6 ms·

With every supercomputer working for 100 years, you can have 0.01% of all accounts, maybe.

by magma1983 5y ago

Tuna-Fish 5y ago
... not even close. 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.
- formerly_proven 5y ago
  This reminds me of a discussion a few years ago where someone was extremely adamant that you'd have to handle the chance of a key collision in a random 256-bit key for the system to be secure :)
  - rocqua 5y ago
    I might agree with them because your random process could be weaker than you think without having any indication until you hit the colision. Anything past detection and panicking might be overkill tho.
    - deleted 5y ago
      [deleted]
- 5e92cb50239222b 5y ago
  > The magnitude of 2^256 is close to the count of atoms in the entire observable universe. 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_content—number_of_atoms https://en.wikipedia.org/wiki/Observable_universe#Matter_con...
  - codeflo 5y ago
    Look more carefully, the estimation according to Wikipedia is 10^80, which is roughly 2^266. (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…)
    - FabHK 5y ago
      > log2(10) = 3.32 or, to put it in simpler terms, 10^3 = 1000 ≈ 1024 = 2^10
    - 5e92cb50239222b 5y ago
      Ah, so it's just me being stupid, as usual. Thanks, at least now I know.
    - deleted 5y ago
      [deleted]
  - V1ndaar 5y ago
    Nope, the rough approximation of atoms in the universe is O(10^80). Big difference!
    - rvense 5y ago
      Quickly checking with Python... 2^265 < 10^80 > 2^266 So it's only 0.1% of the number of atoms in the universe?
      - codeflo 5y ago
        “Only”.
- chokma 5y ago
  The best quote for this is from Bruce Schneier: "... 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." https://security.stackexchange.com/a/82412 https://security.stackexchange.com/a/82412
- edf13 5y ago
  It's a large number but not close to the count of atom: https://www.wolframalpha.com/input/?i=2%5E256 https://www.wolframalpha.com/input/?i=2%5E256 > ≈ 0.0012 × the number of atoms in the visible universe (≈ 10^80)

With every supercomputer working for 100 years, you can have 0.01% of all accounts, maybe.

... not even close. 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.

formerly_proven 5y ago
This reminds me of a discussion a few years ago where someone was extremely adamant that you'd have to handle the chance of a key collision in a random 256-bit key for the system to be secure :)
- rocqua 5y ago
  I might agree with them because your random process could be weaker than you think without having any indication until you hit the colision. Anything past detection and panicking might be overkill tho.
  - deleted 5y ago
    [deleted]
5e92cb50239222b 5y ago
> The magnitude of 2^256 is close to the count of atoms in the entire observable universe. 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_content—number_of_atoms https://en.wikipedia.org/wiki/Observable_universe#Matter_con...
- codeflo 5y ago
  Look more carefully, the estimation according to Wikipedia is 10^80, which is roughly 2^266. (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…)
  - FabHK 5y ago
    > log2(10) = 3.32 or, to put it in simpler terms, 10^3 = 1000 ≈ 1024 = 2^10
  - 5e92cb50239222b 5y ago
    Ah, so it's just me being stupid, as usual. Thanks, at least now I know.
  - deleted 5y ago
    [deleted]
- V1ndaar 5y ago
  Nope, the rough approximation of atoms in the universe is O(10^80). Big difference!
  - rvense 5y ago
    Quickly checking with Python... 2^265 < 10^80 > 2^266 So it's only 0.1% of the number of atoms in the universe?
    - codeflo 5y ago
      “Only”.
chokma 5y ago
The best quote for this is from Bruce Schneier: "... 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." https://security.stackexchange.com/a/82412 https://security.stackexchange.com/a/82412
edf13 5y ago
It's a large number but not close to the count of atom: https://www.wolframalpha.com/input/?i=2%5E256 https://www.wolframalpha.com/input/?i=2%5E256 > ≈ 0.0012 × the number of atoms in the visible universe (≈ 10^80)