3Blue1Brown
2 HN recommenders · recommended in 5 months, 2020–2023
5:06 · 3.7M views · Jul 8, 2017
3Blue1Brown illustrates how enormous the 256-bit search space is, showing how infeasible it is to find a hash or key by guessing and checking.
HN uses it as the go-to illustration of just how large 2^256 is.
5 comments from Hacker News
I wondered the same thing, so I went looking for answers and found this excellent video by 3Blue1Brown: How secure is 256 bit security? : this video
We know that life is evolvable because life exists and we know the biochemical mechanisms involved (DNA + cellular biochemistry). Evolution implies a relatively smooth path through "DNA space" from, say for example, an early single cell eukaryote to a mushroom. However the search space is enormous. Even if we account for billions of years of evolution and a trillions of evolutionary experiments each year, a simple random walk with selection through DNA space should go nowhere because of the numbers involved. The curse of dimensionality[0] means there has to be some other principle of nature to make the search space yield a path from one viable life form to another. The search space of life would have to be 'smooth' in some sense. That 'smoothness' is something we don't understand. If DNA space is just 256 bits (as a dramatic simplification), then 2^256 is a very very big space to search just by chance [1]. Now imagine a space orders of magnitude bigger. [0] [LINK] [1] this video (3Blue1Browns wonderful illustration of how large 2^256 is)
Large number comparisons are difficult for humans to comprehend. If you simplify life to a DNA strand 256 nucleotide long (for the sake of math comparison) - then the search space is 4^256. To comprehend how large a search space this is watch 3Blue1Brown's explanation this video
What was the RSA crack effort you mention? It doesn't seem feasible, considering finding a SHA-256 collision would take so much compute power we don't have words to describe it, and even coming up with thoughts to frame the problem is hard ( this video ). I can't imagine cracking even an RSA2048 key with everyone working on it.
Even if you had your GPU-packed Kilo-Google per person multiplanetary Gigagalactic computer guessing numbers for 37 times the age of the universe, it would still have a 1 in 32 billion chance of cracking. this video