Yeah, I get why the loop is there. But I still think it increases the probability of a collision by nearly 1000x over the probability of a collision without the loop.

Maybe a better way to explain my concern is to consider hashing something once versus twice, rather than 1000 times.

Let h be a hash function and p be the probability P(h(x) = h(y)) for randomly chosen x and y.

Say you have unique inputs a and b.

Obviously, P(h(a) = h(b)) = p.

Now consider P(h(h(a)) = h(h(b))). h(h(a)) = h(h(b)) if:

  h(a) = h(b) [probability p]
     OR
  h(a) != h(b) [probability 1-p], and
  h(h(a)) = h(h(b)) [probability p].

So the total probability when we repeat the hash is p + (1-p) * p

Since p is small, the probability of a collision has nearly doubled just by applying the hash function again.

[note: Higher up in this thread I mistakenly implied that the probability increased linearly. With a low number of iterations and realistic values for p it should be close to linear, but not exact.]

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