The History and Mathematics of Codes and Code Breaking

Tag: Singh (Page 1 of 4)

The Greatest Cipher

Louis XIV's Great Cipher was unique in its complexity, far far beyond the other ciphers used during the time period. Indeed at the time, by far the most popular type of cipher was the mono alphabetic substitution cipher, yet that is easily deciphered by a good cryptanalyst through the use of frequency analysis.  The Great Cipher was much more than a simple mono alphabetic substitution cipher in that it utilized numbers to represent letters, but on top of this, the numbers didn't just stand for letters they also stood for syallables. Since there was not a 1 to 1 relationship between letters and the cipher alphabet, it was nearly impossible to perform traditional frequency analysis on the cipher text. Furthermore, the cipher was brilliantly created with cipher text indicating to ignore the previous syllable or letter, making it tricky for any decoder to figure out what was part of the cipher and what was simply nonsense.

Perhaps the deciphering of the Great Cipher is even more impressive than the creation of such a complex cipher. The amazing creativity and brilliant thinking that Bazeries had to even consider looking at syllables has to be commended. Furthermore, for him to harp on a repeated phrase and be able to figure out what it meant is incredibly impressive. This also illustrates how amazing the cipher was in that it took Bazeries over three ears to crack it even with his uncanny ability to recognize that it is comprised of syllables.

Diffusion of Knowledge and Awareness

In the time of Mary Queen of Scotts, Mary, her conspirators and others trusted the encrypted messages would remain secret, trusted the difficulty of their key, and trusted the inability of others to decipher coded messages. Even though they were not aware that their trust ended in Mary Queen of Scotts death sentence, it was this lack of knowledge and lack of paranoia that allowed this to occur. The environment in Chapter 2 represents that of knowledge and awareness. As people were able to decipher others coded messages it posed the question: who says they can't determine mine? With this increasing awareness of other peoples similar capabilities, this then caused a lack of trust in the system and even deterred from the use of encryption. If an encrypted message was likely to be decrypted by an unknown and unintended recipient, there was not point in writing the message. The ability to decipher others messages also turned into a game. For example, since people did not trust the mail or content of the letters from being discovered, they attempted to write notes in newspapers where at least their identities could remain anonymous. However, cryptanalysts then responded to these messages using the coding system in the previous message. In one instance, a woman aware that her code had been broken warned her recipient through the next newspaper that the code had been broken except she used the same code to relay the message and stated his name. This scenario is humorous as the woman now told the cryptanalysts the recipient's name making the system just as compromised as letters had been. Overall, the new environment caused awareness to increase leading to more caution in transporting private messages, and also led to the yearn to create more difficult coding systems that could not be deciphered easily.

A false sense of security

In Chapter 1 of Singh’s The Code Book, he states that “The cipher of Mary Queen of Scots clearly demonstrates that a weak cipher can be worse than no cipher at all”. Singh means that sometimes having a layer of security can be more detrimental than having none at all because it gives the sender and receiver a false sense of security.

If the sender and receiver are under a false sense of security due to their encryption, they are under the assumption that if it is intercepted it will not be deciphered. Thus, they may be think it is fine to make their intentions clear in the passage, or even worse, give details of other unnecessary information. However, this provides incriminating evidence in ‘black and white’ — literally. This is demonstrated by Babington’s ease in providing details of the plot to Queen Elizabeth as well as providing the names of his co-conspirators. However, if there was no encryption, both sender and receiver would be more inclined to make sure the message didn’t contain any information that could incriminate them as well as taking further measures to ensure that the message doesn’t get into the hands of the enemy, unlike Babington’s trust of Gifford, who was acting as a double agent. Singh also implies that people who, like Babington, tried to keep their messages safe through ciphers often overestimated the strength of their ciphers. This often lead to an incorrect feeling security which in turn ended badly, and in some cases tragically.

To conclude, looking back at the tragic story of Queen Mary, Singh suggests that even though you may encipher your text, you should not feel overly comfortable or safe. Rather, you should err on the side of caution, both in the delivery and in the content of the message that has been encrypted.

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

Divided and Conquered

The Allied cryptanalysts were victorious over the German cryptographers due to a variety of reasons; however, one rather simple reason is often overlooked: the allies had a much larger and much more unified base of cryptologists than the Germans.

Germany had a total of around 30,000 people working in the intercepting, decoding, and coding of messages. The European Axis powers had a grand total of 36,000 people working in those endeavors. The Allied powers had a number closer to 60,000 people doing the same jobs, nearly twice that of the Axis powers. Just think about the implications of this: more people leads to more intercepted messages, which leads to more cipher text to work with (a historically beneficial resource in terms of breaking codes), and more people leads to more brain power trying more techniques to break the same code.

