# Enigma Machine IA

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Hi everyone!

So i am currently studying math HL considering a math ia doing the enigma machine, since i am quite interested in cryptanalysis. But the more i research, the more i feel uncomfortable with it.

Firstly i fear theres not much math going on in enigma machine, allow me to briefly talk about how the Enigma works. So theres this plug board connection 10 pairs of letters and leave the six of them be themselves (E.g. A connected to C and inversely C is connected to A. If B is not connected to anything it would just be itself B). And then theres three rotors to the resulted letter to go (in the case of A to C, C would goes into rotors). These rotors changes as a letter is pressed. And eventually after passing the rotors the resulted later (lets say B) goes back to the plugboard and gets B (as B is not connected to anything.) So whole encryption would be A-->C-->B-->B.

I heard a lot of people suggesting this topic. They say I could re work out how alan turning broke the code back then (since for enigma what u type in can't be what u get eventually, e.g. if u type in T u can't get T as the encrypted message). So we can do some eliminations and work out settings. But theres two problems, one is its extremely time consuming working on hand. Secondly is about originality, i fear that if i follow the way Alan worked my IA would become a report instead of exploration. I always fear that no graphs can be plotted.

Any suggestions for math elements i should be doing for the Enigma Machine? Probability?

Here is a link to how enigma works

and the flaw in enigma

Thanks!

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"No graphs can be plotted" should not be your biggest concern; this is not Math Studies in which you are primarily doing statistical analysis (eg linear regression and t-tests) in the IA. If you can discuss math in terms of combinatorics and graph theory, then this is an excellent topic because IB wants you to connect multiple areas of math in your chosen topic. If you can only talk about either combinatorics or graph theory then you can try to use this topic in a Math EE, otherwise other topics may work better for the IA.

One way to highlight originality is to present your own thoughts/struggles/commentaries of tackling the problem, as opposed to a third-person procedural-like narrative. By using sentences of "I tried ... but it doesn't work, then I did ... which worked", "This reminds me of this other problem, which is similar in that ...", "On thing I did not consider in my initial solution is ...". Ultimately, you are not asked to produce original math (but you are by all means encouraged to), but instead original commentary and presentation of the math.

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In what area of graph theory and combinatorics tho? I heard a lot of people mentioning two terms but I am quite confused about them. For graph theory, is it just a graphical representation of the enigma machine? For combinatorics, is it a way to show the possibilities available for the enigma machine? E.g. With an increase in rotor there is an xxxxxx times increase in possibility?

Thanks!

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@FrosciSnowflakeGraph theory studies mathematical networks of points and lines. Despite having taken Math HL, I have only limited knowledge of mathematics and have not spent time investigating graph theory, or combinatorics beyond high school. The IA encourages personal investigation of a math topic of choice but does not focus much on the end result compared to the process and presentation. If you simply expect straightforward answers from others, then that takes away the joy and reward of the learning process.

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Hey! So I'm planning on doing my Math IA on the enigma machine but like you I'm a bit scared about the math involved. My teacher has approved the topic but I still feel unsure about it. I was wondering if you ended up doing your Math IA of this topic and how you did in terms of the maths involved.

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