Cryptography

The History and Mathematics of Codes and Code Breaking

Tag: The Code Book (Page 1 of 3)

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.

1 Comment

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.

1 Comment

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).

1 Comment

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.

1 Comment

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.

 

9/11 Changed Everything

At the time Singh wrote the novel, there was no blatant reason for the government to use surveillance for the interest of national security. Then September 11, 2001 happened. This day completely changed the interests of both the American citizens and the government. After this terrorist attack, people were willing to give up their privacy in order to achieve more security. I am not saying that the government should have complete control over all communications all the time. What I am saying is that the government should have substantial surveillance over communications in order to prevent other significant threats to the citizens of the United States.

In times of fear, people are willing to give up some of their privacy in order to feel safer. The thing is, cryptography should not disappear. Cryptography will only keep improving, and there is little to nothing that the government can do to slow it down. What the government, mainly the NSA, can do is keep its cryptanalysis above and better than the cryptography present at the time. Then the government can use its cryptanalysis in order to analyze and read encrypted messages. The government used wiretapping in the 1920s, but its new weapon is code breaking. Of course, citizens will always want their information to be private, but with the new information age, the government can use data mining and break through encryptions in order to evaluate certain suspects without any normal computer user ever noticing. The government can give people the illusion of privacy while also providing them with the reality of security.

It’s not so much whether the government can have wide latitude but what it can do with its wide latitude. For all we as normal citizens of the nation know, the government can read any and all of our messages. The government has the technology to break into almost any kind of encryption with its super computers, so as long as the government stays within its boundaries of security and does not blatantly invade its citizens’ privacy, it can continue to successfully use its array of electronic surveillance.

Photo Credit: "tower1-2"  by Damlan Korman via flickr CC.

Photo Credit: "tower1-2" by Damlan Korman via flickr CC.

 

German Confidence Proves Costly

After early domination of the seas by German U-boats, Bletchley desperately needed to end the intelligence blackout. Through a series of dangerous raids on German U-boats, a German Naval codebook was captured, thus making the Naval Enigma transparent. Finally, Ally convoys could evade the deadly German vessels and British destroyers could

"German U-boat" Photo Credit: Joe Neary via Flickr

Photo Credit: "German U-boat" by Joe Neary via Flickr

go on the offensive. The Allied powers went to great lengths to not raise suspicion in Germany that their sacred Enigma machine was compromised. Fortunately for Bletchley, Germans were far too confident in the strength of their encryptions.

Although the Allies were now aware of the locations of numerous U-boats, they had to be careful not to attack all of them because this would warn Germans that they could no longer trust their communications. Therefore, they were careful to prudently attack and never risk destroying too many enemy ships at once. In one case, Bletchley became aware of a numerous amount of German tankers and decided to sink most of them, but not all as to not raise suspicion. The British destroyers successfully sank the ones they were supposed to, but then spotted the remaining German supply ships and sunk those as well because they did not know about this situation. Fortunately for the Allies, when the Germans realized about their lost ships, they thought of it as a misfortune because their Enigma was unbreakable. If the Germans had had less confidence in their encryptions, it is possible that they could have stopped the amount of information they were feeding the Allies, or even have used it against them.

Page 1 of 3

Powered by WordPress & Theme by Anders Norén