Pecha Kucha

Before I share a few Pecha Kucha resources, here's the list of possible titles you generated for blog posts, short papers, or presentations:

  • Turning the Tide of WW2 Cryptography
  • Turing the Mathematics of Cryptonomicon
  • The Beautiful Mind of Lawrence Waterhouse
  • Ending Engima
  • Colors of the Rainbow: Japanese Ciphers of WW2
  • When You Can Go Too Far and Not Far Enough: Ordo and Keys
  • Only as Strong as the Weakest Link
  • Data Havens for Fun and Profit
  • Learning Modular Arithmetic in Three Pages or Less
  • Taking One for the Team: Detachment 2702’s Contribution to WW2
  • Lawrence Waterhouse: A Different View on Everything
  • The Psychology of Bobby Shaftoe
  • How Mathematicians Think
  • The Awesomeness of Bletchley Park
  • When Bits Become Bytes

(For the record, four of those suggestions are mine.)

Now for some Pecha Kucha resources. First, the Pecha Kucha organization, which coordinates Pecha Kucha nights all around the world, including Nashville. The organization has used their network in creative ways to aid in disaster recovery efforts, including the 2011 Japan earthquake.

Here's the sample Pecha Kucha presentation I shared, by the University of British Columbia's Tegan Adams:

For more examples, check out Pecha Kucha Atlanta's website, which features lots and lots.

Finally, if you forget how to pronounce Pecha Kucha, here's a Muppets-themed reminder.

Image: "pecha kucha night book," Brandon Shigeta, Flickr (CC)

Math Behind the Shark

In a section of Cryptonomicon entitled "Cycles," there are a few pages that go into detail explaining how the three wheels in the enigma machine give it a certain security level and how the adding of the fourth wheel in the system Shark increased the security of the machine. It is explained by comparing the chain of letters created by the enigma machine to a bicycle with a weak link in the chain. The "weak link" in the enigma machine is the first chain that is created to encipher the first letter and when the same chain is used again which occurs 17,576 letters later. When the Germans added another wheel they increased the number of links in the chain to 456,976 and since their messages were hardly ever that long the weak link usually never came into play.

This section of the book added onto my understanding of the enigma machine and how the 4th wheel added so much more security. The increased security was explained through a number of pages with a lot of mathematics on them which helped me see more clearly what factors were actually playing a role in increasing the security of the enigma machine when adding the fourth wheel and creating Shark.

 

 

 

 

 

 

Image: "Chain," by Pratanti, Flickr (CC)

Better Safe than Sorry

In the “Tube” chapter, Captain Waterhouse visits Detachment 2702 and discusses with Colonel Chattan the possible height problem of the women working the bombes. All of the women that work with the bombes need to be tall enough to wire up the tall machines, and Waterhouse and Chattan entertain the idea that the Germans can obtain the personnel record of Detachment 2702. The personnel record would reveal that there are an abnormally large number of tall women working at 2702. Waterhouse and Chattan then assume that the Germans have an open channel to retrieve the records and discuss possible solutions.

The dilemma that Waterhouse and Chattan face resembles a situation in which two parties are exchanging messages but do not know that a third party is reading the messages. As seen with Mary Queen of Scots, assuming that one’s cryptosystem is secure can lead to carelessness and result in severe consequences. The conclusion reached in class discussion is to act like there is a third party that can decrypt one’s messages and to take extra measures to conceal the meaning of the message through euphemisms or symbols. The military officers in this scene assume the position that their enemy is able to access their data freely.

Their solution to this problem is quite innovative. Instead of outright closing the channel and blocking their enemy’s access, they keep the channel open so the Germans won’t suspect anything. They also decide to feed false information through the channel to fix the height anomalies in their personnel records. Their strategy effectively turns their disadvantage into an advantage. Using an enemy’s advantage (breaking the cipher) to manipulate them (feeding them false information) is an ingenious strategy. But this strategy requires the knowledge that the original cipher is broken and that a third party can read the message. Employing this strategy requires an essential assumption discussed earlier in the course: no message is completely secure, and to be safe (and paranoid), one should act like the cipher is broken.

Image: "Bombe detail," by Garrett Coakley, Flickr (CC)

The Pursuit of Randomness

The section of Cryptonomicon that really caught my attention was the section between pages 422 and 427. This section describes the British interception of German messages from U-553. These messages are different from the previously intercepted Enigma messages. These messages are encrypted utilizing Baudot Code, a code that used thirty-two characters. The system was based off of a power of two and therefore each character had a unique binary representation that contained 5 binary digits.  As we learned in class, these digits were either 1 or 0.

