The History and Mathematics of Codes and Code Breaking

Tag: The Code Book (Page 1 of 3)

When Cryptographers Die

There were many strong ciphers that seemed impossible to decipher, but only one has the name "Great Cipher." The Great Cipher stood undecipherable for 200 years. Created by Antoine and Bonaventure Rossignol, it was used by King Louis XIV as a way to keep his secrets hidden, "protect details of his plans, plots, and political schemes." He was impressed by the cipher and the Rossignols' so much he gave the father-son duo offices near his apartments.

What made the Great Cipher so great was the combination of its use of syllables as cipher text in the form of numbers, and the death of both Antoine and Bonaventure. The Great Cipher was secure because it turned basic french syllables into cipher text into numbers, specifically 587 of them. As mentioned before, 200 years went by before it was deciphered. Many people tried their hand at the cipher and ultimately failed, died, or gave up before they could solve it. Along with the death of the Rossignols, there was no one to read the messages. This lead to messages being unreadable for years, thus securing the cipher for years until Etienne Bazeries deciphered the Great Cipher. This still took him a total of 3 years of work of using various techniques. Some of these techniques led to gibberish and complete restarts of his journey. He finally considered the numbers could be syllables, then he found a single word, "les ennemis," from a cluster of numbers that appeared several times. From here he could examine the other parts of cipher texts and decipher them.

The Great Cipher is remembered as one of the most secure ciphers in all of history. The techniques used to decipher it are still used in other deciphering techniques, and it is one of the "forefathers" of today's unsolved ciphers.

A False Sense of Security Plus Treason Equals Death

Portrait of Mary, Queen of Scots. BBC

Portrait of Mary, Queen of Scots. BBC

In Singh's The Code Book, the story of Mary Queen of Scots illustrates the dangers of having a false sense of security.  There are countless examples throughout history, but perhaps the most well-known example of a false sense of security is George Washington's crossing of the Delaware to attack the British on that fabled December night in 1776. The British had wrongfully believed that Washington's men were incapacitated and unable to attack, and as such they let down their guard. As we all know, Washington and his men pounced at this opportunity and were able to turn the tide in the American Revolution. If the British had not become so complacent and careless in their actions then the very country we live in probably does not exist today.

In this same sense, Mary and her fellow conspirators "let down their guard" by explicitly detailing plans of attack, names of conspirators, and other incriminating information in their letters. In saying that "The cipher of Mary Queen of Scots clearly demonstrates that a weak encryption can be worse than no encryption at all" (Singh 41), Singh is telling us that if someone believes they are using a strong encryption system, even if it is easy to crack, then they will be apt to send important information via the encryption system. However, if one knows that an encryption system is insecure, then they will be much more likely to restrict the information in the letters. In Mary's case, she fell victim to believing that her encryption system was much stronger than it was, and as a result once Thomas Phellipes easily deciphered the letters, she was sentenced to death. If Mary's group of conspirators had known their code could be easily broken, perhaps they would have been able to successfully take back the throne.

While this would seem to suggest to others using cryptography that they should not send any incriminating information via enciphered text, at the same time there might not be a better option. One has to wonder what better alternatives Mary and her co-conspirators had, even if they had known that their code could be broken. The letters were all being intercepted anyways, so in reality the plan could never have succeeded. However, Mary did teach anyone contemplating the use of encryption at least one thing:

A False Sense of Security + Treason = Death

The Importance of Logic

A confidence boost from winning the First World War led many Allied countries to lose their motivation for solving Enigma as they lacked the driving factors of fear and hardship that had provoked their initial incentive to win the war. This quickly caused German overconfidence in the security of Enigma, instigated by both the lacking effort of the Allied forces and the strength of the code itself. The Germans’ unshakable faith in their coding system would ultimately lead to their defeat as they mistakenly viewed Enigma as unbreakable.

