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Show HN: SHA-256 explained step-by-step visually

sha256algorithm.com

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Re: Show HN: SHA-256 explained step-by-step visually

#51

Post by manceraio »

daenz wrote: post #48
manceraio wrote: post #43

Earlier quoted context omitted.

Thanks :) I first implemented sha256 in js to understand its inner workings. Then I started displaying its variables with react and adding this stepped mechanism. Finally, I added some notes on the left to add some context of what is going on.

Very nice. Have you built any other algorithm visualizations? I have a very strong interest in how algorithms are visualized so that they are more easily understood.

First time doing this type of visualizations. I have this one tailwind.ink which will visualize a color palette on their luminance, chroma and hue values, but it's not really representing the algorithm behind.

Re: Show HN: SHA-256 explained step-by-step visually

#53

Post by spdebbarma »

This comes to my attention at a really convenient time. As a teenager, I initially got interested in Computer Science due to cryptography. Over a decade later, I've gotten into the subject for the first time since then.

For the last few days, I've been writing my own encryption for fun even though it's 100% not secure enough or powerful. My belief is that even though it's not super useful, the experience of attempting to write one is teaching me a lot more than I would have by simply studying it.

Re: Show HN: SHA-256 explained step-by-step visually

#54

Post by jjeaff »

bsedlm wrote: post #44
metalrain wrote: post #39

Earlier quoted context omitted.

Visualized like this it feels like security through obscurity, but there must be reason for this. I did wonder why initialization is like: 1. Initialize hash value h0 to h7: first 32 bits of the fractional parts of the square roots of the first 8 primes 2..19). 2. Initialize array of K constants: first 32 bits of the fractional parts of the cube roots of the first 64 primes 2..311

from what I've seen, there's a lot of "obscurity" to this; there are many seemingly arbitrary choices all over the place. In the end most encryption algorithms boil down to doing 'random' (arbitrary, hard to justify why) things to data and then undoing them exactly in order to decrypt. the math is all incredibly abstract but not all that complex, the high level of abstraction does make it quite difficult to grasp. Wh…

I doubt there is any concerted effort to keep the field small. That would be like saying tech companies don't want people learning how to code so that they can maintain an advantage.

If anything, governments and companies are encouraging people to study cryptography so that they are able to hire more experts in the future.

Now, once you get gatekeeper organizations and special licensing organizations like contractors licensing or beauticians licensing, those are examples of groups trying to keep the pool of experts small.

Re: Show HN: SHA-256 explained step-by-step visually

#55

Post by dragontamer »

picture wrote: post #36

So, how do people come up with these things? I assume every aspect of the design is carefully considered to defend it against various attacks. For example, why "right rotate 7 XOR right rotate 18 XOR right shift 3" and not "right rotate 2 XOR right rotate 3 XOR right shift 4"?

1. You want an invertible operation. Invertible operations do _NOT_ lose information, and therefore have the maximum amount of entropy per step.

2. You want the invertible operation to pass a statistical test called "differential cryptography analysis". Over multiple rounds, it must be difficult / impossible to "predict" how 1-bit of difference changes the state. (ie: 1-bit of difference should lead to 50.0000000% change in every output bit. If its 50.1% or 49.9% change of bits, you fail because someone running cryptoanalysis will pick that up).

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#1 is somewhat easy. It turns out that Data XOR (Rotate-left Data) XOR (Rotate-right Data) is all you need to make an invertible operation. 5-operations, no more (any more is redundant and therefore unnecessary use of compute power), no less (any less is not invertible and therefore loses information / entropy each step).

#2 is complicated: you gotta understand differential cryptoanalysis and run a bunch of tests.

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The discovery that (Data) XOR (Rotate-left Data) XOR (Rotate-right Data) was invertible became extremely popular in the 2010s through 2020s, and has become the cornerstone of XOR / Rotate / Add ciphers (aka: chacha), pseudorandom generators, and hash functions.

I don't know quite when it was originally discovered, but Jenkins was blogging about the importance of invertibility and playing with invertible xor/rotate stuff in (non-crypto) hash functions way back in the 90s.

