There are some topics here that are very helpful on how to find similar pictures.
What I want to do is to get a fingerprint of a picture and find the same picture on
A trivial way to compute a hash would be the following. Get all the descriptors from the image (say, N of them). Each descriptor is a vector of 128 numbers (you can convert them to be integers between 0 and 255). So you have a set of N*128 integers. Just write them one after another into a string and use that as a hash value. If you want the hash values to be small, I believe there are ways to compute hash functions of strings, so convert descriptors to string and then use the hash value of that string.
That might work if you want to find exact duplicates. But it seems (since you talk about scale, rotation, etc) you want to just find "similar" images. In that case, using a hash is probably not a good way to go. You probably use some interest point detector to find points at which to compute SURF descriptors. Imagine that it will return the same set of points, but in different order. Suddenly your hash value will be very different, even if the images and descriptors are the same.
So, if I had to find similar images reliably, I'd use a different approach. For example, I could vector-quantize the SURF descriptors, build histograms of vector-quantized values, and use histogram intersection for matching. Do you really absolutely have to use hash functions (maybe for efficiency), or do you just want to use whatever to find similar images?