Cryptography

The History and Mathematics of Codes and Code Breaking

Author: pollacmr

Intuition

The part of Cryptonomicon that caught my attention was Lawrence Waterhouse's attempt to solve the cipher, or "mathematical exercise" given to him and others by Commander Schoen. Schoen writes out the cipher, a list of 5 groups each with 5 numbers. The numbers are either 1 or 2 digits. Waterhouse instantly recognizes that the greatest number provided is 25, thus he assumes that the numbers must represent the letters in the alphabet. He then decides to run a frequency analysis test using the numbers on the board and realizes the number 18 occurs 6 times. Waterhouse then makes an assumption that the number 18 must be the letter E so he mentally substitutes the letter E into the cipher. Next, Waterhouse observes that the opening 4 numbers are '19 17 17 19'. He then knows that if 19 is a vowel, 17 must be a consonant or vice versa, and since 19 is twice as common in the cipher, he assumes that 19 is a vowel (specifically A). Waterhouse then proceeds by using the context of the message as provided by Commander Schoen earlier. Schoen had said that the message was intended for a naval officer. Using this, Waterhouse was able to guess that the first word was ATTACK. Immediately, he saw the rest of the cipher decrypt before his eyes so he stood up and stated his findings emphatically. The message read: "Attack Pearl Harbor December Seven"

The methods Waterhouse used to solve the cipher reminded me of the discussion we had earlier than year about the use of intuition to solve puzzles. Waterhouse used problem solving techniques and pure logic to decrypt the cipher. By assuming the first word was 'ATTACK' and recognizing that the numbers represented individual letters in the first place, Waterhouse demonstrated the problem solving techniques we have all acquired through basic learning.

Sufficiently Safe

Although it is fair to say that businesses were forced to rely on security that was less than optimal, the security they were using was more than sufficient. The Data Encryption Standard (DES) has a maximum amount of keys of around 100,000,000,000,000,000. This is referred to as 56 bits because when it is written in binary, it consists of 56 digits. Although there is a cap to the amount of keys that can be used, the number is large enough that no civilianwould have a computer powerful enough to determine which key was used. The NSA, which has the most powerful computing abilities in the world, is able to determine which key is used.

I believe that the NSA is justified in doing this because I believe that the NSA has the country's interests in mind. The DESis secure enough to prevent anyone with malicious intentions from deciphering a message; therefore it is affective. The NSA should have the ability to decipher something if it is a matter of national security.

It is comforting to know that in the most dire circumstances, high ranked officials in our nation’s government, who vow to protect all of us, have the ability and access to great resources to do whatever it takes to do so.

Severity Overlooked

In chapter 5, Marcus is released from prison and he returns to his home. He starts up his self-constructed laptop and realizes that something is wrong with it after the power cord refuses to stay connected. He now realizes that the entire casing of the computer was no longer aligned properly. After his parents go to sleep, Marcus rises from his bed and makes room on his desk for his laptop. He removed the outer casing and realized that the keyboard and logic-board weren't connected properly. When Marcus looked more closely, he realized that there was something underneath the cord. It was then that he realized that his computer had been bugged. Doctorow then describes Marcus' overwhelming anxiety and paranoia taking over. This scene stood out to me because I recently wrote a paper on data mining in which I firmly presented my opinion that privacy should be completely discarded in order to maintain security. The panic that ensues Marcus' discovery completely opened my eyes to the seriousness of an individual's right to privacy. Clearly I was biased in the past in that I never dealt with a violation of my rights to the degree that Marcus had to endure. Marcus states, "I'd been feeling paranoid when I got home. Now I was nearly out of my skin. It felt like I was back in jail…". This comparison between a violation of privacy and jail depicts the seriousness of the situation.

Étienne Bazeries: Ahead of His Time

The Great Cipher, used by Louis XIV, was far more complex than any cipher used in the 17th century. It was not simply a substitution cipher nor a homophone cipher. Étienne Bazeries considered that the Great Cipher could be a digraph, which meant that each number represented a pair of letters instead of a single letter. After months of work, Bazeries came to the conclusion that the cipher was not a digraph. He stuck with the concept that each number represented multiple letters, considering that they could possibly represent syllables. After deciphering two words, les ennemis, Bazeries was able to decipher the rest of the text. Another factor that made the Great Cipher so complex was that some of the numbers did not represent single letters nor syllables. Instead these numbers simply deleted the number before them. The Great Cipher was so far beyond its time period that it took centuries for cryptanalysts to catch up and approach the cipher from a different angle.

Relative Scholarship

It is not surprising to me that amateur cryptanalysts today often use an approach like frequency analysis to solve substitution ciphers without any prior training, while Singh states that a certain level of 'scholarship' was required for such a skill. The term scholarship is relative. This level of scholarship that Singh speaks of is much more prevalent today. Although a person may not be masterful in linguistics or statistics, he or she has most likely learned the basics through his or her childhood. The logic and problem solving techniques that set the foundation for deciphering are installed into the minds of children today at a very young age, whether it is through scholastic activities or thought provoking games. Additionally, one should keep in mind the differing levels of intellect altogether. To compare our society to one 500+ years ago is simply unfair. The level of knowledge today throughout all of society is at a significantly higher level than that of an ancient civilization. Another important factor is the overwhelming presence of technology today. Commonly used tools today, like cell phones and computers, require fundamental skills to properly navigate through them. The fact that children are able to correctly use sophisticated technology, sometimes to a greater degree than their parents, demonstrates the rising standard of knowledge for children.

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