While many other Allied countries initially gave up in most of their attempts to solve the code, Poland luckily realized the importance of having skilled cryptanalysts. Poland’s decision to hire mathematicians to solve the mechanical cipher of Enigma was one of the most crucial factors in the Allied success. By taking this mathematical approach, the cryptanalysts studied the machine’s operations and were thus able to analyze the scramblers’ and plugboard cablings’ effects.

Though creativity is an essential part of cryptanalysis, the Allied cryptanalysts used mathematics to focus more on the logical aspect of code breaking. By attacking Enigma through the discovery of repetition within the codes, the Allies were able to find patterns that uncovered the plaintext of the German code. In order to break Enigma, having a well-trained team of mathematicians was critical. Solving this highly advanced technology required a similar scientific approach in cracking its message.

Without Poland’s mathematical approach to solving Enigma, the Allied cryptanalysts would arguably never have cracked the code, as logic was the key factor in exposing the messages created by Germany’s cryptographers.

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The Navajo Code Talkers

A major reason for the Allied success during World War I was German overconfidence in the Enigma.  Because of their overconfidence, they were unaware that the British were deciphering their messages.  Although this played a large role, it is not the sole cause for the victory of the Allies.  In order to win the war, the Allies also had to have some defenses of their own.  One of these defenses came in the form of code.  The United States was in need for an impenetrable code so that its communications could be secure.  The answer came in the form of the Navajo, a Native American tribe.

The Navajo language is incredibly complex; it is unique and does not stem from any other language.  Singh quotes Philip Johnston, the mastermind behind using the Navajo language as code, "the Navajo tribal dialect is completely unintelligible to all other tribes and all other people."  The United States government employed 420 Navajo code talkers.  With these code talkers, the United States had a secure means of communication, which allowed for them to prevent disasters from happening and anticipate potential threats.  After the war, the Japanese even admitted that they had not made a dent in breaking the Navajo code.

Having a secure code is vitally important.  This is evidenced by the German failure to keep a secure code.  Once the British had broken the Enigma, German communications were readily available to the Allies.  This allowed for the Allied forces to gain the upper hand.  On the other hand, with the United States having a secure code, the Allies were able to communicate without fear of German or Japanese decipherment.  The Germans and Japanese may have been able to intercept the messages, but without knowledge of the Navajo language, decipherment was essentially impossible.


Übermensch and Unterseeboots

Who has the right to say how much lives are worth? Could allowing for the death of the few to save many be moral? Do the ends just have to justify the means in order to commit crime?*

Admiral Hall definitely thought so. He thought the protection of his knowledge of the decipherment of the German's message was more important than the lives of Americans due to the fact there was a possibility of prolonging the war should the knowledge of the decipherment reach the Germans.

However, I believe that it was not ethical. There had to be someway the British could have shared the information with the Americans so that the Germans would not expect their cipher had been broken. Gambling with the lives of people when not all the facts are known. At least as it seemed in the The Code Book, Admiral Hall based his decision off of a lot of "probably"s and not hard facts.

It could be said that Hall was just doing what was best for the future of his country, but that does not by any means translate to morality. Just because an action benefits the people around someone does not justify gambling the lives of foreigners.

Although I agree that it was safe for Hall to hold back on the alerting America when only a part of the cipher had been cracked, I think it would have been the best option to still open up about that level of communication. In other words, tell America what has transpired and that they (Britain) will let America know if the decipherment of the rest of the message changes anything. I think by being completely honest about everything will prevent America from distrusting Britain as it said America might do if Britain simply just told them about the decrypted message.


*This idea of taking morality into one's own hands is discussed by the German philosopher, Georg Wilhelm Friedrich Hegel, in his Übermensch theory (way before Nietzsche).

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Contextual Ethics

Ethics in times of war must be thought of differently from ethics in times of peace, however much we may want it to be otherwise. The focus of ethics during wartimes turns to utilitarianism. Utilitarianism is sacrificing the wellbeing of a few for the good of the many. It is “big-picture” thinking, striving to benefit as many people as possible, even if that means a few people must get hurt along the way.

