The D’Agapeyeff Cipher, Unsolved for 80 Years!

[Image courtesy of Derek Bruff.org.]

One of my all-time favorite cryptography stories comes from the book The Spy That Couldn’t Spell, a true-life espionage story about a dyslexic man who hid, then encrypted the locations of, thousands of pages of sensitive documents he had stolen from the U.S government.

Why is it one of my favorite stories? Well, because the man in question FORGOT one of the cipher words he used to encrypt the location of his caches.

And it sort of unravels your master plan when you can’t remember a key element of it.

Amazingly enough, this isn’t the only example of a self-trained cryptographer who forgot how to solve his own creation. In fact, one example of this very dilemma remains one of the most famous unsolved codes and ciphers in the world:

The D’Agapeyeff Cipher.

daga

This is the D’Agapeyeff Cipher. This seemingly simple list of numbers contains a secret message. The only problem is… the creator, Alexander D’Agapeyeff, can’t remember how to decrypt it.

When he published a starter book on cryptography — Codes and Ciphers, first edition — D’Agapeyeff included this chain of 5-digit number bundles as a final challenge for the readers to unravel.

One of the first steps many aspiring cryptographers take is to break the numbers down into pairs instead of groups of five:

daga 2

One result of this is the pattern that every pair has 6, 7, 8, 9, or 0 in the tens column and 1, 2, 3, 4, or 5 in the ones column, which doesn’t seem like a coincidence.

And see those sequences where the same number appears three times in a row? Some cryptographers believe that is also not a coincidence.

Then, they cut off the two double-zero pairings at the end — because they believe they were nulls, empty space-filling characters simply designed to fit the 5-letter groupings pattern of the original code as a way to throw off codecrackers. (And, to be fair, D’Agapeyeff himself wrote about null entries in the book Codes and Ciphers.)

If you remove those double-zero pairings, you can arrange the numbers into a 14×14 pairing grid, like so:

daga 3

See those sequences where the same number appears three times in a row? More of them now.

Many cryptographers consider this to be the true starting point of cracking the D’Agapeyeff Cipher.

But then what?

Some believe that the key to solving the grid lies in the Polybius Square, another encryption device mentioned by D’Agapeyeff.

Essentially, you place the alphabet into a 5×5 grid, and use those numbers to encrypt the letters. Here’s a straightforward example:

daga 4

In this case, the word PUZZLE would be 35 45 55 55 31 15.

Another way to use the cipher is to pick a keyword to start it. For instance, if you chose POLYBIUS as the key word, then you go across, then down, writing POLYBIUS and then the rest of the unused letters of the alphabet in order, like so:

daga 5

Instead of 1-5 both across and down, you could do 1-5 across the top and 6-0 across the side, reflecting the pairings in the D’Agapeyeff Cipher.

Or, as someone pointed out, perhaps we’re thinking in the wrong language. Triple-letters are uncommon in English words, but more common in Russian words, and D’Agapeyeff was Russian born.

Overlooking simple things like that can make you miss crucial ways into an encrypted message.

So, do you have any thoughts on how to solve this 80-year-old encrypted challenge, fellow puzzlers? Let us know in the comments section below! We’d love to hear from you.


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Puzzles in Plain Sight: Spinning Yellow Circles edition

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About six months ago, I shared the story of a secret code lurking in plain sight, sitting atop the Capitol Records Building in Los Angeles. It’s not the only time that buildings have made their way into the blog; in previous posts, we’ve discussed the giant crossword adorning the side of an apartment building in Lvov, Ukraine, as well as the optical illusion awaiting art lovers in a Roman palace.

But it was the only time we’ve discussed a secret code being shared on the side of a building.

Until today, that is.

Yes, my friends and fellow puzzlers, there’s another building out there broadcasting secret messages for all to see. It’s also in California. And this one is more devious than the blinking light on the Capitol Records Building.

adobe semaphore 1

Say hello to Almaden Tower, the San Jose headquarters of Adobe, the software company behind Acrobat, Illustrator, and numerous other editing programs.

As you can see, there are four bright yellow circles beside the Adobe logo. These 10-foot-high digital lights all rotate. And if you pay enough attention, you might discover the secret message being broadcast.

The messages began transmitting in 2006. The code was cracked for the first time in 2007, and it wasn’t a brief message either. The lights were secretly transmitting the entire text of the Thomas Pynchon novel The Crying of Lot 49.

You see, the rotating circles allow for a form of semaphore alphabet, a way of secretly forming letters or symbols based on the position of each of the circles. They can be horizontal, vertical, a left-leaning diagonal, or a right-leaning diagonal. The various combinations of these positions create a semaphore alphabet of 256 possible characters.

adobe semaphore 2

But this was only the first part of the encryption. Even if you uncovered and charted this pattern, you still had to decode the secret messages detailing specific key words that would help you break the Vigenere encryption of the actual text.

