Craig Bauer: The Ongoing Mystery of Unsolved Ciphers (and new hope)

When a civilization first develops writing and few people are literate, simply putting a message down on paper can be all that is required to keep an enemy from understanding it. As literacy spreads, a more sophisticated method is needed, which is why codes and ciphers, a.k.a. “secret writing,” always follow closely on the heels of the discovery of writing. Over the millennia, ciphers have become extremely sophisticated, but so too have the techniques used by those attempting to break them.

In recent decades, everyone from mathematicians and computer scientists to artists and authors have created ciphers as challenges to specialists or the general public, to see if anyone is clever enough to unravel the secrets. Some, like the first three parts of James Sanborn’s sculpture Kryptos and the ciphers appearing in the television show Gravity Falls, have been solved, while others remain mysteries. The highly secretive online society known as Cicada 3301 has repeatedly issued such challenges as a means of talent scouting, though for what purpose such talented individuals are sought remains unknown. One unsolved cipher was laid down as a challenge by former British army intelligence officer Alexander d’Agapeyeff in his book Codes & Ciphers (1939). Sadly, when frustrated letters of enquiry reached the author, he admitted that he had forgotten how to solve it! Another was made by the famous composer Edward Elgar in 1897 as a riddle for a young lady friend of his. She, along with various experts, all failed to ferret out the meaning and Elgar himself refused to reveal it.

 

Elgar's cipher

Elgar’s cipher

 

Many unsolved ciphers appear in much more serious contexts. The serial killer who referred to himself as “The Zodiac” was responsible for at least five murders, as well as the creation of several ciphers sent to San Francisco newspapers. While the first of these ciphers was solved, others remain unbroken. Could a solution to one of these lead to an identification of the killer? Although many have speculated on his identity, it has never been firmly established. The Zodiac is not the only murderer to have left us such mysterious communiques, he is just the best known. Other killers’ secrets have persisted through relative obscurity. How many readers have heard of Henry Debsonys? In 1883, a jury sentenced him to death for the murder of his wife, after deliberating for only nine minutes. But this unfortunate woman was Henry’s third wife and the first two died under strange circumstances. Had Henry killed all of them? Will the ciphers he left behind confirm this? I think his ciphers will be among the first to fall this year, thanks to a major clue I provide in my book, Unsolved: The History and Mystery of the World’s Greatest Ciphers from Ancient Egypt to Online Secret Societies. There are many more such criminal ciphers. One deranged individual even sent threatening letters containing ciphers to John Walsh of America’s Most Wanted fame! The FBI’s codebreakers maintain a list of their top unsolved ciphers. At present, only two of these are known to the public, but many others that didn’t make the top 10 are available for anyone to try to crack.

How do codebreakers, whether amateur or professional, meet the challenges they face? Statistics and other areas of mathematics often help, as do computers, but two of the codebreakers’ most powerful tools are context and intuition. This is why ciphers have often been broken by amateurs with no programming skills and little knowledge of mathematics. Enter Donald Harden, a high school history teacher, who with assistance from his wife Bettye, broke one of the Zodiac killer’s ciphers by guessing that the egotistical killer’s message would begin with “I” and contain the word “KILL.” Context allows the attacker to guess words, sometimes entire phrases, that might appear in the message. These are known as cribs. During World War II, the German word eins (meaning one) appeared in so many Nazi messages that a process known as “einsing” was developed, searching the cipher for the appearance of this word in every possible position. In today’s ciphers, the word President appears frequently.

Of course, time and again cribs and intuition can lead in the wrong direction. Indeed, the single most important attribute for a codebreaker is patience. A good codebreaker will have the ability to work on a cipher for months, for that is sometimes what it takes to reach a solution, ignoring the body’s normal demands for food and sleep; during World War I, the French codebreaker Georges Painvin lost 33 pounds over three months while sitting at a desk breaking the German ADFGX and ADFGVX ciphers.

Fig 2

Fig 3Is it possible that some of the earliest known ciphers, dating from the ancient world, have survived unread by anyone other than those they were created for? I believe this is the case and that they’ve been hiding in plain sight, like the purloined letter in Poe’s classic tale. Those studying ancient cultures have long been aware of so-called “nonsense inscriptions.” These appear on Egyptian sarcophagi, Greek vases, runestones, and elsewhere. They are typically dismissed as the work of illiterates imitating writing, merely because the experts cannot read them. But all of these cultures are known to have made use of ciphers and some of the contexts of the inscriptions are so solemn (e.g. sarcophagi) that it’s hard to believe they could be meaningless. I’d like to see a closer examination of these important objects. I expect some of the messages will be read in the near future, if cryptologists can form collaborations with linguists. These two groups have worked together successfully in military contexts for many decades. It is time that they also join forces for historical studies.

With a very large number of unsolved ciphers, spanning millennia, having been composed by a diverse group of individuals, it seems likely that it will take a diverse group of attackers, with skills ranging over many disciplines, to solve them. Some mysterious texts may reveal themselves to clever computer programmers or linguists, others to those taking the psychological approach, getting into the creator’s head and guessing phrases he or she used in the cipher, and some may be broken by readers who manage to discover related material in government archives or private hands that provides just enough extra information to make the break. I look forward to seeing the results!

