Been digging into post quantum cryptography lately and why lattice based crypto feels convincing. I've noticed most people talk about quantum threats from a Grover perspective: “Quantum computers just search faster” “Security gets roughly cut in half” “Increase key sizes and you’re mostly fine” It makes intuitive sense to me but what actually broke RSA/ECC wasn’t “faster searching” it was Shor discovering hidden structures that quantum interference could exploit. RSA/ECC turned out to contain periodic structure, fourier exploitable structure and clean algebraic order. Shor effectively changed the representation of the problem into something naturally solvable by a quantum system. What’s been bothering me is how confident can we be that lattice cryptography is truly resistant to Shor like structural attacks… Are we confident lattice cryptography is fundamentally resistant to Shor like attacks or are we mainly confident because no one has discovered the right mathematical representation yet?…