Cryptography

The History and Mathematics of Codes and Code Breaking

Author: Malakm

The Onetime Pad

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On November 12, 2012

In Student Posts

In “The Castle,” Lawrence Waterhouse arrives at the Castle in Outer Qwghlm, serving as the advance party to Detachment 2702. He is responsible for surveying the Castle and setting up appropriate accommodation away from the prying eyes of the servants. He finds a place that can adequately serve the purposes of Detachment 2702 and requests the required materials using a onetime pad to encrypt his message.

The onetime pad has been proved to be the only unbreakable method of encryption and its security lies in the randomness of its keys. Sheets of paper, or pads, containing these random keys are distributed to men in the field, and messages are enciphered accordingly. To increase the strength of its security, Waterhouse discards the letter ‘J’ and replaces it with ‘I’ in his messages. He also only uses every third line of the onetime pad. In addition, instead of simply enciphering his message using the conventional Vigenere square, he uses modular arithmetic to convert the letters into numbers and then back to letters again.

One of the impracticalities of the onetime pad is guaranteeing that everyone is using the correct sheet of keys. To overcome this obstacle, serial numbers that are unique to each sheet are typed across the top to indicate which sheet is being used. Another problem facing people who use the onetime pad is the generation of truly random keys. The men in Detachment 2702 get around this issue by using a device used in bingo parlors to produce random letters. The device containing 25 balls, to represent the 25 letters of the alphabet exclusing ‘J’, is rotated and a random ball is selected. The letter on the ball is then typed onto the sheet and so on.

In conclusion, Cryptonomicon has enhanced my understanding of onetime pads by suggesting several ways of strengthening this encryption technique as well as offering methods of overcoming the obstacles associated with its use.

 

The Lucifer Controversy

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On November 5, 2012

In Student Posts

My Calculus professor always says, “If you’re trying to dig a small hole in your backyard, you don’t bring in a bulldozer. It’s costly and it’s inefficient. You just take out a shovel and get the job done.” What she basically means is that if you have a small task, you use small tools, and if you have a big task, you use big tools. The same applies to the commercial use of cryptography.

In the 1970’s, businesses were looking for a secure method of encryption that they could rely on to communicate confidentially with one another (Singh 248). Lucifer, which was generally regarded as one of the strongest commercially available encryption systems, was a candidate for the standard (Singh 249). Before Lucifer was officially adopted as the Data Encryption Standard, the NSA limited the number of possible keys, just to the point that no civilian computer could feasibly crack the encryption (Singh 250). This provided businesses with just the right amount of security they needed to conduct their communications.

There are two other reasons that justify the NSA’s actions. The first is that a country’s security agency should have the strongest available encryption system and limiting the number of keys available to the public enabled it to do so.  The second is that public use of this system would compromise the NSA’s operations. For example, if businesses were using an unlimited Lucifer system, then it would be in the interest of many individuals and organizations to crack the encryption system. However, if the NSA were the only body using the encryption system, then less people would be interested in cracking it, thus providing the NSA with more security.

Defining Moments

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On October 9, 2012

In Student Posts

There are moments that last forever; moments that completely change your life and define who you become. In the second chapter of Cory Doctorow’s book, Little Brother, Doctorow cleverly depicts an everlasting and defining moment in Marcus Yallow’s life. Just as Marcus and his friends are about to uncover the next clue to a game they are dedicated to, their lives are changed forever. Doctorow produces this effect by changing the laidback and unconcerned style of his sentences to an abrupt, immediate and urgent one. He uses the words “sickening lurch” to describe that nauseating feeling you get right before a catastrophe transpires. The sentences that follow return to the eerily slow-paced and calm style, stretching out the mere seconds in which all the events occurred, into a long description of everything that ensued in them. Doctorow uses words such as “roaring,” “punishing,” and “sirens” to paint both a visual and aural scene as well as create the intensity of the explosion.
This moment eventually comes to dominate the course of Marcus Yallow’s life, defining his goal of defying the Department of Homeland Security and his struggle to attain his right to privacy.

