[tryauuum]

Can anyone recommend any good content to learn cryptography? Like, even if I read the algorithm for AES I have zero understanding about why it works this way

I've finished the Cryptography I on Coursera already. Can't recommend it enough

[rramadass]

1) Understanding Cryptography by Christof Paar et al. I learnt cryptography from the 1st edition. Its very practical and highly recommended - https://www.cryptography-textbook.com/

2) Cryptography: Theory and Practice by Douglas Stinson et al. This is a more mathematical treatment and hence a nice complement to the Paar book above - https://www.routledge.com/Cryptography-Theory-and-Practice/S...

3) For understanding how cryptography is used in Networks see the classic Network Security: Private Communication in a Public World by Radia Perlman et al. The 2nd edition is where i started my journey into network security/cryptography needed for my then job. Highly recommended - https://www.amazon.com/Network-Security-Charlie-Kaufman/dp/0...

The first two books give you the "mechanisms" (and theory) of cryptography i.e. the building blocks. The last book puts everything together to implement "policies" via practical applications (eg. IPSec/SSL etc.) for the real world. They are complementary and hence should be studied together to get the full picture.

[coldstartops]

I've been through Introduction to Modern Cryptography by Katz and Lindell. Can recommend, as it starts with Caesars cipher, one time pads, and builds towards modern cryptography.

[pet_the_bird]

"Cryptography Made Simple" By Nigel Smart and "A Graduate Course in Applied Cryptography" by Dan Boneh and Victor Shoup are excellent resources for people that have affinity with Math and CS. The second resource can be a tough read, and I would strongly recommend not skipping the first few chapters.

[yason]

Back in the day, I read Applied Cryptography (by Schneier) and clarity rained upon many things.

[tptacek]

More damage has been done by that book than by any Herbert Schildt C language book.

[krupan]

It's honestly been a long time since I've encountered this attitude around cryptography, where not even Schneier can be trusted and you have no hope of actually understanding cryptography so don't even try (yes, I'm referring to your math comments too). Welcome back!

For those feeling like this guy is being a dick, that's a normal reaction, but try to understand that this attitude was cultivated and used by enlightened individuals back when many people thought they were making secure software without even salting and hashing their users passwords. People thought md5 was good enough, https was barely being used, people had to be convinced to use ssh instead of telnet and ftp, and so forth. Drilling the idea into people that cryptography and security is difficult and that you should listen to experts had to be done. Don't take it personally.

So yes, as you study cryptography, do keep in mind that it's extremely unlikely that you'll learn enough to come up with something better on your own, that you will very likely make mistakes if you try to write your own implementation of any cryptographic algorithms, and that you should still just use existing libraries and the recommendations of experts on best practices.

[tptacek]

I understand this sentiment but don't know what to do with it. "Not even Schneier can be trusted" is "not even wrong". Schneier has very little to do with modern cryptography! But a long time ago, someone created a "Bruce Schneier facts" meme site, and now it's like an article of faith that he's a cryptography engineering expert. No, not so much, and I don't think he'd disagree.

He's a perfectly nice guy with a lot to say about information security and its intersection with public policy. But I think it's been plural decades since he basically declared himself outside of modern cryptography (you could call it at the point where he said he didn't "trust the math" of elliptic curves, which he left out of Practical Cryptography, over 26 years ago).

It's not so much that you should or shouldn't take "Applied Cryptography is bad" personally; rather: if you think Applied Cryptography is a useful reference or learning tool, it's pretty important to know that it is not.

[esafak]

This is news to me. Is it him in general or just that book?

[tptacek]

Just that book. The followup (Practical Cryptography, now called Cryptography Engineering, though it's the same book) is much, much better --- though it's also totally out of date at this point, and would also get you in trouble.

[LPisGood]

Can you elaborate?

[tptacek]

It's a book that is much more interested in presenting an almanac-esque survey of everything that was happening in cryptography at the time it was written (also unhelpful: it was written at a particularly un-rigorous point in the evolution of cryptography) than it is in teaching readers how to accomplish anything safely.

[philangist]

https://mit6875.github.io/ - MIT's Foundations of Cryptography is publicly available with full lectures, lecture note pdfs, and 5 problem sets. It's very rigorous and proof-driven which can be hard at times, but the professor's enthusiasm for the subject is infectious and makes the lectures a pleasure to watch.

[zOneLetter]

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?

[krupan]

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.

[tptacek]

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.

[mswphd]

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.

[gucci-on-fleek]

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

[mswphd]

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.

[gucci-on-fleek]

> 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.

[mswphd]

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.

[PaulStatezny]

I would highly recommend the free book Crypto 101.

https://www.crypto101.io

[cumshitpiss]

https://cs.ru.nl/~joan/papers/JDA_VRI_Rijndael_2002.pdf

A large part of this book is aimed at the readers who want to know why we designed Rijndael in the way we did. For them, we explain the ideas and principles underlying the design of Rijndael, culminating in our wide trail design strategy.