Show HN: SHA-256 explained step-by-step visually
81–90 of 145 posts
Re: Show HN: SHA-256 explained step-by-step visually
#82Can 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.
Maybe I'm being incredibly naive, but it seems like this would be trivial. Can you just start with the output hash and then essentially run the algorithms backwards? Obviously the resulting "input" would be random-ish garbage, but it seems like if all you care about is the output, you can pretty much just "pick" any data for the last step that produces the output. Then do likewise for the step prior, and so on.
Re: Show HN: SHA-256 explained step-by-step visually
#83So, 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"?
>why not "right rotate 2 XOR right rotate 3 XOR right shift 4"
In this case, you generally want shifts that are far apart so bits that far apart have a chance to influence each other. The other operations have only local effects on bits (and, or, xor affect only the same bit position; add affects the same bit position and perhaps a few that follow via carries). Only the shifts/rotates give a chance for "non-local" effects.
Re: Show HN: SHA-256 explained step-by-step visually
#84Does anyone have any good references, preferably a book but a good detailed website is fine, on cryptography, hashing, public/private keys, tokens, encryption, etc. as it relates to a software engineer? I don't necessarily want to know all the nitty gritty details of how these things are implemented. Rather, I think I would prefer simply understanding them and how to use them, piece them together, etc. to build something out of them.
I just have very little knowledge in this area. I'm going through a how to build a blockchain book right now, and I find myself struggling a little bit where I'm just calling some library functions but not necessarily knowing how to compose things properly.
Re: Show HN: SHA-256 explained step-by-step visually
#85Does anyone have any good references, preferably a book but a good detailed website is fine, on cryptography, hashing, public/private keys, tokens, encryption, etc. as it relates to a software engineer? I don't necessarily want to know all the nitty gritty details of how these things are implemented. Rather, I think I would prefer simply understanding them and how to use them, piece them together, etc. to build somet…
For that I like this one: https://cryptobook.nakov.com/
Re: Show HN: SHA-256 explained step-by-step visually
#86Does anyone have any good references, preferably a book but a good detailed website is fine, on cryptography, hashing, public/private keys, tokens, encryption, etc. as it relates to a software engineer? I don't necessarily want to know all the nitty gritty details of how these things are implemented. Rather, I think I would prefer simply understanding them and how to use them, piece them together, etc. to build somet…
JP Aumasson is one of the authors of the BLAKE hashes and wrote "Serious Cryptography":
https://www.amazon.com/Serious-Cryptography-Practical-Introd...
Re: Show HN: SHA-256 explained step-by-step visually
#87Earlier quoted context omitted.
Sure, that would be a pretty high difficult factor, but its possible.
But is it provably possible for SHA-256? An n-bit cryptographic hash function should ideally cover every n-bit output value, given slightly more than n bits of input, but I don't know whether this has been proven for any real-world functions.
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Re: Show HN: SHA-256 explained step-by-step visually
#88Can 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.
Maybe I'm being incredibly naive, but it seems like this would be trivial. Can you just start with the output hash and then essentially run the algorithms backwards? Obviously the resulting "input" would be random-ish garbage, but it seems like if all you care about is the output, you can pretty much just "pick" any data for the last step that produces the output. Then do likewise for the step prior, and so on.
As a comment above stated, part of the "input" is the initialized values:
> Initialize hash value h0 to h7: first 32 bits of the fractional parts of the square roots of the first 8 primes 2..19).
My guess is h0 to h7 change throughout the algorithm. If you perform each step in "reverse" as you suggest, "picking" any input at each step that produces the required output for that step, then you may not arrive to the correct initial state with the square roots of the first 8 primes.
You'll arrive at "random-ish garbage".
Re: Show HN: SHA-256 explained step-by-step visually
#89So, 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"?
You may not get an exact answer for SHA-1 or SHA-2, because they were designed by NSA, and I'm not sure whether a complete design doc has been published. SHA-3, by contrast, was designed in an open competition, and is completely different from SHA-1 and SHA-2. But here's a rough go at it. First of all, the overall form. SHA-2 is a Merkle-Damgård construction, meaning that it has a "compression function" which takes a…
About linearity, that just means that there's no "multiply" or "exponent" function equivalent to our primitives.
For example: if "add Foo" were our primitive, then 64-rounds of "add-Foo" could be broken by simply "data + 64 * Foo". IE: We found a "trivial shortcut" and someone else can break our cipher way faster than we can use it.
Addition is linear over numbers, because of multiplication.
XOR is linear over numbers: because XOR undoes itself. (5 x (XOR-Foo) is equivalent to 1x (XOR-Foo)).
It turns out that combining addition and XOR together results in a non-linear function over numbers and non-linear function over bits.
We can't "shortcut numbers", because the XOR-messes up our "number math". We can't "shortcut bits" because Add has this really annoying "carry" that basically has a 50% chance of shuffling bits around.
As such, we "expect" that combinations of Addition, XOR, and Shifts are non-linear. I'm not sure if it's been mathematically proven however, but no one has been able to show a "shortcut" thus far.
Re: Show HN: SHA-256 explained step-by-step visually
#90Can we have a video of this on youtube/dailymotion/vimeo/etc which we can download with yt-dlp?