In 2013 George Lasry broke a ciphertext many had considered unbreakable. In the wake of this success, a few crypto experts created a similar challenge with an even higher level of difficulty. Is this one unbreakable? So far, nobody has solved it.
The story of today’s unsolved cryptogram began in 1999, when Otto Leiberich, the former president of the German crypto authority Zentralstelle für das Chiffrierwesen (ZfCh), published an article in Spektrum der Wissenschaft. This article (written in German) is now available online (unfortunately, the box with the most interesting part is missing).
The Double Columnar Transposition
In his article, Leiberich mentions the “Doppelwürfel”, also known as the Double Columnar Transposition (DCT), an encryption method that was used by East Erman agents during the Cold War. The DCT is a cipher that can be carried out solely with paper and pencil – no machine or computer program is needed. It is one of the best manual ciphers known.
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 TOTO BE
Now, we sort the columns of the table such that the letters of the password stand in alphabetical order:
AINR ---- OBET RNOO OTOT E B
Next, we read out the message column-wise: ORNOBNTEEOOTOTB. 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.
During the Cold War, Otto Leiberich and his team worked intensively on the cryptanalysis of the DCT. In 1974, one of their results led to the exposition of spy Günter Guillaume, who was chancellor Willy Brandt’s senior aide.
In order to encourage research on the DCT, Leiberich suggested in his article that a double transposition challenge be put forward. Leiberich’s recommendations for this challenge included the following:
- Both keywords should have 20 to 25 characters.
- The lengths of the two keywords should be co-primes (no common divisor except 1).
- The length of the ciphertext should not be a multiple of the length of either keyword.
- A ciphertext of approximately 500 characters (which is approximately the product of the lengths of the two keys) should be used.
As Otto Leiberich never published a challenge of this kind himself, I decided to do so.
For my challenge, I chose an English plaintext and encrypted it using two keywords, both derived from English phrases longer than 20 letters. The length of the plaintext was 599. I published this challenge in 2007 in my book Codeknacker gegen Codemacher and on the internet. The cryptographic challenges site, MysteryTwister C3, took it over. In 2013, I published the DCT cryptogram in my top 25 unsolved cryptograms series (in German). Here it is:
I never expected that the DCT cryptogram could be broken. Neither did Otto Leiberich, who was very interested in this challenge.
Later in 2013, I received an email from a certain George Lasry from Israel. He claimed to have solved the DCT challenge.
As I receive mails of this kind quite often, I didn’t pay much attention to it. I decided to take a look at this alleged solution later, when I had more time. However, after three weeks, the people from MTC3 informed me that George’s solution in their view was correct. So, I checked George’s mail and I realised that the MTC3 people were right.
The DCT challenge was solved.
It turned out that George had learned about the DCT challenge in a video that shows Craig Bauer talking about unsolved cryptograms. He spent months trying to solve it. He developed new methods to attack a DCT cryptogram, and in the end, he even found two different ways to break the challenge. He published a detailed description of his success in Cryptologia.
When an article I wrote about the DCT challenge for Focus Online was read by Israeli journalists, George became almost a media star in his home country. He even was invited to a TV show.
Meanwhile, George and I are friends. I still feel sorry that I let him wait for three weeks before I confirmed his success.
DCT reloaded challenge
Now that the DCT challenge was solved, Arno Wacker, Bernhard Esslinger (both involved in MTC3) and I decided to create a new (and even harder) successor. In fact, we created even three new challenges. The most difficult one is titled “DCT Reloaded 3”. Here are the basic facts about it:
- Both key words have a length of 27-34 characters.
- Both key words are chosen randomly.
- The plaintext is in German.
- The plaintext was written by ourselves, not taken from an internet source (in fact, Jim Gillogly, another well-known codebreaker, had shown that the first DCT challenge could be broken by searching the internet for a text of the same length containing the same letters).
Here’s the ciphertext of the “DCT Reloaded 3” challenge:
There’s no doubt that this challenge is an extremely hard one. I expect that it will never be solved. However, I said the same about the first DCT challenge. And I was wrong.
Further reading: The Top 50 unsolved encrypted messages: 45. The World Record Challenge