A recurrence relation question

2000-03-25 Thread Bram Cohen
This isn't obviously crypto-related, but I'll explain if there's a simple solution. Given that f(x+1) = f(x) * f(x) + c, does anybody know how to express f(x) in closed form? -Bram Cohen

Re: A non-parellelizable form of hashcash

2000-03-25 Thread Bram Cohen
It turns out my memory of what it's difficult to find square roots modulo was wrong. The fixed version is below. Alice wants to force Bob to do w 'units' of computation in such a way that he can't do the computation in parallel and she can verify the result expending relatively little resources.

Re: recurrence relation (iterated nonlinear map)

2000-03-25 Thread John Denker
At 12:50 PM 3/25/00 -0800, Bram Cohen wrote: Given that f(x+1) = f(x) * f(x) + c, does anybody know how to express f(x) in closed form? Well... That's an example of an iterated nonlinear map. Such things have been extensively studied. For some values of c, for some initial conditions, the