BauerCraig P. Bauer is professor of mathematics at York College of Pennsylvania. He is editor in chief of the journal Cryptologia, has served as a scholar in residence at the NSA’s Center for Cryptologic History, and is the author of Unsolved!: The History and Mystery of the World’s Greatest Ciphers from Ancient Egypt to Online Secret Societies. He lives in York, Pennsylvania.

Keith Devlin: Fibonacci introduced modern arithmetic —then disappeared

More than a decade ago, Keith Devlin, a math expositor, set out to research the life and legacy of the medieval mathematician Leonardo of Pisa, popularly known as Fibonacci, whose book Liber abbaci has quite literally affected the lives of everyone alive today. Although he is most famous for the Fibonacci numbers—which, it so happens, he didn’t invent—Fibonacci’s greatest contribution was as an expositor of mathematical ideas at a level ordinary people could understand. In 1202, Liber abbaci—the “Book of Calculation”—introduced modern arithmetic to the Western world. Yet Fibonacci was long forgotten after his death. Finding Fibonacci is a compelling firsthand account of his ten-year quest to tell Fibonacci’s story. Devlin recently answered some questions about his new book for the PUP blog:

You’ve written 33 math books, including many for general readers. What is different about this one?

KD: This is my third book about the history of mathematics, which already makes it different from most of my books where the focus was on abstract concepts and ideas, not how they were discovered. What makes it truly unique is that it’s the first book I have written that I have been in! It is a first-person account, based on a diary I kept during a research project spread over a decade.

If you had to convey the book’s flavor in a few sentences, what would you say?

KD: Finding Fibonacci is a first-person account of a ten-year quest to uncover and tell the story of one of the most influential figures in human history. It started out as a diary, a simple record of events. It turned into a story when it became clear that it was far more than a record of dates, sources consulted, places visited, and facts checked. Like any good story, it has false starts and disappointments, tragedies and unexpected turns, more than a few hilarious episodes, and several lucky breaks. Along the way, I encountered some amazing individuals who, each for their own reasons, became fascinated by Fibonacci: a Yale professor who traced modern finance back to Fibonacci, an Italian historian who made the crucial archival discovery that brought together all the threads of Fibonacci’s astonishing story, an American math professor who fought against cancer to complete the world’s first (and only) modern language translation of Liber abbaci, and the widow who took over and brought his efforts to fruition after he lost that battle. And behind it all, the man who was the focus of my quest. Fibonacci played a major role in creating the modern commercial world. Yet he vanished from the pages of history for five hundred years, made “obsolete,” and in consequence all but forgotten forever, by a new technology.

What made you decide to write this book?

KD: There were really two key decisions that led to this book. One was deciding, back in the year 2000, to keep a diary of my experiences writing The Man of Numbers. My first history book was The Unfinished Game. For that, all I had to do was consult a number of reference works. It was not intended to be original research. Basic Books asked me to write a short, readable account of a single mathematical document that changed the course of human history, to form part of a series they were bringing out. I chose the letter Pierre De Fermat wrote to his colleague Blaise Pascal in 1654, which most experts agree established modern probability theory, in particular how it can be used to predict the future.

In The Man of Numbers, in contrast, I set out to tell a story that no one had told before; indeed, the consensus among the historians was that it could not be told—there simply was not enough information available. So writing that book would require engaging in a lot of original historical research. I had never done that. I would be stepping well outside my comfort zone. That was in part why I decided to keep a diary. The other reason for keeping a record was to ensure I had enough anecdotes to use when the time came to promote the book—assuming I was able to complete it, that is. (I had written enough popular mathematics books to appreciate the need for author promotional activities!)

The second decision, to turn my diary into a book (which only at the end found the title, Finding Fibonacci), came after The Man of Numbers was published in 2011. The ten-year process of researching and writing that book had turned out to be so rich, and so full of unexpected twists and turns, including several strokes of immense luck, that it was clear there was a good story to be told. What was not clear was whether I would be able to write such a book. All my other books are third-person accounts, where I am simply the messenger. In Finding Fibonacci, I would of necessity be a central character. Once again, I would be stepping outside my comfort zone. In particular, I would be laying out on the printed page, part of my inner self. It took five years and a lot of help from my agent Ted Weinstein and then my Princeton University Press editor Vickie Kearn to find the right voice and make it work.

Who do you expect will enjoy reading this book?

KD: I have a solid readership around the world. I am sure they will all read it. In particular, everyone who read The Man of Numbers will likely end up taking a look. Not least because, in addition to providing a window into the process of writing that earlier book, I also put in some details of that story that I did not fully appreciate until after the book had been published. But I hope, and in fact expect, that Finding Fibonacci will appeal to a whole new group of readers. Whereas the star of all my previous books was a discipline, mathematics, this is a book about people, for the most part people alive today. It’s a human story. It has a number of stars, all people, connected by having embarked on a quest to try to tell parts of the story of one of the most influential figures in human history: Leonardo of Pisa, popularly known as Fibonacci.

Now that the book is out, in one sentence if you can, how would you summarize writing it?

KD: Leaving my author’s comfort zone. Without a doubt. I’ve never been less certain how a book would be received.

DevlinKeith Devlin is a mathematician at Stanford University and cofounder and president of BrainQuake, an educational technology company that creates mathematics learning video games. His many books include The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter That Made the World Modern and The Man of Numbers: Fibonacci’s Arithmetic Revolution. He is the author of Finding Fibonacci: The Quest to Rediscover the Forgotten Mathematical Genius Who Changed the World.