I&#x27;ve wondered about another system, and perhaps someone here can point me in the right direction. Fully homomorphic encryption (FHE) has total control of two operations. Partially homomorphic encryption (PHE) has one operation. We can do PHE pretty well, and we&#x27;re currently very very bad at doing FHE in reasonable amounts of time.<p>In Craig Gentry&#x27;s FHE schemes (and all current ones that I know of) are all based off of an idea of bootstrapping, where each operation performed introduces some additional noise and every so often one must work to limit the noise and re-extract the signal. But somehow, as more operations are performed, simply too much effort goes into understanding the signal and noise.<p>But let&#x27;s say that I had a FHE scheme in which I could do a limited (and relatively small, on the order of 100) operations, but no more. I suspect this has a name, but I&#x27;m not familiar with it. If I had to name it something, I would give it the confusing name Limited FHE, or perhaps Finite FHE.<p>Then my question is: what sorts of things could we do with Limited FHE? Is this a question that people have thought about?