It took MONTHS for two tech workers to figure out the semaphore language, decipher the code, and uncover the final message.

So naturally, just like the hidden alien language in the animated sci-fi comedy Futurama, it was replaced with a second, more complex code to be unraveled.

That code, which started transmitting in 2012, wasn’t broken until 2017 when a math professor started streaming footage of the Adobe building and charting the various positions of the circles.

But his examination led him to believe that it wasn’t just text being broadcast this time… it was an audio message. After discovering a chain of symbols that he believed was a space or bit of silence in an audio broadcast, he graphed the results, which resembled an audio wave.

It turns out, his suspicions were correct, and further analysis resulted in the true audio being uncovered: Neil Armstrong’s famous message from the moon landing.

Apparently, a new code and message are currently being brainstormed for Adobe’s devious puzzle monument. Who knows what Ben Rubin, the designer, has in store for solvers this time?


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A Puzzly Discovery Under the Sea!

We’ve talked quite a bit about the importance of Enigma machines in the past.

The quest to crack the unbreakable Nazi code machine spanned the Atlantic Ocean and resulted in never-before-seen collaborations between analysts, codebreakers, and puzzlers from all walks of life, dedicating hours upon hours every day to trying to unravel the secrets of German communications. Cracking the code would be the key to intercepting crucial information and outmaneuvering the Nazi war machine.

We’ve discussed those twin decryption locations — Arlington Hall in the US and Bletchley Park in the UK — as well as the efforts of codebreakers like Elizebeth Smith Friedman to dismantle the work of Nazi spymasters both during and after World War II.

The story of Alan Turing is inextricably linked with that of the Enigma device, even though there were three Polish mathematicians — Rejewski, Rózycki & Zygalski — who had already demonstrated that the Nazi code was breakable and even managed to reverse engineer an Enigma machine.

Strangely, we rarely talk about the Enigma machines themselves. They were dangerously efficient, as explained in this article from Atlas Obscura:

When the Nazis needed to send confidential messages, they entered the dispatches into the machine, which substituted every letter using a system of three or four rotors and a reflector, encrypting the message for a recipient Enigma machine to decode.

Getting Allied hands on one during the war was a top priority, so much so that the standing orders on German ships and U-boats was to throw them overboard and let the sea claim them, rather than risking the chance of the Allies getting ahold of one.

underwater enigma

But the sea doesn’t always keep secrets forever, and a recent dive by a marine biologist team discovered the remains of an Enigma machine in the Bay of Gelting:

He noticed a contraption tangled up in the fishing line the crew had headed down to collect. The device, which at first seemed like an old typewriter sitting under at least 30 feet of water, was a Nazi Enigma machine, likely one of hundreds abandoned and thrown overboard in the dying days of the German war effort.

And those devices still contain valuable information decades later.

Each Enigma machine has a serial number, and if this machine’s number is still legible after decades underwater, it could reveal which ship or Nazi unit the Enigma machine belonged to. This would allow researchers to track the use of the device and what impact its use or its absence had on the war effort overall.

Yes, it’s not just mussels and fish that call this device home, but a readily accessible history of the device itself, if we can only read it.

underwater enigma 2

And now, instead of being protected at all costs by German officers, this machine is now protected by archaeologists and researchers, sitting in a tank of demineralized water in order to flush out the salt and salt water that has so corroded the machine over time. It will spend almost a year in that tank before any restoration efforts can proceed.

Successful recoveries of these machines are understandably rare, and this is a chance to add to the historical record of codebreaking and puzzling during World War II. Here’s hoping we can stumble upon more of these lost treasures in the future.


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Does the History of Cryptography Begin in Ancient Egypt?

Puzzles in various forms have been with us for thousands of years.

We can look back at examples like riddles from ancient Greece and Sumeria, the Smyrna word square from 79 AD, or inscriptions from New Kingdom-era Egypt between the 16th and 11th centuries BC, which can be read both across the rows and down the columns. (These are informally referred to as “Egyptian crossword puzzles.”)

As it turns out, if we turn our attention to ancient Egypt, we may just find the earliest known example of an encrypted message as well.

If you go hunting on the Internet for the earliest examples of cryptography or encryption, you pretty much get one of three results:

  • The ancient Greek scytale
  • The Caesar cipher
  • The Tomb of Khnumhotep II

Naturally, as someone who fancies himself a puzzle historian, I’ve heard of the first two entries on that list.