Deciphering the Beale Ciphers

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On September 26, 2012

In Student Posts

Although the Beale Ciphers have continually eluded cryptanalysts, they remain a hot topic of interest. There are two possible reasons for the persisting enthusiasm to decrypt the mysterious ciphers. The first is that cryptanalysts are, by nature, drawn to solving puzzles. The harder the puzzle, the more rewarding it is when they finally manage to reveal its content, and the less they can resist the urge to do so. An additional factor is the fame and recognition associated with deciphering such an elusive piece of history. The second reason lies in the content of the message. Cryptanalysts are likely motivated to decipher the text by their desire to access the treasure it describes. Both these reasons have caused many people to dedicate their lives to this so-far futile pursuit.

Layer Up

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On September 19, 2012

In Student Posts

You know how people say you should layer up to keep the cold out in the winter? That’s exactly what the Rossignols did with their cipher to protect it from the prying eyes of enemy spies.

Because they had been successfully working on decrypting ciphers for so long, the Rossignols were able to identify the weak points in the ciphers they intercepted. Their hard work, coupled with this insight led to the production of The Great Cipher, used by King Louis XIV to encrypt his most secret messages. Generations upon generations of cryptanalysts were stumped by The Great Cipher, and it remained an enigma for almost two centuries.

To create such a secure cipher, the Rossignols added several layers of complexity to it. The first layer appears in the fact that they used numbers instead of letters, which although, in essence, is the same as using a regular alphabet, is still counterintuitive.

The second layer is that there are thousands of numbers. Specifically, five hundred and eighty-seven different ones, which means that each letter in the alphabet is not assigned to exactly one number in the cipher text. In fact, each number is not even assigned to a letter, or a combination of letters, but is instead assigned to a syllabic value. This brings us to our next layer of complexity.

The syllabic values were often misleading, because they were not only assigned to syllables but also to single letters, meaning there was no clear pattern that cryptanalysts could identify, and follow to determine the rest of the cipher alphabet.

To add a final layer of complexity, the Rossignols laid traps within the cipher text. They used operational numbers that represented neither syllables nor single letters, but instead had a functional role. For example, some numbers deleted the previous number, thereby removing additional syllables in words.

The Appreciation of Scholarship

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On September 3, 2012

In Student Posts

In chapter one of The Code Book, author Simon Singh argues that it requires a “sufficiently sophisticated level of scholarship in several disciplines,” such as Linguistics, Statistics and Mathematics, to arrive at the Frequency Analysis method in decrypting substitution ciphers. Opponents of this argument contend that mere amateurs are now intuitively using this technique, and that this is evidence against such a claim.
As Dr. Bruff has previously mentioned in class, the very popular daytime game show, “Wheel of Fortune,” is perhaps a child’s first introduction to Frequency Analysis. He/she would sit in front of the TV and enthusiastically attempt to solve the puzzle. Eventually, he/she realizes that there is a common pattern and that certain letters appear more often than others, thus effectively employing the Frequency Analysis technique. At this point, it is important to ask ourselves: does the fact that children can perform Frequency Analysis make this method any less sophisticated? The answer is no.
The simplest way to demonstrate this is by drawing an analogy. We have all, at one point in time, been in a situation similar to this one: you find yourself struggling with a Biology concept and approach your mother, who happens to be a doctor, for help. Before she goes on to explain it to you, she comments that what you are studying now is what she only began to learn in freshman year of college. Does this mean that the Biology concept has become outdated and is no longer relevant? Certainly not. Medicine and other fields of Biology would not have advanced had it not been for this seemingly trivial concept, and it still required a refined level of thought to arrive at that point. The same applies to Cryptanalysis.
Although Cryptanalysis is quickly advancing and new methods of decrypting ciphers are always being discovered, it is still important to appreciate the initial techniques that led to this progression. Therefore, when we respond to the question of whether or not it required a sophisticated level of scholarship to arrive at the Frequency Analysis method, it is important to value the skill and knowledge it involved and not take it for granted like we do with Biology concepts.

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