I looked at the recommendations under your comment, but I don't think I'm capable of these either lol
Any recommendations for a technically competent person, but for someone with math knowledge trailing off at Calc 2?
I looked at the recommendations under your comment, but I don't think I'm capable of these either lol
Any recommendations for a technically competent person, but for someone with math knowledge trailing off at Calc 2?
The math isn't that difficult once you grok mod math. It's like time, like doing addition and subtraction on a clock. What's 10 + 4 on a clock? 4 hours past 10 is 2.
The math stays difficult after basic discrete concepts and gets more difficult as you go. :)
It's straightforward to get yourself to a place where you can do cryptographic things and feel somewhat comfortable with what's happening. Truly understanding it to the point where you can reason safely about it is deceptively harder.
yeah I generally would say that learning about the actual schemes (tends to be) doable by a casual enthusiast, but learning about how the SOTA attacks work (which motivate scheme design for sure) is much more difficult.
Hmm, I've studied a lot of math, and I disagree. Cryptography is mostly number theory, which always looks simple on the surface, and often only needs "elementary" tools, but I still find it much harder than other areas of math.
For example, the proof that there are infinitely many primes looks simple [0], but it's still pretty hard to understand, let alone derive yourself independently. And the other important cryptography/number theory theorems like Euler's totient theorem [1] are even trickier.
[0]: https://en.wikipedia.org/wiki/Euclid%27s_theorem
[1]: https://en.wikipedia.org/wiki/Euler%27s_theorem
yes, deriving all of the math cryptography depends on independently would not be easy. Fortunately, that's not really how anybody learns.
Along those lines, you do not need to understand the proof of Euler's totient theorem to understand cryptography. It is a distraction. All you need (at most) is to know that the result is true, and even then it's only fundamentally important for RSA, which you likely shouldn't bother learning about these days. RSA simultaneously
1. looks very simple (though the simple version is horrendously insecure), and 2. does not have particularly good performance, and 3. does not have particularly good security (either post or pre quantum), and 4. has been in the process of being phased out for quite some time now.
this is not a good combination of properties. The fact that cryptography textbooks cover it is mostly due to historical tradition. I would personally argue it is time to omit it from instruction materials.
> Along those lines, you do not need to understand the proof of Euler's totient theorem to understand cryptography.
Well, I had to when I learned cryptography, but I learned it from a class offered by the math department, so I guess that's rather unsurprising :).
> even then it's only fundamentally important for RSA […] this is not a good combination of properties
Strong agree here.
in general the math is not actually that hard. It will be things you don't know beforehand, but a general undergraduate cryptography class will not assume the undergraduates have that much of a better math background than you. Typically just
1. comfort with logical operations/arithmetic over F2 2. discrete probability over finite sets 3. some basic complexity theory (mostly to reason about running time, though being familiar with proofs by reduction can help as well if you actually want to do security proofs).
a decent idea might be to take some "good" undergraduate cryptography class's course resource and use that. For example, Mihir Bellare is an extremely accomplished cryptographer. The course materials for his undergrad course F2018 are
https://cseweb.ucsd.edu/~mihir/cse107/slides.html
He's also written a longer series of lecture notes on cryptography that's freely available. I don't know where it is on his webpage these days, but you can find it below
https://www.cs.tufts.edu/comp/165/papers/Goldwasser-Bellare-...
the difficult part with this approach is not being able to ask questions that easily. To "fix" this, you can either
* use AI, though that has its own issues, or * use some community forum, such as crypto.stackexchange.com
if you want a full book, the typical (undergradute) one that roughly matches the above syllabus is "An Introduction to Modern Cryptograph" by Katz and Lindell.
I've also heard good things about Mike Roseluk's the joy of cryptography
https://joyofcryptography.com/
Boneh and Shoup have a decent (freely available, and very comprehensive) textbook at the graduate level
https://toc.cryptobook.us/
but it is following (roughly) the standard undergraduate curriculum, so if the slides I linked too are too sparse at some point, you could look up that topic in Boneh and Shoup (or use Boneh and Shoup as context to ask an LLM more targeted questions).
That all being said, the main difficulty for someone in your position is likely determining "what to learn" in cryptography. The easy thing would be to follow the standard undergraduate track, but if you're interested in any particular topic there are likely better routes to take.
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