Re:IBM will soon launch a 53-qubit quantum computer
by ChrisLomont on Thursday September 19, 2019 @10:39PM
(#21022839)
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.
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.