See my answer above. Shoes factoring is efficient because period finding mod N is exactly discrete log. To attack ECC it is directly discrete log, where quantu

See my answer above. Shoes factoring is efficient because period finding mod N is exactly discrete log. To attack ECC it is directly discrete log, where quantum is exponentially faster than classical. Grover reduces unstructured search from O(N) to O(sort N), only a quadratic speedup, insufficient to weaken crypto more than 1 bit out of a key length, which is too weak to be a threat. Page 2 of your link does not state how QC attacks problems; it dies say ECC is discrete log, though. Both systems break precisely because QC solve DLP in these cases exponentially faster than classical, and this is all that’s needed.