The scytale is an encryption method where a piece of leather, hide, or parchment (let’s say leather for this example) is wound around a wooden cylinder of a certain width and length. A message is then written on the wound piece of leather. When removed from the cylinder, the message disappears, leaving only a strip of leather with what looks like a jumble of letters on it. Only someone with an identical cylinder can wrap the piece of leather around it and read the intended message. Our earliest verifiable reference to the scytale is from the Greek poet Archilochus in the 7th century BC.

The Caesar cipher is the most famous example of a letter-shifting substitution code where numbers or other letters represent the letters in your message. For example, if B is K in your cipher, then C is L and D is M, as if the alphabet has shifted. See? Simple. Your average cryptogram puzzle is more complex because you’re not simply shifting your letter choices, you’re randomizing them. The Roman historian Suetonius references Caesar’s use of the cipher in his writings during the rule of Hadrian in the second century AD.

But what about this Egyptian tomb?

The tomb in question was built for Khnumhotep II, a nobleman who lived in the twentieth century BC. He carried many impressive titles, including Great Chief of the Oryx nome, hereditary prince and count, foremost of actions, royal sealer, and overseer of the Eastern Desert. (Seriously, with titles like this around, modern companies can clearly do better than manager, CEO, or senior editor. But I digress.)

The main chamber of his tomb features an inscription carved around 1900 BC. This inscription features some strange hieroglyphics. What makes them strange is that they’re in places where you would expect more common hieroglyphs, and it’s believed by some Egyptologists that these substitutions are no accident.

Some do pass it off as an intentional effort to describe the life of Khnumhotep II in more glowing or dignified terms, utilizing loftier verbiage that would be uncommon to any commonfolk readers, similar to how legalese is used today to impress others or intimidate readers.

But others believe it to be the earliest known example of a substitution cipher, utilizing hieroglyphs rather than letters or numbers. For what reason, you ask? To preserve the sacred nature of their religious rituals from the common people.

Unfortunately, this disagreement among scholars makes it hard to point definitively at the tomb of Khnumhotep II as the first written evidence of cryptography.

I guess this falls into the same black hole as the first bit of wordplay, the first anagram, the first pun, or the first riddle. We’ll never know, because the first examples of all of these would most likely be spoken, not written. It’s not until someone decides to record it — in pictograph form, in a carving, in a bit of ancient graffiti to be discovered centuries later — that it becomes evidence to be discovered centuries later.

And who’s to say that the linguists and cryptography believers aren’t both correct? A substitution cipher is, at heart, simply an agreed-upon way to say one thing represents or means another thing. A euphemism, an idiom, a common slang word… heck, a word you say in front of your kids instead of a swear. These are all very simple substitution ciphers.

The truth is probably somewhere in the middle.

What we do know is that there was some wordplay afoot in the tomb of Khnumhotep II, even if we can’t be sure if the history of ciphers and codes started there.


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Musical Cryptography: Hiding Messages in the Music!

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In previous posts, we’ve explored many ways that messages can be encrypted or hidden. We’ve talked about legendary encryption methods like Caesar ciphers and Vigenere ciphers, as well as simpler auditory ones like Morse code and tap codes. We’ve seen encryptions through blinking lights, woven through crossword grids, and even knitted into scarves.

But did you know that composers can encode messages in their music, and have done so for centuries?

No, we’re not talking about subliminal messaging or tales of backwards messages hidden in metal songs. We’re talking about musical cryptography, and it turns out there’s not just music between the notes, but messages among them as well.

haydn

Now, to be fair, there is no evidence that musical encryption has ever been used for spycraft. (Sorry, Outlander fans.) Most of the time, composers simply entertained themselves by hiding the letters of their name or the names of others into compositions just because they could.

This sort of musical wordplay appears in compositions by Ravel, Debussy, and Shostakovich among others. Johann Sebastian Bach did this often enough that the succession of notes B-A-C-H is now called a Bach motif.

According to Western Michigan University Music Professor David Loberg Code:

Sometimes a musical version of a name is a subtle reference in the piece of music… Often it is very prominent; it is the main theme of the piece and is heard over and over. In that case, whether or not you know exactly how the composer translated the name into musical pitches, it is obvious that it is meant to be heard… They were not secretive about it.

It even proved therapeutic for some composers.

Johannes Brahms incorporated the notes A-G-A-H-E in bars 162 to 168 of the first movement in his 1868 piece “String Sextet No. 2 in G major.” By doing so, he included the name of Agathe von Siebold, a young woman he had fallen in love with. He and Agathe made plans to wed, but he later broke off the engagement to focus on his musical career.

But, by encoding her name into one of his works, he both honored her and gave himself closure on a relationship that would never be.

notes

The musical nature of this encryption technique makes it effective — because casual listeners wouldn’t notice anything hidden — but it also means that longer messages are harder to include naturally.

