Ecologically speaking, there is a term called “carcinization” the evolutionary tendency for different organisms to independently evolve crablike forms. The condition for carcinization is usually described as a kind of “shared condition.” After reading this article, that is what I felt. In other words, from the perspective of shared conditions, isn’t it possible that systems receive similar pressures when they need to…
There are parts of this that I consider a reach but the whole thing—despite that—feels sensible and looks a useful way to hang some things together which are normally separated. These are well-expressed thoughts on a really hard subject.
Why are neural networks and cryptographic ciphers so similar? (2025)
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Re: Why are neural networks and cryptographic ciphers so similar? (2025)
#42Earlier quoted context omitted.
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.
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.
Re: Why are neural networks and cryptographic ciphers so similar? (2025)
#43Earlier quoted context omitted.
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.
Re: Why are neural networks and cryptographic ciphers so similar? (2025)
#44E.g. graphs, matrices, linear algebra systems, digital photos (and much more) can be all perfectly transformed into each other, or in other ways this are all different ways to look at the same data. (This is also not just hypothetical * 2)
As a side effect saying things are similar "because they are just matrix algorithms" is meaningless, because most things are "just a matrix algorithm". (It's also meaningful for the same reason, as it means you can transform many problems into such with well understood solutions.)
And the high level abstraction of "encoder -> state -> decoder" structure is another of such "too generic/meaningless" things. As state can be anything and encoding is just "process input to generate state" and decoder is just "generate output from state" wen can model most algorithms with that. Like the identity function is now `encode(input): state=input; decode(state): output=state` (and indeed as long as state is large enough wrt. the input (or unbound) you can train encode decoder network to do exactly that, as meaningless as that seems.
Similar you can treat everything as everything you have in cryptography itself: All of hash, PRNG, stream cipher can be easily(kinda, * 3) build from another and like most algorithms in existence they can be formulated to "consume data and then produce output", i.e. as encoder decoder pattern ;)
So IMHO it's mostly an combination of observer bias due to how we like to model things (in a very high level POV). And a construction bias from that and what computer can compute well (in a slightly less high level POV when looking at somewhat "arbitrary choices").
I know some of the examples here might sound a bit ridiculous, but it's some of the most important insights in CS:
- a lot of algorithms can be transformed (or modeled as) a lot of other algorithms, take advantage of it
- just because something looks alike, it neither means it is alike nor that it being alike has any deeper meaning (e.g. two graphs might look alike, but only for the subset of sample data you happen to use to plot them)
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(* 1): Anything related to quantum physics seems be especially bad affected by it.
(* 2): you navigation system might navigate by mapping a navigation graph to a matrix and then compute on the matrix, where steps involved might treat it as a linear algebra system solved using some fast approximation.
(* 3): At least some of the conversion directions are easy. Some are a bit less intuitive. Also this assumes you either have perfect properties on the used building block or don't have to estimate how the imperfect properties map to properties of the created construct... Oh and naturally you can use some simple operations in the transformation (add, xor) as long as they are used in a straight forward way. E.g. PRNG(seed, offset) = HASH(encode(seed, offset)), with encode being a bijektive pairing function (e.g. `bytes_128bit_le(seed)+bytes_64bit_le(offset)`). E.g. for encryption you chunk, xor every chunk with a single time used key and generate the key using HASH(encode(key, nonce, chunk_idx)), or PRNG(encode(key, nonce), chunk_idx). That is how AES-CTR/AES-GCM does encryption. It (roughly) uses XOR(AES(key, encode(nonce, offset)), chunk). (Yes AES is more used like a hash then a block cipher in most modern AES ciphers...)
Re: Why are neural networks and cryptographic ciphers so similar? (2025)
#45Can 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
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?
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
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.
Re: Why are neural networks and cryptographic ciphers so similar? (2025)
#46Earlier quoted context omitted.
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.
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 crypto…
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.
Re: Why are neural networks and cryptographic ciphers so similar? (2025)
#47I would argue that they are not the same, but there is a symmetry between them. The central problem of cryptology is to prevent inference about either the key or the plaintext, despite the requirement to be able to reconstruct the plaintext from the ciphertext+key. So ciphers have to almost perfectly mix information. Machine learning is possible because in the absence of perfect mixing, inference is possible (given m…
yesn't
most modern stream ciphers basically use XOR for encryption with one time use keys per chunk (like. AES-CTR, AES-GCM, AEGIS, ChaCha20, etc.)
no mixing of bites is needed there just high entropy uniformly distributed one time use keys being generated per block, i.e. you need a "good enough" PRNG
practically the easiest way to get them is by doing something similar to a hash on the state(key, nonce, index) in some form. Which is likely done by mixing up information, hence the yes in yesn't.
but any PRNG with sufficient properties would do, and there probably are some which use some clever math which you probably wouldn't describe as "mix information".
It's just "shuffling bits" + "bad one way function" is often "sufficient" secure and faster then alternatives.
And historical many ciphers (e.g. AES block cipher) come from a time where we didn't yet had grate frameworks/know-how about how to assess security properties and write cryptography. Hence why they did all kinds of ways of mixing information and chaining which sometimes is quite.. arbitrary.
It might be easy to assume AES stuck around as it's "just grate" but that is plain wrong. It stuck around because it spread everywhere (including standards/requirements) before we knew how to best do things and due to that then ended up with hardware acceleration support on most chips. But no one would create it that way anymore (it is prone to side channel attacks if you don't have HW accl. xor use bitslicing trickery which makes it slow). But due to everything having AES hw acceleration it became a very fast building block. Hence why most modern cipher still use (part of) it and even some hashes and other algorithms use it... It's another example of how a "good enough" and wide spread technology often wins, not the best.
Re: Why are neural networks and cryptographic ciphers so similar? (2025)
#48I would argue that they are not the same, but there is a symmetry between them. The central problem of cryptology is to prevent inference about either the key or the plaintext, despite the requirement to be able to reconstruct the plaintext from the ciphertext+key. So ciphers have to almost perfectly mix information. Machine learning is possible because in the absence of perfect mixing, inference is possible (given m…
> So ciphers have to almost perfectly mix information. yesn't most modern stream ciphers basically use XOR for encryption with one time use keys per chunk (like. AES-CTR, AES-GCM, AEGIS, ChaCha20, etc.) no mixing of bites is needed there just high entropy uniformly distributed one time use keys being generated per block, i.e. you need a "good enough" PRNG practically the easiest way to get them is by doing something…
Re: Why are neural networks and cryptographic ciphers so similar? (2025)
#49Earlier quoted context omitted.
Back in the day, I read Applied Cryptography (by Schneier) and clarity rained upon many things.
More damage has been done by that book than by any Herbert Schildt C language book.
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.
Re: Why are neural networks and cryptographic ciphers so similar? (2025)
#50Earlier quoted context omitted.
More damage has been done by that book than by any Herbert Schildt C language book.
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 enlighten…
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.