When thought of in that context, Britain’s Admiral Hall’s decision not to tell American President Woodrow Wilson about the Zimmerman telegram makes perfect sense. If he had told President Wilson the contents of the telegram, the Germans would have been alerted to the fact that the British were able to read their messages, and would have changed their codes and created additional obstacles for Britain’s cryptanalysts, potentially costing Allied lives. The danger posed to America by Germany’s U-boat warfare, by comparison, put far less lives at risk, especially because it seemed likely that the United States would enter the war after the beginning of the U-boat attacks.

The reason Admiral Hall’s decision would seem unethical in the context of today is that the major powers of the world have not been involved in a worldwide or home-turf war in some 70 years, since the end of the Second World War. The focus of ethics has shifted from utilitarianism to a more deontological ethical viewpoint. Deontology, contrary to utilitarianism, concentrates on how ethical an action is without consideration for the consequences of the action. In this situation, it would seem Admiral Hall had a moral obligation to inform President Wilson of the Zimmerman telegram, simply because it would be “the right thing to do.” However, when thought of in the context of the First World War, Admiral Hall’s decision to bring the United States into the war in a more roundabout way seems the more logical and ethical choice.


Ancient Influences On A Modern World

In a world enveloped by constant communication and endless data transfer, the necessity for privacy remains a top priority. With the aid of cryptography, society hopes to maintain secrecy in various interests, ranging from personal matters to governmental espionage. Yet how secure can we ever truly become?

As human civilizations advanced, the intricacies of cryptography drastically changed over time. New solutions resulted in the drive to develop more difficult codes. When discussing cryptography, one must also closely analyze the circumstances surrounding a particular time period. Cryptanalysis methods and current information in one period can quickly become obsolete in only a few decades. Historical events may also cause rapid advances, such as in the Islamic golden age, or slowed progress, such as during the dark ages in Europe.

In The Code Book, Simon Singh notes that "Cryptanalysis could not be invented until a civilization had reached a sufficiently sophisticated level of scholarship in several disciplines, including mathematics, statistics, and linguistics" (Singh 15). Despite this, amateur cryptanalysts today can easily begin deciphering messages thought impervious in previous times. This can make Singh's statement seem contradictory, as these individuals develop the same approach as previous crpytanalysts without being taught.

However, Singh's statement still remains true. Today's individuals enter the world surrounded by a highly sophisticated society, much different than that of the previous societies. Many factors can influence the intellectual capacity of these amateurs, such as income level, access to necessities, or even parental support. Yet one thing remains certain - today's amateurs prove much more equipped to tackle these difficult ciphers than the best of the ancient world. While young students in previous centuries worried immensely over the seemingly constant political warfare, risk of being drafted into the army, or strong possibility of suffering from diseases, today's cryptanalysts can focus their minds strictly on their studies. Thus, despite never having learned about cryptography, the mere rigor and new advances of modern education and technology equips these individuals to quickly process and develop possible solutions to decipher these codes.

Cryptographic Darwinism

In the prologue of The Code Book, Singh introduced the “evolution of codes” and explained how codes are becoming more impactful in today’s society (Singh xiv). From encrypting simple user passcodes to concealing entire online databases, cryptographic methods are evidently becoming more and more widespread.

Along with the evolution of codes, we can also see an explosive evolution in technology and similarly in the media, which is one of the vital reasons why so many people, despite their lack of training in cryptanalysis, are able to utilize frequency analysis to solve substitution ciphers. For example, the many online resources that teach people about cryptography are easily more accessible today than they were decades ago.

Furthermore, considering the long history of cryptography, it is no surprise that methods of substitution cyphers, especially those that are elementary, are made public and passed on from generation to generation, and thus has become common knowledge to even the amateur cryptanalyst. Take The Code Book itself as an example; anyone who reads the book is exposed to, at the very least, the most basic frequency analysis approach in solving substitution cyphers. They can even be completely oblivious to what cryptography was before reading the book, but by simply comprehending the first chapter, the person has enough knowledge to create and solve simple substitution ciphers. Of course, the degree to how complex the ciphers they’ve created or can solve is probably not as high as what an expert cryptanalyst can achieve.

