"... brute-force attacks against 256-bit keys will be infeasible until computers are built from something other than matter and occupy something other than space."
I've always heard that even 2¹²⁸ is significantly larger than that number (which is closer to 2⁸⁰). This page seems to support that:
https://en.wikipedia.org/wiki/Observable_universe#Matter_con...
(BTW, when converting 10^x to 2^x, times 3 is what I use for very rough back of the envelope estimations. Times 10/3 is actually almost precise, as log2(10) = 3.32…)
or, to put it in simpler terms,
10^3 = 1000 ≈ 1024 = 2^10
2^265 < 10^80 > 2^266
So it's only 0.1% of the number of atoms in the universe?
https://www.wolframalpha.com/input/?i=2%5E256 > ≈ 0.0012 × the number of atoms in the visible universe (≈ 10^80)
Anything past detection and panicking might be overkill tho.
2^256 is a very large number. If you could build a computer that required a single atom, and could test the balance of a single account in a single nanosecond, and then converted the entirety of the earth into such computers, it would take ~2.8 million years for you to check 0.01% of all accounts.
Brute-forcing modern cryptography isn't something that can happen. The magnitude of 2^256 is close to the count of atoms in the entire observable universe.