You see, the “spelling” can affect the music. Obviously, the more complex the message, the more it interferes with the actual musical composition and flow of the piece. To the untrained ear, this wouldn’t necessarily jump out, but to a trained ear, or at least a person experienced in reading music, it would be fairly obvious that something was amiss.

Musical ciphers are attributed to various composers (like Haydn) and even to writers like Francis Bacon, but arguably the greatest success story in musical cryptography goes to French composer Olivier Messiaen.

messiaen

His cipher matched a different note to each of the 26 letters in the alphabet. Unlike many other composers, he managed to develop a cipher that closely mirrored his own compositional style. Because of the similarities between his cipher and his traditional musical works, there was less of a chance that listeners would detect anything was off.

He managed to translate the words of philosopher Thomas Aquinas into an organ piece called “Méditations sur le mystère de la Sainte Trinité,” and cryptographers and musical historians alike praise him for doing so with complex rhythms and rich tones without spoiling his own works.

It’s clear that it takes both an artistic flair and a puzzler’s mind to make the most of musical cryptography. But then again, those two pursuits have crossed paths many times before, as evidenced by musically minded solvers like Dan Feyer, Patrick Blindauer, Jon Delfin, and friend of the blog Keith Yarbrough.

Perhaps the best of musical cryptography is yet to come.

[For more details on musical cryptography, check out this brilliant Atlas Obscura article by Christina Ayele Djossa.]


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Where Puzzles, Knitting, and Spycraft Combine!

You might have seen the news story last year about a woman who chronicled numerous train delays with her knitting while she worked on a scarf. (Though you probably didn’t hear that it sold on eBay for over 7,000 Euros.)

Knitting is a clever way to both eat up downtime waiting for the train and also document how long that train made you wait. Moreover, it’s sending a message in an unusual fashion — an image that speaks volumes.

And one thing we’ve learned over the years is that when you can send a message without words, spy agencies will jump on that bandwagon.

So it should come as no surprise to you that knitting has been part of spycraft techniques for decades.

True, it is far more common from someone to simply passively observe the enemy WHILE knitting and hiding in plain sight. This was very common in countries all over Europe. When you consider how often volunteers were encouraged to knit warm hats, scarves, and gloves for soldiers during wartime, it wouldn’t be unusual to see people knitting all over the place.

Some passed secret messages hidden in balls of yarn. Elizabeth Bently, an American who spied for the Soviet Union during WWII, snuck plans for B-29 bombs and other aircraft construction information to her contacts in her knitting bag.

Another agent, Phyllis Latour Doyle, had different codes to choose from on a length of silk, so she kept it with her knitting to remain inconspicuous. She would poke each code she used with a pin so it wouldn’t be employed a second time — making it harder for the Germans to break them.

But there was a small contingent of folks who went deeper, actually encoding messages in their knitting to pass on intelligence agencies.

It makes sense. Knitting is essentially binary code. Whereas binary code is made up of ones and zeroes (and some key spacing), knitting consists of knit stitches and purl stitches, each with different qualities that make for an easily discernable pattern, if you know what you’re looking for. So, an attentive spy or informant could knit chains of smooth stitches and little bumps, hiding information as they record it.

When you factor Morse code into the mix, knitting seems like an obvious technique for transmitting secret messages.

[What is this Christmas sweater trying to tell us?]

During World Wars I and II, this was used to keep track of enemy train movements, deliveries, soldiers’ patrol patterns, cargo shipments, and more, particularly in Belgium and France. There are examples of codes hidden through knitting, embroidery, hooked rugs, and other creations, often right under the noses of the enemy.

As more intelligence agencies picked up on the technique, it started to breed paranoia, even in organizations that continued to use knitters as passive spies and active encryption agents.

There were rumors that Germans were knitting entire sweaters full of information, then unraveling them and hanging the threads in special doorways where the letters of the alphabet were marked at different heights, allowing these elaborate messages to be decoded.

Of course, this could be apocryphal. There’s no proof such overly detailed sweaters were ever produced or unraveled and decoded in this manner. (Plus, a knitter would have to be pretty exact with their spacing for the doorway-alphabet thing to work seamlessly.)

During the Second World War, the UK’s Office of Censorship actually banned people from using the mail to send knitting patterns abroad, for fear that they contained coded messages.

Naturally, a puzzly mind could do all sorts of things with an idea like this. You could encode secret love notes for someone you admire or care for, or maybe encrypt a snide comment in a scarf for somebody you don’t particularly like. It’s passive aggressive, sure, but it’s also hilarious and very creative.

Now if you’ll excuse me, I need to unravel this gift from my aunt and see if she’s talking crap about me through my adorable mittens.

Happy puzzling, everybody!

[For more information on this topic, check out this wonderful article by Natalie Zarrelli.]


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