Kryptos - The Cipher (Part 2)

This is Part 2 about Kryptos and the first post can be found here. In this post i will focus more on
speculations, brainstorming and solutions attempts.


One noticeable fact is, that the letters KRYPTOS somehow are involved in the decryption process of all previous ciphers. In K1 and K2 they were directly used as one of the keywords in the Vigenère-Variant Quagmire3. For K3 there are several ways to transpose the ciphertext in order to reveal the plaintext, but one of them has to do with ordering/reordering the letters of KRYPTOS alphabetically. So, it seems plausible, that also in K4 these letters play a role in one or the other way. A further hint towards this is, that the letters of KRYPTOS all appear on the right side or in direct neighborhood on the left side, as marked below:

$\small{\texttt{25| E C D M R I P F E I M E H N L S S T T R T V D O H W ? }}$$\small{\texttt{ O B }}$$\small{\texttt{ K R }}$
$\small{\texttt{26| U O X O G H U L B S O L I F B B W F L R V Q Q P R N G K S }}$$\small{\texttt{ S O }}$
$\small{\texttt{27| }}$$\small{\texttt{ T }}$$\small{\texttt{ W T Q S J Q S S E K Z Z W A T J K L U D I A W I N F B N }}$$\small{\texttt{ Y P }}$
$\small{\texttt{28| V T T M Z F P K W G D K Z X T J C D I G K U H U A U E K C A R }}$

The position of the seven letters for KRYPTOS are all touching each other. This seems too strange to be by chance and i am not the first who mentioned this [1].

Kryptos - The Cipher (Part 1)

Introduction

KRYPTOS - Von Jim Sanborn - Jim Sanborn, CC BY-SA 3.0,
https://commons.wikimedia.org/w/index.php?curid=8253447

Since I think that KRYPTOS does not need any introduction, I will only give you a brief description of one of the most famous and only partially solved ciphers known today:

1. KRYPTOS was constructed in Nov. 1990 on the ground of the CIA Headquarter in Langley, Virginia by Jim Sanborn
2. It contains 4 ciphers (K1,K2,K3,K4) on its left side and some kind of Vigenère-Table on its right side.
3. K1, K2 and K3 were solved by James Gillogly in 1999. Afterwards, the CIA and later the NSA claimed that they had a solution to the first three ciphers at an earlier point in time.
4. Ed Scheidt, a cryptoanalyst and former director of the CIA, gave Sanborn the input of possible cryptographic techniques to use.
5. K1 is a variant of the Vigenère-Cipher (Quagmire 3) with the codewords KRYPTOS and PALIMPSEST
6. K2 is a variant of the Vigenère-Cipher (Quagmire 3) with the codewords KRYPTOS and ABSCISSA
7. K3 is a Transposition cipher
8. Jim Sanborn said that the previous ciphers K1,K2 and K3 contain information that will help to solve the last cipher K4
9. 2010 Sanborn published the clue that the 6 letters from 64-69 of the ciphertext K4 decrypt to 'BERLIN'. Four years later, he revealed that the characters 70-74 decrypt to 'CLOCK'
10. However, K4 remains unsolved. 

This post is more of introductory nature, so if you already know a lot of KRYPTOS you will probably not learn anything new.

D'Agapeyeff Cipher (Part 2)

❚ I don't know why, but in the last days I used my spare time to think about the good old D'Agapeyeff Cipher.

      75628 28591 62916 48164 91748 58464 74748 28483 81638 18174
      74826 26475 83828 49175 74658 37575 75936 36565 81638 17585
      75756 46282 92857 46382 75748 38165 81848 56485 64858 56382
      72628 36281 81728 16463 75828 16483 63828 58163 63630 47481
      91918 46385 84656 48565 62946 26285 91859 17491 72756 46575
      71658 36264 74818 28462 82649 18193 65626 48484 91838 57491
      81657 27483 83858 28364 62726 26562 83759 27263 82827 27283
      82858 47582 81837 28462 82837 58164 75748 58162 92000

Remark: In the first post, i wrote that the puzzle only appeared in the 1939 version of the book but meanwhile i got new information. The puzzle is still contained in the reprinted version from 1949. The first version that comes without the puzzle is the version that was published in 1952.

