[hashcash] Re: Statistics of hashcash collisions

  • From: Hubert Chan <hubert@xxxxxxxxx>
  • To: hashcash@xxxxxxxxxxxxx
  • Date: Thu, 27 May 2004 01:08:19 -0400

>>>>> "Anonymous" == Anonymous  <cripto@xxxxxxx> writes:


Anonymous> The time for hashcash collisions of a substantial number of
Anonymous> bits, 10 or more, can be represented by a Poisson
Anonymous> distribution.

I think you are mixing up your distributions.  The *time* taken to find
a collision follows a geometric distribution, which is a discrete
distribution, and is approximated by the exponential distribution,
which is a continuous distribution.

The number of hashcash collisions that we will find after N trials
follows a binomial distribution, which is approximated (for large N) by
a Poisson distribution.

time to mint a single token ~ exponential distribution
number of tokens minted after a fixed time ~ Poisson distribution

Your analysis seems to be correct, though.  But it could be rendered
simpler by using the right distribution (and your introductory sentence
could benefit from the precision).

Hubert Chan <hubert@xxxxxxxxx> - http://www.uhoreg.ca/
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