In addition to this, Germany did not have a central cryptology base like the Allies did at Bletchley Park. The Germans were spread out among 6 different bases, and would often overlap in each other's efforts, duplicating each other's work and thus wasting time and resources. There was some collaboration but not nearly to the degree of the Allies. In Andrew's blog post, he discusses the importance of collaboration in the field of cryptology so I will not expand upon this as much.

Finally, the Germans never created a bombe-like machine that could decipher messages which can very easily be attributed to the division and smaller size of the German forces. Without this key technology, Germans had to do a lot of the leg work manually which is much much more time-consuming and much less reliable. The bombe and other machines like it (Colossus and Tunny) exponentially increased the cryptographic progress of the Allies, catapulting them far ahead of the Axis powers.


Click here to see my primary source.

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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.

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The Morality of Admiral Hall's Actions

Upon learning the intended plans of the Germans from deciphering the Zimmerman telegram, it was ethical of Admiral Hall to withhold such information from the President.


One may argue that Admiral Hall should morally concede the information to the President so that Britain may be subsequently informed, and lives could be potentially saved during the outbreak of unrestricted submarine warfare. Yet, if America was to intervene before German acted out their plan, they would’ve “concluded that their method of encryption had been broken,” leading them to “develop a new and stronger encryption system” (Singh 113). This grants the possibility of the German’s using an extremely more complicated encryption system, one that the cryptanalysts in Britain’s Room 40 may never solve in their lifetime, to act out their unrestricted submarine warfare unopposed. This, in turn, could’ve led to a higher number of wartime casualties, especially among passenger ships. Thus, through decrypting future German telegrams without their knowledge that their encryption system had already been broken, Admiral Hall’s actions could potentially save many more lives than he would’ve had he passed on the information.


Furthermore, as history proved, by not informing the President, Admiral Hall ensured that the Germans did not realize the Americans had broken their encryption system, granting the Americans an advantage in decrypting any future German messages encrypted by the same system. Eventually the Mexican version of the Zimmermann telegram led America to retaliate, granting the same outcome had the Admiral actually passed on the information, but without the Germans discovering their blunder.


Changing perspectives on cryptography

It is not surprising that using frequency analysis to solve substitution required a sophisticated level of scholarship in the 9th century. It might take decades of textual study, statistics knowledge and mathematical insights for the Arabian cryptanalysts to successfully find this method. In The Code Book, Singh also suggests that the Muslim civilization provided an ideal cradle because “every Muslim is obliged to pursue knowledge in all its forms” and the scholars “had the time, money and materials required to fulfill their duty.” (Singh 16)

Today’s amateur cryptanalysts seem to still fulfill these “requirements”. Nowadays people with only a few years of education would already have certain level of knowledge in such fields. The resources are so accessible now that they no longer need to be“scholars” but indeed anyone with any intention or interest about cryptography. Undoubtedly only a small amount of people will be trained as professional cryptanalysts, but it’s incredibly easy for anyone to search about cryptography, share thoughts with others about the ciphers they write, or take an online cryptography course.

Today’s generation is a group of people that are taught to solve puzzles when little and raised with films or literature talking about cryptography often in one form or another. With the emerging technologies in hand and a broad access to the subject, people nowadays have entirely new perspective on cryptography. On the other hand, people back in time were strictly limited by the resources they had and the little exposure to the knowledge. Politics might also come into play since a large proportion of citizens interested in inventing or breaking codes might not be the best interest of a monarchical government at that time.

Easier to Learn, or Easier to Access?

I believe that, while a high level of scholarship was required to develop the frequency analysis approach, it is not critical to the use of this approach. When the world was new to this subject--when it had just discovered ciphers and keys and cryptanalysis--all of the knowledge was completely new. It was the cutting edge, so not many people understood it yet. It was essential to attain a high level of education to comprehend the mysteries of cryptology. However, with the modern education system, and modern technology, people have the information necessary more readily available. People can access the "mathematics, statistics, and linguistics" necessary to equip themselves for code making and codebreaking. Also, the easy access means that the information surrounds the human population. We have billions of pieces of data sitting at our fingertips, just waiting in that ever-present "cloud." Because of this access, and as a result of the heightened academic expectations, "amateur" cryptanalysts can use previously lengthy and difficult methods of analysis with much more ease. The civilization has reached a "sufficiently sophisticated level of scholarship in several disciplines," and therefore the people of that civilization may achieve the same accomplishments which the Islamic civilization discovered. However, as a result of the constant inundation of information prevalent in our society, and the resultant size of the body of common knowledge, amateur cryptanalysts can now use approaches such as frequency analysis, which was so arduously sought out, without any formal training.

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.

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