Crypto Challenge: The Mystery of the German Soldier’s Letter | Technology

Berlin was desolate. We were walking through the ruins of the Zoo Garden when I saw Martin’s body. We had met at the University of Erlangen, before the world went crazy. His arms were clutching a sheet of paper. Ilya, my partner, immediately launched for the sheet, then quickly throwing it to the ground when he realized that it was a handwritten note and not a bond or promissory note (which, on the other hand, would have had little value at that point). I picked up the note and put it in my pocket. That night when, like so many others, I couldn’t sleep, I opened the letter and began to read.

I woke up early and found Ilya to tell him about the letter. Now he seemed very intrigued by what could be so important to Martin that he wasted the last of his strength to get it written in a language secret.

“I doubt it’s a language exactly,” I corrected him. You have simply used some method to substitute other characters in the original message. A cryptographic method. I knew that German soldier. His name was Martin. I studied with him in Erlangen, and that’s why I can guess what art is hidden behind that letter. You may even be able to find out its content. With him I attended a seminar on the history of Cryptography in which the speaker began by explaining how Julius Caesar transformed his messages with a simple translation, replacing each letter with the one that occupied three positions ahead in the alphabet. Thus, following this method, the A is replaced by a D, the B by an E, and, when we reach the end of the alphabet, when the W has been changed to an X, we start again by sending the X to the A. For example , the message “Divide and conquer”, ignoring the accent, would be encrypted as “glylgh b yhqfhudv”.

“Well, this Caesar didn’t try too hard either,” Ilya interrupted.

-He didn’t need to – I replied with annoyance – surely the transmission was well protected by other means. But let’s go to ours. That encryption method, known as a Caesar cipher, can be implemented with a fixed jump of any number of positions, not just three. One option is that the letter has been encrypted in this way, so to decrypt it we would only have to find the size of the jump, which is not difficult (in the worst case, it would be enough to try the 25 possible jumps if we use the 26-letter alphabet).

– But you don’t think Martin used that method, do you?

– The truth is, no. One of the characteristics of the Caesar cipher is its determinism: each word is always encrypted the same. In the letter text, however, no two words are identical. Although it is a short text, it is unlikely that it will not contain any article or conjunction (el, la, en…) more than once. In the seminar we were told about a kind of advanced Caesar, called the Vigenère cipher, which is more or less like using several Caesar ciphers at the same time. A kind of “jump key” is fixed, which could be a string of the type (3, 17, 5) and the messages are encrypted letter by letter, using in each block of letters (in this case, of length three) that jump sequence. That is, if we encrypt the word CASA, the C is encrypted with jump 3, giving F, the A with jump 17, obtaining R, and the S with jump 5, resulting in the letter X. With the next A we start again, that is, we use jump 3 again, therefore encrypting it as D. Thus, the word CASA is encrypted as FRXD, and it cannot be detected that there is a repeated letter in the source text (which is usually called plaintext).

– Well, we’re ready. – Ilya said annoyed – If you used such a jump sequence, that card is undecipherable.

-You’re kind of right. In fact, the Vigenère cipher was for a time called the unbreakable cipher. But that nickname is quite large. And, it is also very possible that we have before our eyes the sequence of jumps. The sequence of hops that forms the key of a Vigenère cipher can be transmitted via a keyword; its length indicates the length of the jump sequence, and its letters indicate each specific jump to be made. It’s very simple, if the key is ESTA, the sequence of jumps is 4, 18,19, 0. Those numbers indicate the length of the jump from A to the letters E, S, T and A successively. But it is easier to explain this with a table.

– Pay attention. Row 0 is the one that corresponds to not skipping, that is, there is the clear text. On the other hand, if we want to encrypt using the ESTA jump sequence, we would look in the second column for the letters associated with the jumps (4, 18, 19, 0), which correspond to the letters of the ESTA keyword. At the time of encryption, the letter of the alphabet in plain of row 0 is replaced by the one below in the table, right in the row that indicates the corresponding length of the jump. And, well, to decrypt it would be necessary to reverse this process. Maybe, just maybe, the keyword is hidden in the soldier’s letter. It may also be that he is not, that Martin was cautious and agreed with his beloved Helga on a code word before leaving for the front. In that case we would be in a hurry. Nevertheless…

– However, is there another way? Ilya asked impatiently.

– Yes, Ilya, there is. Is there nothing else in the letter that catches your attention? – My interlocutor seemed to hesitate.

– Well… yes, actually…, well, I don’t speak German but I don’t understand why you bothered to include a poem in the letter.

-Exactly. And, even if you don’t know German, you can see that there is something strange in that poem, right? Count the syllables. She tries to read it. Is it really a poem?

-No. It does not rime. But what do I know about poetry…

-It is a quite famous poem, by the romantic poet Theodor Storm. But it is cut in a strange way, the written phrases do not match the verses… – solved the puzzle, I could not stop smiling. – I’m back to rest, Ilya. I’ll leave you alone to think about it, and, if you like, this afternoon we’ll read the letter together.

Crypto challenges will be published every 15 days. Readers can leave their solutions and discuss the problem in the comments on this page, so anyone who wants to solve it on their own is advised not to read it until they have cracked the puzzle. You can also email your responses [email protected]. In each new challenge we will publish the solution of the previous one, accompanied by a comment with some original or inspiring ideas that we have received.

Maria Isabel Gonzalez Vasco She is a professor of Applied Mathematics at the Rey Juan Carlos University and a member of the Governing Board of the Royal Spanish Mathematical Society.

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