Note that the puzzle was not altered in any way in the 1949 reprint. This can be seen as a clue, that D'Agapeyeff still believes that the puzzle itself was correct (e.g., not printed in a erroneous way).

Schmeh's cryptogram finally solved after 6 years!

Heureka, the cryptogram that was published in 2007 by Klaus Schmeh [1] was finally solved on 26.11.2013 by George Lasry. MysterieTwister (user: george4096) made today the official announcement about his achievement.

The Dorabella Cipher (Part 4)

Ok, let us shortly recall what we know:

1. As far as I know, all existing images of the Dorabella cipher do not show Elgar's original message, but Penny's rewritten version, which she published in her memoirs. Perhaps this act of rewriting removed some information that might have been helpful. For example: the orientation of the symbols; the length of the lines; since a horizontally reversed symbol is also a valid symbol, perhaps she wrote everything upside down; sometimes the cipher symbols are ambiguous, did she get the right direction of each symbol? etc...
2. Elgar used his cipher symbols at least four times: Lisz-Fragment, Courage Card set, Dorabella cipher, notebook.
3. The suggested solution(s) for each of these parts do not fit together, i.e., a solutions for the Lisz fragment can not directly be applied to the, e.g., dorabella cipher. 
4. This either means that those solutions are wrong, or that Elgar slightly varies his system each time, or that Elgar just uses his symbols as a replacement for the alphabet and executes each time a different encryption method, and those do not have anything in common except these symbols.
5. The only more or less convincing solution is the one from Tim Roberts, but which has shortcomings in its explanation how Elgar derived the mapping from a letter to a cipher symbol.
6. The last usage of his symbols was 23 years after he wrote the Dorabella cipher. In his notebook he wrote several possible orderings of his cipher symbols and also encrypted a few words. Figure 1 shows again this notebook page.
   One additional thing he does on this page is, that he writes the sentence "DO YOU GO TO LONDON TOMORROW" on the left side and counts the number of the occurrences of the letter "O". Is the related to his encryption method?
   

Double Columnar Transposition (Part 1)

Even in the 21st century, there still exists cipher methods that can be executed by pencil and paper and that are concurrently strong enough to resists the computational power of modern PCs quite well. One of those cipher systems is the Double Columnar Transposition Cipher (DCTC), or for the german speaking readers Der Doppelwürfel.

[Double Columnar Transposition Cipher]. The DCTC works as follows: Assume a plaintext $\mathcal{P} = n_1 n_2 ... n_k$. Pick two key words from an (e.g.) english dictionary or even better two short sentences: $\mathcal{K}_1$ and $\mathcal{K}_2$ of length $s_1$ and $s_2$ respectively. To encrypt a message, write the plaintext in a block (or matrix) layout with $s_1$ columns. Now sort the columns regarding the first keyword $\mathcal{K}_1$. E.g. using the plaintext THIS IS IMPORTANT and the first keyword DOUBLE:

