Open Research Challenge

1. Basis Conversion (BConv)
   involves two different sets of moduli in the experiments, which currently utilizes Barrett Reduction because Montgomery reduction would require bringing all data from the Montogmery domain of the old modulus back to the raw domain and then convert into the Montgomery domain of the new modulus. The chain overhead of domain conversion with actual Montgomery reduction makes the overhead higher than the pure Barrett reduction.
2. Automorphism
   Automorphism requires a shuffling at the degree dimension, how to break such shuffling into a sequence of two matrix multiplication so that they could be fused into the previous computation remains an open research question.
3. Automated Scheduling Optimization
   How to automatically search the optimal scheduling of HE kernels for different security parameters? Specifically, how to schedule the kernel-level operations such that the majority of off-chip memory access could be hidden behind computation?

Open Engineering Challenge

1. Implement rational rescaling to allow more multiplication depth.