> in fact hashes remain secure under quantum computing.
Hashes will see their security cut in half, in terms of the effort needed to find a pre-image.
(EDIT: security in bits = log of #evaluations needed)
E.g. finding a SHA256 pre-image, which amounts to a search over a space of 2^256 candidates, can be sped up using Grover's algorithm, to roughly 2^128 hash evaluations.
Hashes will see their security cut in half, in terms of the effort needed to find a pre-image. (EDIT: security in bits = log of #evaluations needed)
E.g. finding a SHA256 pre-image, which amounts to a search over a space of 2^256 candidates, can be sped up using Grover's algorithm, to roughly 2^128 hash evaluations.