My blog post for our last essay dealt with the Lorenz teleprinter cipher and the Lorenz machine. These new messages that Waterhouse has discovered are in fact encrypted with the Lorenz cipher. The idea behind the Lorenz cipher was that if the paper used in communication was pre-punched with a completely random set of excess or obscuring characters, the cipher would be unbreakable. However, both the sender and receiver would have to have this paper, which is impractical in wartime. In Cryptonomicon, Waterhouse figures this out and he and Alan conclude that the obscuring characters in the cipher text could only be pseudo-random. This lack of complete randomness, and German error, lead to the British being able to crack the Lorenz cipher without ever seeing a Lorenz machine.

This section also discussed the building of Colossus, the first electronic calculator. Colossus is ultimately used to decrypt many intercepted German messages, crack the Lorenz cipher and lead to many Allied victories. The issue of the Lorenz Cipher reinforces our class lesson on binary numbers and further discusses the idea of a one-time pad and whether something is truly random and unbreakable. This example in Cryptonomicon helped me understand how difficult pure randomness is to achieve, especially in a wartime situation.

Image: "Binary Blanket," by quimby, Flickr (CC)

Computer Cryptography

In the chapter titled “Forays,” of Neal Stephenson’s Cryptonomicon, bit-key encryption is introduced as a method maintaining secrecy between the characters Randy and Avi. Unlike the other characters of the novel, Randy and Avi occupy the modern times and must resort to computer cryptography in order to protect Epiphyte, which is no more than “an idea, with some facts and data to back it up,” thus making it “eminently stealable.” They therefore employ a program referred to as “Ordo,” which converts their e-mails and data into streams of digital “noise,” or indistinguishable numerical nonsense. Interestingly enough, the function by which Ordo operates has recently been a topic of discussion in class.

by NIMATARADJI Photography

In the passage, Randy is directed to choose a key length of 4096 in order to communicate securely with Avi. This key length, as suggested by Randy, is entirely secure. However, because random generation of a larger key length requires tiresome effort on Randy’s behalf, he argues that even an inconceivably large super computer would have no hope of breaking a 4096-bit encryption key. Avi retorts with the implications of Moore’s Law, which argues that computing power doubles approximately every two years, and the prospect of quantum computers further validates the possibility for factoring large numbers with ease. The length of a key is thus of utmost importance, even if it is impervious to the efforts of current computing power.

A 4096-bit key, however, is notably secure, as this key length equates to  24096 possible keys. As mentioned in the novel, a key 2048 or 3072 bits in length would halt even the greatest cryptanalysts in their tracks, whereas a 768-bit key would provide security for years to come. This is because a key length does not directly signify the number of possible keys, provided that a key length of 400 generates double the number of possible keys as does 399-bit key.

This passage was captivating for me because my new found knowledge of computer cryptography and key length allowed me to appreciate its implications within the novel just that much more. Furthermore, the argument of Moore’s Law was quite noticeable to me, despite its lack of explicit mention in the passage. Most interesting to me, however, was the theoretical argument that a supercomputer composed of every particle in existence would take “longer than the lifespan of the universe” to crack a 4096-bit key encryption.

Turning Wheels

Cryptonomicon creates a fictional setting in which Neal Stephenson recreates the chaos of World War II cryptography. A passage of particular interest involved the relation of Turning's bicycle wheel to the cipher machine. Waterhouse eyes the bent spoke and weak link in the chain of Turning's bicycle and his mind immediately goes to the mathematical implications of the weak parts. By describing the math involved to figure out when the chain will entirely fall off - which only happens once the weak link of the chain and bent spoke come into contact with each other - and applying it to the mathematics involved in the rotors of an Enigma machine. Just as Turning's bicycle wheel has a certain period of rotation until the chain will fall off and the bicycle will be useless, Stephenson explains that the rotors also have a period. With three rotors, the period, or the number of times until the nth letter is enciphered with the same letter as the first letter of the message, is 17,775;

This passage not only represents the complicated mathematics involved in solving the Enigma, but also the ingenuity on part of the Germans in adding another rotor to their cipher machine. Because the period of the machine increased by a factor of twenty-five, and messages sent are unlikely to reach a length of 456,976 characters, the Germans greatly increased the security of their cipher through the introduction of the fourth and fifth rotors, a concept we have previously discussed, but the mathematics presented in this passage helped me to further understand the exact implications of the addition. yet, with a fourth rotor added, this period increases to 456,976 letters.

Image: Yellow Bike, Flickr

Understanding the Enigma

Cryptonomicon by Neal Stephenson is an interesting and informative novel tying together different generations of cryptography.   A passage I found most interesting was in the chapter ‘Cycles’.  In this chapter, Stephenson expands on the fundamental mathematics behind the Enigma machine: modular arithmetic.

