I'm looking for some suggestions on what to read (papers, notes, book chapters?) on homomorphic encryption in order to understand the most recent (more optimal) schemes, as well as optimized use cases (e.g. Gazelle for CNNs).
My end goal is a list or DAG, that has at least these components:
Math background, e.g. rings/polynomial fields. I don't need a list of resources, just a list of topics. You can assume a basic intro cryptography class that covers things like defining computational indistinguishability. (It may even introduce homomorphic encryption and garbled circuits, but in my experience, these classes don't have enough time to dive into HE). I'm only asking for the math background so that I can give this to colleagues, who may not know about polynomial fields, etc. If it is needed for HE (like understanding lattices may be necessary), please include it in the background.
Borrowing from Fully Homomorphic Encryption without Modulus Switching from Classical GapSVP terminology, first-generation schemes which are really Gentry's first construction with optimizations.
Second generation schemes (e.g LWE, RLWE)
Whatever else there is (I should admit that I don't know the history after LWE, although I'm aware of the schemes).
My motivation is that I seem to be studying this backward. I read papers on accelerators (think GPU/FPGA) for HE in use case X, which uses scheme D, which is a straightforward optimization of scheme C, which is an improvement over scheme B (uses a different setting i.e. RLWE instead of LWE), ... etc.