4 ms·

1024 bits seems a bit too much for the birthday problem to be a thing. I looked at [1] to do the calculation but (2^1024)! is a number too large for any of my

• rjmunro 3y ago
  2^1024 ≈ 10^300. There's only ≈10^80 atoms in the whole known universe. And we haven't even done the factorial.
• saagarjha 3y ago
  Stirling’s approximation?
• Dylan16807 3y ago
  This isn't the birthday problem. That would be the chance of two random links overlapping. The birthday problem scales with n^2, while trying to guess links scales with m * n, number of guesses multiplied by number of links. (Well, before you apply the logistic taper to it. So you wanted an approximation? There you go. Until you get the chance of a hit to be quite high, it's basically equal to guesses * valid links / 2^1024.)
  • ta1243 3y ago
    The chance is less than guessing a random 128 bit username and random 128 bit password. And then guessing a completely different username and password on the very next go. You'd get far more return on investment breaking bitcoin wallets. 2^1024 is 10^308 Lets say there are 12 billion links per person, and 8 billion people. That's 100 billion billion, or 10^20 links. 10^20 / 10^308 is zero. Lets say you can test 10 trillion links a second, and started when the big bang happened, you'll have tested 10^30 links so far. The number of links you'll have found so far is zero.
    • Dylan16807 3y ago
      Yes, but I'm not sure why you replied to me?