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.
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
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.