin{align*}
&\texttt{SLOWLYDESPARATLYSLOWLYTHEREMAINSOFPASSAGED}\\
&\texttt{EBRISTHATENCUMBEREDTHELOWERPARTOFTHEDOORWA}\\
&\texttt{YWAS}
\end{align*}\begin{align*}
&\texttt{SLOWLYDESPARATELYSLOWLYTHEREMAINSOFPASSAGED}\\
&\texttt{EBRISTHATENCUMBEREDTHELOWERPARTOFTHEDOORWAY}\\
&\texttt{WAS}
\end{align*}

The reason why he maybe left of the E can be as simple as the argument that he wanted to whole K3 text make up a perfect rectangle (which is suitable for his chosen encryption method).

In [1] you can further read, that Jim went on to say that he still believes there’s something to be gained if we study his encryption charts that he released to the New York Times. He talked about how he released those in the context of we all wondered if the misspelled words were really mistakes, but he didn’t elaborate past that. JS was also involved in some smaller group discussions where individuals said he brought up his K1/K2 matrix and seemed mystified no one has gotten any thing more from it.

Jim: Okay, well, I mean, really, it's six characters out of 97. And I dangled the clue Berlin, but I also divulged - or gave images - of my original decoding charts, the ones that I - well, actually, for me they were encoding charts. And I think once the Krypto-philes study it in a forensic manner, there might be revelations in there. So in a way, I gave more than just Berlin. I think I gave other information as well.

▊ The missing USGS marker and the Kryptos Mini-Statue. According to [1] also the following conversation took place:

Someone asked if anything was buried on the CIA grounds relating to Kryptos and Jim said YES and went on to explain how a USGS marker was buried somewhere but was removed later.
Klaus: Was something placed by kryptos that we need access to to solve kryptos?
Jim: Yes, there is something buried adjacent to Kryptos. Jae and I went back to visit a couple of years ago, and they had removed it, but it is important.
Donna: Well, since it is not there anymore, can you tell us what it was or do you want to wait for that?,
Jim: The thing that was buried is a bronze USGS marker. It was half buried. It had little cross hairs on the top of it.

Bronze USGS marker with crosshair. Source:
kryptosfan.files.wordpress.com/2013/10/bronze-10.jpg

As you can see on the left, a USGS marker contains at lot more information than just little cross hairs. He says "... but it is important", but perhaps the information are not only important but also essential.









▊ The Kryptos Mini-Statue. I think many people dont know that there exists also a Kryptos Mini-Statue (see Figure below). The decryption of its ciphertext is the following:

\begin{align*}
& \texttt{CODESMAYBEDIVIDEDINTU}\\
& \texttt{TWODIFFERENTCLASSESNA}\\
& \texttt{MELYSUBSTITUTIONALAND}\\
& \texttt{TRANSPOSITIONALTYPEST}\\
& \texttt{HETRANSPOSITIONALBEIN}\\
& \texttt{GTHEHARDESTTODECHPHER}\\
& \texttt{WHTHOUTTPNQJHFCDZDHIU}\\
\end{align*}The decryption with correction:

Codes may be divided into two different classes — namely, substitutional and transpositional types (the transpositional being the hardest to decipher without the key).

The cipher algorithm was again the Viginere chipher with the short keyword 'RUG'. You can read more about this on [5] (german).

Kryptos Mini-Statue. Source:
scienceblogs.de/klausis-krypto-kolumne/files/2015/10/Kryptos-2015-020.jpg

▊ Miscellaneous

Below you can find some collections of conversations that took place at some points in time which i found on various websites:

Unknown: can we solve K4 without solving K1-K3 first?
Sandborn: Yes, but K5 cannot be solved without K4.

Kelly: Once this fourth passage is solved, if it is solved, you have said that there's actually - that that's just the beginning, that there's a riddle embedded across the entire sculpture. Elaborate.
Sandborn: Yeah, I mean, there - it is a riddle within a riddle. And the final passage will lead in several directions. The word directions is - I use intentionally. And that's it. I mean, what can I - if I say any more, I, you know, perhaps give away too much.

Unknown: Do you have to be on the CIA grounds in order to solve Kryptos?
Sandborn: No.
Unknown: So just by reading the text taken from Kryptos and posted online, you can solve the puzzle?
Sandborn: Well, yeah. That doesn't mean that what I've said in the piece doesn't do something physically there at the agency. So the effect of the piece might affect something at the agency so that you'd have to see what I did at the agency.
Unknown: What do you mean?
Sandborn: In part of the code that's been deciphered, I refer to an act that took place when I was at the agency and a location that's on the grounds of the agency. So ... you have to decipher the piece and then go to the agency and find that place. There are, for example, longitude and latitude coordinates on the piece, which refer to locations of the agency.
Unknown: When you say act do you mean an act that you did or that happened while you were there?
Sandborn: An act that I could have carried out. I refer to something I'd done out there.
Unknown: Something that you did do?
Sanborn: I made reference in the encoded text to something I could have done there.

At many places he admits that nobody has reversed the ciphers the exact way as he did it. Nor did anyone found how the derive the keys for K1 and K2 (PALIMPSEST, ABSCISSA). They were found via dictionary brute force, but this was the supposed way to do it.

Go to Kryptos - The Cipher (Part 4)

[1] https://kryptosfan.wordpress.com/tag/jim-sanborn/
[2] http://cryptocrap.blogspot.de/2011/07/kryptos.html
[3] http://elonka.com/kryptos/sanborn/IRS.html
[4] https://www.youtube.com/watch?v=25YFYKKKkDo&t=2104s
[5] http://scienceblogs.de/klausis-krypto-kolumne/2015/10/30/kryptos/
[6] https://www.dailymotion.com/video/x35x1vc
[7] http://www.geocities.ws/pf008/kryptos/kquotes.htm