Using the console:

I wrote a wrapper function around the site generator that took a callback so the next string to test would be called recursively. If a public key matched the public key I was aiming for, I dumped the response to the console, otherwise I just called the wrapper function again.

Then I wrote a function that iterated over a list of strings and output an array with all the possible permutations.

Then I just fed an array of the userids of the top 20 users into that function and fed that function into my wrapper.

I opened 5 browser windows and fed each of them 20 userids to take advantage of multiple cores, but I'm not entirely sure that makes sense to do.