Years ago, Otto Leiberich, the former president of the West German cipher authority, told me about a little known encryption system developed by his team. Can you break a challenge cryptogram I have created with this system?

The  Double Columnar Transposition (DCT), also known as Double Cube (or “Doppelwürfel” in German) is a manual encryption system. It was used by East German agents during the Cold War. It is one of the best pencil-and-paper ciphers known.

 

How the DCT works

To explain the DCT, let’s encrypt the sentence TO BE OR NOT TO BE. We use RAIN as the keyword. First, we write the plaintext below the password:

RAIN
----
TOBE
ORNO
TTOB
E

Now, we sort the columns of the table such that the letters of the password stand in alphabetical order:

AINR
----
OBET
RNOO
TOBT
   E

Next, we read out the message column-wise: ORTBNOEOBTOTE. What we have done so far, is a single columnar transposition. If we apply the same procedure again (with a different keyword), we get a DCT.

The DCT has been examined intensively over the last few years. Blog reader George Lasry broke a DCT challenge I had created in 2007. Details about this story are available here.


Source: Schmeh

DCT with disturbed complex

Otto Leiberich (1927-2015), the former president of the West German cipher authority, was especially interested in the DCT. An article about cryptography he published in the German magazine Spektrum der Wissenschaft in 1999 can be regarded as the seminal publication about this crypto system (it is available online, but the box about the DCT is missing). Based on this article, I created my DCT challenge.

I met Otto Leiberich several times, and the DCT was always one of the things we talked about. In one of these conversations, Leiberich mentioned an improved variant of the DCT he called “Doppelwürfel mit gestörtem Komplex”, which translates to “DCT with disturbed complex”. I will use the abbreviation DCTDC for this method.

The DCTDC works like the DCT, except that a rectangular area in the matrix below the key word is not used. The size and the position of this area are a part of the key. For instance, if we encrypt the text ABCDE… with the keyword COMPUTER and the rectangular area (1,2,3,4), it looks like this:

COMPUTER
--------
ABCDEFGH
IJKLMNOP
Q***RSTU
V***WXYZ
A***BCDE
F***GHIJ
KLMNOPQR
...

To make things clearer, we encrypt the cleartext WILLIAM FRIEDMAN WAS A CRYPTOLOGIST with the keywords PARIS and MADRID and the rectangle (2,2,3,4). Here’s the first step:

PARIS
WILLI
AMFRI
ED
MA
NW
AS
ACRYP
TOLOG
IST

Now we change the order of the columns:

AIPRS
ILWLI
MRAFI
D E
A M
W N
S A
CYARP
OOTLG
S IT

This gives us the following intermediate result: IMDAW SCOSL RYOWA EMNAA TILFR LTIIP G

Now we use the keyword MADRID:

MADRID
IMDAWS
COSLRY
OW   A
EM   N
AA   T
IL   F
RLTIIP
G

Again, we change the column order:

ADDIMR
MDSWIA
OSYRCL
W A O
M N E
A T A
L F I
LTPIRI
    G

Here’s the ciphertext: MOWMA LLDST SYANT FPWRI ICOEA IRGAL I

 

The challenge

Now the question is: how secure is the DCTDC? It looks more difficult to solve than the ordinary DCT, but as far as I know, nobody has ever published any cryptanalysis results about this method (I don’t know any publication at all about the DCTDC). So, I created a challenge.

The following text is encrypted with the DCTDC:

VIGREWRIAOUEORSSAAIDAS
SGESRSIHUAWBMROURCHSNE
SLAODODOERDYBOLEINATGD
TBAATNNEEHSAREINSSLOYE
RRSSIMALHGISSEAOODRENE
GOIESERAYNUESLRLEUERSO
WILAALHTILTMORROBODAGS
GSOLATKRO

The plaintext and both keywords are taken from the English language. The keywords consist of 12 or less letters each. The size and the position of the rectangle are the same in both encryption steps.

Can you break this cryptogram?


Further reading: The low-tech cipher LC4

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Kommentare (8)

  1. #1 Detlev
    16. Februar 2019

    There is an “O” too much: TO BE OR NOTO TO BE:

  2. #2 Klaus Schmeh
    16. Februar 2019

    @Detlev: You’re right, sorry. I corrected it. This mistake doesn’t influence the challenge.

  3. #3 Richard SantaColoma
    http://proto57.wordpress.com/
    16. Februar 2019

    Well I didn’t get very far, and please forgive me if this is obvious. But I was stuck on the means of describing the rectangular missing portions. I see that this rectangle is defined by (1,2,3,4) in the “COMPUTER” example, and by (2,2,3,4) in the PARIS/MADRID example.

    And they are some sort of coordinates to designate the associated rectangular blanks sections, I’m supposing (I had thought maybe designating the diagonal corners, or like that). But I’ve not been able to see the way this is done. Can someone explain? Sorry if it is obvious, and I have missed it.

  4. #4 Klaus Schmeh
    16. Februar 2019

    @Rich: Sorry for not giving a more detailed explanation.
    (A,B,C,D) means that there are A columns left of the rectangle and B rows above it. The rectangle consists of C columns and D rows.

  5. #5 Richard SantaColoma
    http://proto57.wordpress.com/
    16. Februar 2019

    Thanks much! I probably should have figured that out… and my not doing so, probably an indicator of my chances of solving your challenge.

  6. #6 TWO
    Lubjanka, Russia
    17. Februar 2019

    ABC
    ABCD

  7. #7 Jerry McCarthy
    England, Europa
    17. Februar 2019

    Abo

  8. #8 George Lasry
    Givataim
    18. März 2019

    Klaus – I am back from a trip, looking now at this challenge. Question: are the keywords single words, or possibly some combinations of words (e.g. sentence or expression)?