$$ \begin{bmatrix}
\textbf{D} & \textbf{O} & \textbf{U} & \textbf{B} & \textbf{L} & \textbf{E} \\
- & - & - & - & - & - \\
\text{T} & \text{H} & \text{I} & \text{S} & \text{I} & \text{S} \\
\text{I} & \text{M} & \text{P} & \text{O} & \text{R} & \text{T}\\
\text{A} & \text{N} & \text{T} & & & \\
\end{bmatrix} \stackrel{\text{sort}} {\rightarrow}
 \begin{bmatrix}
\textbf{B} & \textbf{D} & \textbf{E} & \textbf{L} & \textbf{O} & \textbf{U} \\
- & - & - & - & - & - \\
\text{S} & \text{T} & \text{S} & \text{I} & \text{H} & \text{I} \\
\text{O} & \text{I} & \text{T} & \text{R} & \text{M} & \text{P}\\
 & \text{A} & & & \text{N} & \text{T}\\
\end{bmatrix}  \stackrel{\text{read column by column}}{\rightarrow}$$
(The keyword above the text is only displayed for clarity reasons.) After sorting, read the text column by column from the block, thereby skipping the empty places in the last row. In this order write the text again in block-size form, this time with $s_2$ columns. Again, sort the block according to the second keyword $\mathcal{K}_2$, here CUBE:
 $$ \begin{bmatrix}
\textbf{C} & \textbf{U} & \textbf{B} & \textbf{E} \\
- & - & - & - \\
\text{S} & \text{O} & \text{T} & \text{I} \\
\text{A} & \text{S} & \text{T} & \text{I} \\
\text{R} & \text{H} & \text{M} & \text{N} \\
\text{I} & \text{P} & \text{T} &
\end{bmatrix} \stackrel{\text{sort}} {\rightarrow}
\begin{bmatrix}
\textbf{B} & \textbf{C} & \textbf{E} & \textbf{U} \\
- & - & - & - \\
\text{T} & \text{S} & \text{I} & \text{O} \\
\text{T} & \text{A} & \text{I} & \text{S} \\
\text{M} & \text{R} & \text{N} & \text{H} \\
\text{T} & \text{I} & & \text{P}
\end{bmatrix}\stackrel{\text{read column by column}}{\rightarrow}$$
Read the text once again column by column from the block, which is the resulting ciphertex:

 TTMTS ARIII NOSHP

The Dorabella Cipher (Part 3)

Today, only a very small update regarding the Dorabella cipher.


Below is a timeline showing the 4 points in time when Elgar used his cipher symbols. If anyone knows of another point and can tell me what Elgar did with his symbols or what he wrote about them, please let me know.


Timeline:

1 - - - - - - - - - - 2 3 - - - - - - - - - - - - - - - - - - - - - - 4

1: 1885/86 - That is the Lisz-Fragment; the annotation he wrote on the side of some musical nodes [Figure 5,6, in Part 1].

2: 1896 - The Courage card set. He wrote his cipher symbols [Figure 3, in Part 2] on the first card of the set of nine cards on which he explained his solution of the Pall Mall Magazin cipher challenge.

3: 1897 - The Dorabella cipher [Figure 1, in Part 1].

4: 1920 - His notebook, that contains the example subsitutions [Figure 2, in Part 1].

Based on this timeline, one can see, that the timespan between $3$ and $4$ is $23$ years. Thus the cipher scheme approach written in his notebook could very well be some kind of effort to remind his old cipher system. The two events that are close in time are $2$ and $3$, that are the symbols from the Courage card set and the Dorabella cipher. Perhaps he used the idea of the challenge cipher (Nihilist cipher) in combination with his cipher symbols to construct the Dorabella cipher?

The Dorabella Cipher (Part 4)

D'Agapeyeff Cipher (Part 1)

The 1939 edition of D'Agapeyeff's book

Alexander D'Agapeyeff was a Russian-born cartographer who lived most of his life in London. He became famous for his excercise cipher, he left for the readers on the last page of the first edition of his book "Codes and Ciphers" published in 1939.

In the later revisions of his book, he removed this exercise. The reason, he said, was that he had forgotten how he did the encryption.

Perhaps he has not really forgotten how to do it, but he has made some mistakes that prevent him and everyone else from deciphering the message.

What makes me a little angry is that he did not reveal what he remembered. He probably still knew what method he was supposed to have used and some of the words that were in the message. Just as he knew that many people were working on a solution, why did he not support them with a little information?

