Should I expect that the Pollard rho method
1. x ← 2; y ← 2; d ← 1;
2. While d = 1:
1. x ← g(x)
2. y ← g(g(y))
3. d ← gcd(|x - y|, n)
3. If d = n, return failure.
4. Else, return d.
will work for Gaussian integers? With a minor change due to gcd?
In my blog Forth & math I use the method for single cell numbers and in works fine for 64-bit numbers. For integers I use the function $\;x^2+1$ and a complete factorization is delivered immediatly. Now I will try to define an adequate routine for Gaussian integers and I guess that the method reasonably often will deliver some non trivial factors, but how long would the cycles be before they repeat them selves? Do anyone know if this has been tried?
I have now implemented Pollard rho for Gaussian intergers on my blog and it seems to work fine.
However, $g(z)=z^2+1$ doesn't work for all Gaussian numbers, i.e. not for $4+3i$ but the function $g(z)=z^2-1$ is well tested and works. See my answer on stack overflow:
https://stackoverflow.com/questions/2269810/whats-a-nice-method-to-factor-gaussian-integers