by xoa | 2025-10-06 02:22:27+00:00
Whew, that's actually a hard one! It's been long enough since I was getting into it that I'm not really sure what's the best present path on it. In terms of books, JP Aumasson's "Serious Cryptography" got a 2nd edition not too long ago and the first edition was good. Katz & Lindell's "Modern Cryptography" and Hoffstein's "Introduction to Mathematical Cryptography" are both standard texts that I think a lot of courses still get started with. Finally I've heard good things about Esslinger's "Learning and Experiencing Cryptography with CrypTool and SageMath" from last year and Smart's "Cryptography Made Simple", which has a bunch of helpful visuals.

For online stuff, man is there a ton, and plenty comes up on HN with some regularity. I guess I've been a fan of a lot of the work Quanta Magazine does on explaining interesting science and math topics, so you could look through their cryptography-tagged articles [0]. As I think about it more, honestly though it might almost seem cliche but reading the Wikipedia entries on cryptography and following that along with reference to the links if you want isn't bad either.

Just keep in mind there's plenty of pieces that go into it. There's the mathematics of the algorithms themselves. Then a lot of details around the implementations of them into working software, with efforts like the HACL* project [1] at formal mathematical verification for libraries, which then has gone on to benefit projects like Firefox [2] in both security and performance. Then how that interacts with the messy real world of the underlying hardware, and how details there can create side channels can leak data from a seemingly good implementations of perfect math. But then also that such attacks don't always matter, it depends on the threat scenarios. OTP, symmetric and asymmetric/pub-key (all data preserving), and cryptographic hash functions (which are data destroying) are all very different things despite falling under the overall banner of "cryptography" with different uses and tradeoffs.

Finally, there is lots and lots of history here going back to well before modern computers at all. Humans have always desired to store and share information with other humans they wish while preventing other humans from gaining it. There certainly have been endless efforts to try to subvert things as well as simple mistakes made. But we've learned a lot and there's a big quantitative difference between what we can do now and in the past.

>My (rudimentary, layman) understanding is that encryption is almost like a last line of defense and should never be assumed to be unbreakable.

Nope. "We", the collective of all humanity using the internet and a lot of other stuff, do depend on encryption to be "unbreakable" as a first and only line of defense, either truly and perfectly unbreakable or at least unbreakable within given specified constraints. It's the foundation of the entire the global e-commerce system and all the trillions and trillions flowing through it, of secure communications for business and war, etc.

Honestly, I'm kind of fascinated that apparently there are people on HN who have somehow internalized the notion of cryptography you describe here. I don't mean that as a dig, just it honestly never occurred to me and I can't remember really seeing it before. It makes me wonder if that feeds into disconnects on things like ChatControl and other government backed efforts to try to use physical coercion to achieve what they cannot via peaceful means. If you don't mind (and see this at some point, or even read this far since this has turned into a long-ass post) could you share what you think about the EU's proposal there, or the UK's or the like? Did you think they could do it anyway so trying to pass a law to force backdoors to be made is a cover for existing capabilities, or what? I'm adamantly opposed to all such efforts, but it's not typically easy to get even the tech literate public on-side. Now I'm curious if thinking encryption is breakable anyway might somehow play a role.

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0: https://www.quantamagazine.org/tag/cryptography/

1: https://github.com/hacl-star/hacl-star

2: https://blog.mozilla.org/security/2020/07/06/performance-imp...