The D'Agapeyeff cipher is one of those ciphers, from which is believed that it is no hoax, but a serious challenge to the cryptanalysists. Since Alexander was not a cryptologist, it is assumed that he used a cipher method from his book, or perhaps a combination of them. The cipher was also mentioned in various journal publications, like the Cryptologica [1] or the Cryptogram [2].

D'Agapeyeff cipher:

      75628 28591 62916 48164 91748 58464 74748 28483 81638 18174
      74826 26475 83828 49175 74658 37575 75936 36565 81638 17585
      75756 46282 92857 46382 75748 38165 81848 56485 64858 56382
      72628 36281 81728 16463 75828 16483 63828 58163 63630 47481
      91918 46385 84656 48565 62946 26285 91859 17491 72756 46575
      71658 36264 74818 28462 82649 18193 65626 48484 91838 57491
      81657 27483 83858 28364 62726 26562 83759 27263 82827 27283
      82858 47582 81837 28462 82837 58164 75748 58162 92000
 

The Dorabella Cipher (Part 2)

Elgar seems to have been so familiar with his cipherbet, that he even was able to quickly write some notes or annotations. Which means, that he either learned this cipherbet by heart or he could quickly deduce the corresponding cipher symbol from a given letter. And if so, why shouldn't it be possible that he quickly writes to Penny the more or less irrelevant note

  "P.S. Now drocp beige weeds set in it – bure idiocy – one endtire bed! Luigi Ccibunud lu'ngly tuned liuto studo two."

or reinterpreted 

"P.S. Now droop beige weeds set in it - pure idiocy - one entire bed! Luigi Ccibunud luv'ngly tuned liuto studo two."

as Tim Roberts solution suggests? In Figure 1 one can the three Pigpen circles for his solution.

Figure 1. The Pigpen circles for T. Roberts solution.

The red marked letters indicate symbols that are not used in the Dorabella cipher. Of course, he did not use this representation but used the key setence "LADY PENNY, WRITING IN CODE IS SUCH BUSY WORK", but this is how it would look like.

Figure 2. The cipherbet of Roberts (borrowed from www.ciphermysteries.com)

Applying this cipherbet to the Liszt-Fragement yields gibberish, which is not surprising, since he seems to (if Roberts is right) have chosen a special version for this Dorabella cipher.

To be honest, the chances that Robert's recovered plaintext is wrong are almost negligible. If a simple monoalphabetic substitution of a ciphertext yields not only English words, but in a meaningful order, then it is hard to believe that it is just a coincidence. There are so many letter dependencies in the text that it has to be correct somehow.

So, albeit i think it is overall the correct solution, it still bothers me that there are some shortcomings in its explanation.

In 1896, the Pall Mall Magazine published a code challenge, said to be "uncrackable", which finally was solved by E. Elgar. It was the Nihilist cipher and he was so proud of his solution that he painted it later on a wooden floor. He explained the solution on a set of nine cards (the Courage card set). On the first of these cards he drew the symbols:

Figure 3. The symbols from the Courage card set. Order unknown.

I am not sure if the order is correct. Since this is a full rotation of the 3-cusps symbols concatenated with the two other symbols in upright direction, its hard to believe that this encodes a word. What could have be his intention to draw this symbols on that card set?

The Dorabella Cipher (Part 3)

The Dorabella Cipher (Part 1)

Below, in Figure 1, you can see the famous Dorabella Cipher, which Edward Elgar wrote to Miss Dora Penny 1897.

Figure 1. The Dorabella Cipher (1897)

You can read more details about the background of Elgar, Penny and their families in the linked wikipedia article.

What makes this cipher so special is, that it was sent by Elgar (who liked to play around with ciphers and word puzzles) to a Lady who had no particular background or interest in ciphers. They only met a few times and yet Elgar was sure that she could somehow decipher his message.

Over the years, several solutions to the cipher have been proposed, but none has been accepted as correct by the community. It is thought to be a simple monoalphabetic substitution cipher and was not solved because of the short ciphertext, which neglects attacks based on letter frequencies.

