Cryptography

The History and Mathematics of Codes and Code Breaking

Tag: mathematicians

21st Century Cryptanalyst

In chapter one of The Code Book, Simon Signh writes, “Cryptanalysis could not be invented until a civilization had reached a sufficiently sophisticated level of scholarship in several disciplines, including mathematics, statistics, and linguistics.” (p. 15) This is a valid point. However, the necessity of education to become a cryptanalyst during the period of deep reflection in 610 AD, has changed dramatically in the modern world.

600 AD was not, by any means, a time of accessible education. Ptolemy’s influence had just reached the world in 100 AD, and Brahmagupta, who developed rules for the mathematical applications of 0, was just becoming prominent. Some of our basic principles were still being discovered. Needless to say, not everyone could afford the luxuries of schooling, even in basic subjects. 

Today, we have much more than ever before. Public schooling is essentially available to all of the western world, and many more people have the ability to learn the disciplines required to be an amatur cryptanalyst without prestiguous schooling. The fact that we can now use the “on our own” approach to achieve what many long before us needed ages to accomplish, is not something that should be looked upon shamefully, but instead as an indication of how far society has come.

 

Illegal Math: Fact not Fiction

I chose the beginning of chapter 17, when Marcus and Ange went to the journalist, Barbara Stratford, to expose the rampant abuses of power that were occurring in San Francisco. During this, they discovered that Barbara herself had covered the original ‘crypto wars’ in the 90’s. Barbara describes how the government had labeled cryptography as a munition and made it illegal to use it or export it, all in the name of national security. While I thought this was really interesting, the next sentence blew my mind. This means that we had ILLEGAL math. MATH, made illegal.

Can you imagine there being a time when certain equations and formulae were considered illegal? This interests me most because less than two decades after this illegal math, we are taking a class specifically about this illegal math. We’ve seen in class how cryptography has been used throughout history, and it always has been, and probably always will be, a part of life in government. However, it was always that it was only accessible to the wealthy, and those in government. No one else could afford the knowledge required, so we couldn’t keep secrets from the government. With the rapid spread of computers and advancement in technology, suddenly average citizens could afford to encode their messages, and it is very interesting to me that the government was so threatened by this that they felt the need to ban this knowledge.

Of course, it is also my opinion that, like Prohibition, this just proliferated the use of cryptography, but with even less government control. My favorite part of class so far has been our discussions about the intersection of cryptography, government, and privacy, which is why Little Brother, and especially this chapter hold my interest so well. With cryptography and cryptanalysis becoming ever more advanced, it will be exciting to see how the government handles all this as well.

Variation of Disciplines

Cryptography is an ever evolving field, and this held especially true around the time of World War II. Up until this point, most cryptanalysis had been performed by linguists and people trained in language. However, as cryptography evolved and became increasingly mathematical and technological, the personnel involved in cryptanalysis needed to evolve as well. One of the primary reasons the Allies had success over the German cryptographers was the Allies use of cryptanalysists from across many disciplines.

As discussed in class, there are many factors which go into solving a code. To break the German code required some each of creativity, logic and luck. One of the best ways to solve an abstract problem, such as breaking an enciphered message, is to think about it from many different angles and have different people each with their own different way of thinking attempting to solve the problem. As Singh noted, there were a great variety of cryptanalysists working on the German codes from mathematicians and linguists to artists and chess players. Having such varied ways of thinking ensured that if one person couldn’t come up with an idea, someone else down the line would most likely be able to. Also, British cryptanalysits were specialized into various “huts” on the lawn of Bletchley park. Each of these huts had a specific directive, from working on the German Naval enigma to intelligence gathering and translation. With many different types of thinkers working on them simultaneously, each of the various tasks were able to be completed with the utmost efficiency, saving lives and ultimately helping the Allies gain a pivotal upper hand in the war.

"Hut 6, Army/Airforce Enigma codebreaking" Photo by Matt Crypto-Licensed under Public Domain by Wikimedia Commons

“Hut 6, Army/Airforce Enigma codebreaking” Photo by Matt Crypto-Licensed under Public Domain by Wikimedia Commons

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