Cryptography

There were many mathematical concepts related to modern cryptography introduced in this chapter. One topic I was familiar with already was the use of binary digits and modular arithmetic because we had learned about them in class. However, I was not aware of modular arithmetic prior to taking this course and I had only the most basic understanding of binary numbers. I still do not have much knowledge on either topic beyond an elementary level. For example, I was confused by the idea of the Y^x (mod P) function. I do not really understand how it works and how it relates to encryption and communication. I am not sure if this speaks to Singh’s ability (or lack of ability) to explain technical mathematical topics, or my ability (or lack of ability) to understand technical mathematical topics through words rather than examples and someone showing me how they work.

I was also confused about the concept of the mangler function as what the mangler function is exactly was never elaborated upon in the chapter. However, this might be because the function is too complicated or complex for the average individual to understand, so Singh didn’t even bother trying to break it down. I think Singh does a so-so job explaining the more technical sides to cryptography throughout his book, not just this chapter. Some explanations make sense, such as in the first chapter when he introduces the different types of historical ciphers. Others have me completely lost, such as his explanation for how the enigma machine functions. (I still don’t understand how it works!) I understand it is very difficult to explain such advanced and complex concepts to people with no knowledge on the topic, and this will be important to keep in mind when explaining how our cipher works for our podcasts.

What I found most interesting about the Numbers Station episode from 99% Invisible was the eerie fact that many of these numbers stations can still be widely heard today. Despite knowing that their message could be intercepted by a wide array of individuals and agencies, the transmitters of the numbers are confident enough in their encryption strength to broadcast their message on an open channel. The podcast producer kept the audience interested in the content in a variety of ways. They brought in other speakers to help analyze these seemingly-random messages, and most importantly employed seemingly-off/creepy music and other sound effects when talking about the number stations. This music helped keep the listener alert and interested in the material; this strategy particularly paid off when the producers began discussing the more technical aspects of the material.

When discussing the history of numbers stations or why they existed, the producers would have multiple people put forth their ideas and debate, and then intersperse bursts of odd music or a numbers station message. This helped provide a sense of variety to the reader, kept them alert with the odd music and seemingly-random messages, and provided them with more technical information on numbers stations. Based on this episode, I am interested in making a podcast that deals with some mysterious facet of cryptography, whether that be a specific example of cryptography gone wrong or just the secrecy behind encryptions. I would like to use multiple media, viewpoints, and stories to narrate my podcast, thereby keeping the content “fresh” with variety as well as offering more useful information and informative debates to my audience.

When reading Singh’s The Code Book, it can be easy to lose track of how difficult it can be to break a piece of ciphertext. Remember that a simple monoalphabetic substitution cipher took us a fair amount of time and careful consideration to break, even with all of the advantages we had as cryptanalysts: we knew, or at least were fairly sure of, the method used to encrypt the plaintext, we used methods that had already been invented and documented to break the ciphertext, and the plaintext was chosen specifically to be broken because its purpose was to teach us cryptography, not to communicate military secrets.

Contrast our situation with real-world cryptography and it makes a little more sense why cryptanalysis is so difficult. Firstly, when a new cipher is invented, cryptanalysts have no starting point, no angle from which to approach the problem, and no way to tell if the piece of ciphertext they’re working with is indeed ciphertext or if it’s just gibberish sent out to throw them off the scent. Secondly, even when the method of encryption is discovered, a way to crack it doesn’t just materialize out of thin air. Remember that it took more than a few centuries for the Arabs to invent frequency analysis. Thirdly, a good cryptographer will keep encrypted messages short or confusing or both in order to minimize the amount or the helpfulness of the reference material that cryptanalysts have to work with.

With the benefit of hindsight, any code can seem simple to crack, but we should remember that it often takes the best cryptanalysts in the world years or even centuries to defeat a good code.