once you know what your probability distribution is...
I’d merely stress that that’s an enormous “once.” When you’re writing a program (which, yes, I used to do), normally you have only the foggiest idea of what a typical input is going to be, yet you want the program to work anyway. This is not just a hypothetical worry, or something limited to cryptography: people have actually run into strange problems using pseudorandom generators for Monte Carlo simulations and hashing (see here for example, or Knuth vol 2).
Even so, intuition suggests it should be possible to design PRG’s that defeat anything the world is likely to throw at them. I share that intuition; it’s the basis for the (yet-unproved) P=BPP conjecture.
“Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin.”—von Neumann
once you know what your probability distribution is...
I’d merely stress that that’s an enormous “once.” When you’re writing a program (which, yes, I used to do), normally you have only the foggiest idea of what a typical input is going to be, yet you want the program to work anyway. This is not just a hypothetical worry, or something limited to cryptography: people have actually run into strange problems using pseudorandom generators for Monte Carlo simulations and hashing (see here for example, or Knuth vol 2).
Even so, intuition suggests it should be possible to design PRG’s that defeat anything the world is likely to throw at them. I share that intuition; it’s the basis for the (yet-unproved) P=BPP conjecture.
“Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin.”—von Neumann