Nonetheless, the technology today allows even amateurs to be able to solve substitution ciphers despite their lack of a “sufficiently sophisticated level of scholarship” (Singh 15).

Don't Overlook the History of Seemingly Simple Things

Cryptography and cryptanalysis are two fields whose progress is intertwined; both make advances to either get an advantage over the other or to compensate for a breakthrough the other has made. As societies have progressed, the need for more complex methods of both encryption and decryption has risen along with the complexity of society.

Messages have been hidden and encrypted from prying eyes since the fifth century B.C. (Singh 4), but it wasn't until around 800 A.D. in the flourishing Arab empire that cryptanalysis was invented (Singh 17). Singh notes, "Cryptanalysis could not be invented until a civilization had reached a sufficiently sophisticated level of scholarship in several disciplines, including mathematics, statistics, and linguistics" (Singh 15). But ever since, the battle between cryptographers and cryptanalysts has employed the growing knowledge and technology of civilization, to the point where the decryption methods discovered by the greatest of Arab thinkers is now almost common sense for any elementary school child.

Why is that? Well consider for example how mathematical technology has advanced along with society. The abacus appeared in China as early as 500 B.C., followed by the invention of Arabic numerals in 1202, and just think of all the different models of TI-calculators that can be found at Target now (source). For a young child, counting with Arabic numerals is pretty simple, but the use of more complicated and advanced calculators takes more work and learning. The same goes for code-breaking: basic substitution ciphers can be easily figured out, but more complex codes and ciphers will take more time and effort.

This shows how far society has come in a couple thousand years; it shows how human knowledge builds upon itself to reach even higher. The breakthroughs by Arab cryptanalysts over a thousand years ago sparked entire industries and professions, and who knows, maybe a discovery in 2015 could change the entire future of cryptography and cryptanalysis.

The Evolution of Ciphers and the Human Mind

Over two thousand years ago, Julius Caesar's methods of secret keeping were deemed groundbreaking.  His use of the substitution shift cipher was effective and secure.  Today, however, many would find his seemingly indestructible cipher to be elementary.

Like most human inventions, codes and ciphers have constantly evolved over the years to become more complicated and much more difficult to break.  Because of this advancement, what were once the world's best ciphers and codes thousands of years ago have become simple puzzles that high schoolers, even middle schoolers, can deconstruct.

According to the author of The Code Book, Simon Singh, "[c]ryptanalysis could not be invented until a civilization had reached a sufficiently sophisticated level of scholarship" (Singh, 15).  The Muslim civilization achieved this heightened academic prowess due to its emphasis on being well-rounded, insightful humans.  Citizens studied a wide range of subjects, "including mathematics, statistics and linguistics" (Singh, 15).  Europeans, conversely, were stuck in the Dark Ages, unable to pursue the high scholastic level of the Islamic civilization.  While the Arabs were creating new ciphers and breaking old ones, Europe was far behind.

The Arabs had a significant advantage over the Europeans due to their overall knowledge of various subjects.  Similarly, humans today have an advantage over the Muslim civilization.  The ciphers that the Arabs were creating and breaking were much simpler than the ciphers are today, and after studying history and learning of ciphers and codes from old times, people today are able to easily decrypt old ciphers and codes.  Presently, individuals do not have to be trained in cryptanalysis because subjects such as mathematics and statistics are available to the average citizen.  Society today focuses almost entirely on “secular subjects” (Singh, 16), which is what led to the success of the Muslims.  People today also have greater opportunities to learn and have learned from history, so we are able to combat difficult problems, specifically ciphers, on our own, using past methodology, logic, creativity, and luck.

The evolution of the cipher is directly connected to the expansion of the human mind.  Substitution ciphers that were used by Julius Caesar are now commonly recognized and easy to decipher.  People today have a much more extensive knowledge of ciphers and codes, making the ciphers and codes easier to figure out.  As humans continue to advance, so will ciphers and codes and the means to breaking them.


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