I know Knuth's "Art of Computer Programming" book 2, Seminumerical Algorithms, discusses the importance of invertibility in random number generators, which is closely related to hashing / cryptographic procedures. So this "understanding" has been around for decades, but has only "become popular" in the SHA256 / Blake3 / pcg-random era.

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In the 90s, ciphers were mostly using SBoxes for this step ("confusion", to grossly change a value to another value without losing information). But today, modern CPUs are much faster at add/xor/bitshift operations than reading/writing to memory. So SBoxes are no longer a high-speed methodology / primitive for these kinds of operations.

It makes more sense to change our algorithms to use a new "invertible confusion operation" (aka: what SBoxes did before, and what ((Data) XOR (Rotate-left Data) XOR (Rotate-right Data)) does today).

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EDIT: Remember: the modern crypto-primitive is just a combination of "confusion" principles and "diffusion" principles.

1. Confusion "lossless transforms" numbers into other numbers. (A "set permutation" of sorts)

2. Diffusion "moves" bits from one number into other numbers.

Iterating over confusion + diffusion many times (IIRC, SHA256 is 64 rounds) is all you need to make a cryptographic cipher. If you "just" need a pseudo-random number generator or hash function, maybe 5 to 10 rounds is all you need.

Re: Show HN: SHA-256 explained step-by-step visually

#56

Post by jjeaff »

userbinator wrote: post #6

This reminds me that I've always wanted to make a huge interactive combinatorial circuit that computes SHA-256 and shows all its internal state, then put it on a site with the claim that anyone who can make its output match a certain clearly-constructed value (e.g. 0123456...ABCD...) will win a prize. No mentions of hash algorithms or other such phrasing to deter anyone. I wonder how many people would try such a "log…

I think making a problem more accessible like that is the fastest path to a solution.

It reminds me of the Stephen J Gould quote:

"I am, somehow, less interested in the weight and convolutions of Einstein’s brain than in the near certainty that people of equal talent have lived and died in cotton fields and sweatshops."

Re: Show HN: SHA-256 explained step-by-step visually

#58

Post by zahllos »

spdebbarma wrote: post #53

This comes to my attention at a really convenient time. As a teenager, I initially got interested in Computer Science due to cryptography. Over a decade later, I've gotten into the subject for the first time since then. For the last few days, I've been writing my own encryption for fun even though it's 100% not secure enough or powerful. My belief is that even though it's not super useful, the experience of attemptin…

Rather than write crypto, what I'd actually recommend is to break it. Schneier put together a block cipher cryptanalysis course a long time ago and while I don't usually recommend his crypto books these days, the course is good: https://www.schneier.com/academic/archives/2000/01/self-stud... (in this case, his crypto book might actually be useful, because it documents some of these out of date ciphers. There's (was?) a mistake in the DES code though iirc).

It is essentially a tour of all the early cryptanalysis literature, complete with suggestions of ciphers to target (e.g. FEAL). This will give you a sense of how the attacks work. Many of the ciphers are old, but I wouldn't let that put you off.

The study technique for this would be a) implement each cipher with toggles to control rounds and any other features, then implement attacks. Most of the papers should be open access by now since the 'course' was written in the year 2000. You could also 'catch up' on the constructions and attacks that have come out since.

I would caveat this with: what I am advising is purely for potential interest. Bear in mind there is little need to implement new block ciphers these days (what I'm saying is: this is a very specialized skill and most people won't find jobs in it).

Re: Show HN: SHA-256 explained step-by-step visually

#59

Post by y42 »

p1mrx wrote: post #31

Can it be proven whether values of m exist such that SHA256(m) == 0? If I were omnipotent and wanted people to believe in me, I would write a book that hashes to 0, so that anyone could verify its authenticity.

Sure, that would be a pretty high difficult factor, but its possible.

Re: Show HN: SHA-256 explained step-by-step visually

#60

Post by kzrdude »

picture wrote: post #36

So, how do people come up with these things? I assume every aspect of the design is carefully considered to defend it against various attacks. For example, why "right rotate 7 XOR right rotate 18 XOR right shift 3" and not "right rotate 2 XOR right rotate 3 XOR right shift 4"?

MD5 and SHA-1 are predecessors, and they are simpler, so certainly by starting from the understanding of the simpler ones. Just to say it wasn't all conceived in one go.
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