So far, there is only one solution which seems somehow promising to me (Tim S. Roberts, Solution). It is because of the very meaningful recovered plaintext, but it still contains some really strange inconsistencies and doubtful steps. There are many websites that discussed his solution and i will not restate any of them here.

The symbols used in the Dorabella Cipher reminds one of a Pigpen Cipher. And this theory could be supported with some further hints:

The E-like symbols from the Dorabella Cipher also appear in some of Elgar's notebooks, see for example Figure 2. You can see, that Elgar is playing around in order to find a suitable letter-to-symbol configuration. On the bottom left you can see circles with a cross in them and those little marks at eight distinct positions.

Figure 2. Notes from Elgar (from 1920?) where he plays around with the same symbols.

This looks very much like a Pigpen Cipher approach to arrange symbols in a certain way to find a easy to recognize mapping from the alphabet to the cipher symbols. He also used the symbol-to-alphabet mapping, that is shown in the top left, to encode three messages on the page:

1. "MARCO ELGAR" (the name of his dog)
2. "A VERY OLD CYPHER"
3. "DO YOU GO TO LONDON"

In the 3. message, some symbols seem to be quite wrong or at least ambiguous, if we assume that he really wants to encode "DO YOU GO TO LONDON" as written in plaintext on the right side. And I have no clue why he adds the word "TOMORROW" on the right. Note that these notebook entries are made 23 years after the Dorabella cipher. Perhaps he was trying to remember his method.

Elgar used three different types of cipher symbols and each one could be oriented in eight different directions, thus in total 24 possible symbols. As usual, see also Figure 2, the letters I and J as well as U and V are combined to reduce the alphabet from 26 to 24 characters.

Figure 3. A Pigpen circle and a possible symbol mapping.

For such a Pigpen circle, there are \(2^8\) ways to orient the little marks on that \(8\) segments, either on the left or on the right side of the corresponding line. In Figure 3, you can see a possible configuration of the Pigpen circle. Since Elgar drew such circles several times, it is possible that he also used such circles for the Dorabella Cipher.

But even if he used this circles as the base for his Pigpen Cipher, in what order did he assign the letters to the circles segments? And did he used the same Pigpen circle for all 24 symbols or do they differ for the three different symbol types? Or did he somehow encoded all 24 symbols in one such circle? The last question is backed-up by the fact, that there are exactly 24 little lines on that circle. So each such line could represent a symbol rather than three of them.

This approach was also taken by Tony Gaffney and produced the, so called, Hellcat Solution.

Figure 4. Tony Gaffney's Pigpen circle for his solution.

The outcome is the text:

"B Hellcat ie a war using effin henshells! Why your antiquarian net diminuendo? Am sorry you theo o’ tis god then me so la deo da — aye"

I can not believe that this is the correct message, although i like the approach using this particular Pigpen circle. Surprisingly, in 1885, already a decade before writing the Dorabella cipher, Elgar used these symbols to make an annotation against a couple of lines of music.

Figure 5. Elgar's annotation from 1885.

You have to rotate the page about 90 degrees clockwise in order to read the cipher symbols correctly as done in Figure 6.

Figure 6. Rotated annotation text. Known as the "Liszt Fragment".

The Pigpen circle that Elgar used for this ciphertext is nowhere shown. This fragment became known as the Liszt fragment. Tony Gaffney suggests using a similar pigpen circle as for his Hellcat solution, which produces the plaintext:

"Mes it's one Frn seezhup"

Other annotations or pieces of text along the music lines in his notebook are said to be something like "Very good performance", "slightly out of tune", "poor", "beautiful", "I think you know this a little", "very well done august" and so on. Why should he wrote the itself rather cryptic sentence "Mes it's one Frn seezhup"? And why would he encrypt an musical annotation at all while leaving many others in plaintext?

The Dorabella Cipher (Part 2)