Poster: Loop Circuit Optimization with Bootstrapping over Fully Homomorphic Encryption

Fully Homomorphic Encryption (FHE) enables us to compute arbitrary circuits over encrypted data without decryption. To evaluate a complex circuit, a time-consuming operation called bootstrapping is required. Reducing the number of bootstrapping operations leads directly to reducing the entire computation time of the circuit. An optimization problem which minimizes the number of bootstrapping operations is called bootstrap problem, which is NP-complete. In previous work to tackle the problem, objective circuits must be represented as a directed acyclic graph. Thus, the previous methods cannot handle loop-carried dependencies for the circuits containing any loop, which results in no optimization over iterations. In this paper, we propose a method to decide a near-optimal placement of bootstrapping operations in a loop circuit by adopting loop unrolling technique. Compared to a naïve method, our method successfully reduced the number of bootstrapping operations per loop iteration up to 50 percent for a toy circuit, and up to 63 percent for a nearest neighbor classification circuit. Keywords—FHE, bootstrapping, loop unrolling