Oh hey, this is something I've actually done some real work on!<p>> Just try converting that into a circuit<p>Hmm. I think this article is a little behind the times. Loops are not a problem with Homomorphic encryption, as we can create circuits that work exactly like a transistor-based CPU.<p>In fact, I've got an implementation of one that I've been working on here: <a href="https://github.com/mmastrac/oblivious-cpu" rel="nofollow">https://github.com/mmastrac/oblivious-cpu</a><p>The trick to making this work is that you may not know how long the computation is going to take, so you need to either add a set number of iterations to run (ie: clock cycles), or send back encrypted updates as you run to give your trusted computer a chance to determine when the calculation has finished.