Stephenson compares modular arithmetic to Turing’s bike.  For some reason, Turing’s bike has a rear wheel with one bent spoke and a weak chain link.  When the spoke comes into contact with the chain at a certain position the chain will fall apart.  The mathematical take on this occurring utilizes a series of variables.  We assume that the spoke is at a degree of 0 (Θ=0) and the position of the chain (C) is at C=0, when the spoke can break the chain.  The weak link is numbered 0, and follows, with I equaling the total number of links in the chain. The sprocket has n teeth, and after one full revolution of the wheel C=n (after two revolutions Θ =0 but now C=2n).  With these variables, Stephenson draws an incredible connection to modular arithmetic.  While C increases infinitely, the number of links does not, and at C=I the chain returns to C=0.  According to Stephenson’s example, if there are 100 links (I=100) and 135 links have passed, C will equal 35 instead of 135.  To put this into mathematical terms, C = 135 mod 100.  In this way, Turing’s bicycle offers an interesting connection to the way an Enigma machine works.  According to the period of an individual cycle within the machine, the difficulty in cracking a code increases.  This period is similar to how Turing’s bicycle returns to Θ=0 and C=0.  How exactly does this help determine when the chain will fall apart? According to Stephenson, this will happen when a multiple of n is also a multiple of I.  This perspective provided me with a better understanding of modular arithmetic and showed how complex the Enigma machine can be when the period increases.

Image: "Hydroelectric Turbine," by Guy Mason, Flickr (CC)

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.

From Letters to Numbers

"Triple Locked" by Darwin Bell

Though Neal Stevenson's novel Cryptonomicon is fictional, its story of cryptography geniuses Lawrence Waterhouse, Alan Turing and Rudy von Hacklheber during World War II gives a very accurate account of the processes and drama experienced by these experts in their field. World War II fueled one of the greatest transformations in cryptography, and these three men were at the head of the changes. Cipher analysis had always been based off of knowledge of language, pattern recognition and frequency analysis, but Waterhouse, Turing and von Hacklheber shifted the focus away from language analysis and toward mathematical analysis.

In one of the turning points of the novel and cryptography history, Waterhouse discovers non-Enigma messages in the German U-boat U-553 that have stumped his analysts. After further examination, Waterhouse discovers that the code is made of a 32 letter alphabet. This number is significant because it is a power of two, meaning that each letter in the alphabet was first substituted by a number and then by a five character binary sequence. This type of code is called the Baudot code and was used by the Germans on teletype machines. The teletype machines converted 32 characters into five number sequences of 1's and 0's. These could then be represented by either holes or no holes on a strip of paper or could be transmitted by wire or radio through changes in electrical voltages to represent the 1 or 0.

By encrypting the Baudot code again through one time pads, the Germans further increased their security. What the Germans failed to realize was that their "random" one time pads were generated through an algorithm and where therefore only "pseudo-random." Though truly random one-time pads are impossible to crack, Turing and Waterhouse were able to design a precursor to the modern computer called Colossus that could find the weakness in the one-time pads.

Turing and Waterhouse's transformation from using frequency analysis to using formulas and computers to decipher a message marks a sudden change in cryptography history. Turing's first computers and the use of binary to encode messages would forever change the standard methods of cryptography. No longer was cryptography power based on weak letter based codes, but rather almost unbreakably powerful number based codes that would revolutionize cryptography less than a century later with public key encryption.

The Interference of Secrecy

 

 

 

 

 

 

 

 

The Cryptonomicon brings up an interesting idea when Sergeant Shaftoe, Corporal Benjamin and Lieutenant Monkberg get in an argument after they ram their ship into Normandy. The reader already knows the purpose of the mission because it is alluded to in earlier chapters, but only Lieutenant Monkberg knows the exact orders, which causes problems when he tells them to do something that seemed like treason. The purpose of the mission was to leave behind the Allies' code book in order to have an excuse to change their codes, which they know the Germans have cracked, without alerting the Germans that they have cracked Enigma. Hiding the fact that they have cracked Enigma while still taking advantage of what they know  is basically the entire purpose of Detachment 2702. The concept of Detachment 2702 raises an interesting point because they have to deliberately hurt themselves in order to not reveal their resources. The concept behind 2702 is an answer to one of the things discussed in class, mainly the problem of revealing that a code has been cracked. Because of Detachment 2702, the Allies were able to fool the Axis into believing that Enigma was same and because of that, the Allies were able to keep a crucial advantage that was desperately needed in order to gain the upper hand in World War II. The Allies even had 2702 fooled, they couldn't possibly comprehend why they would ever leave behind the code book, though this secrecy turned into a double sided sword. When Corporal Benjamin is told to leave behind the code book, the Corporal assumes that his commanding officer is a spy and it didn't help that Lieutenant Monkberg was the only person that had received the orders. If they would have continue with taking the code book with them, they would have failed in their mission though they wouldn't realize it and it would have ended up costing Allied lives because the Allies would have needed to come up with a new way in which to justify switching code books, and until then all Allied conveys would be at risk of being destroyed by German U-boats.

Picture: U-Boat Surrender by Wessex Andy (Flickr)