I know, that ECDSA could be broken by quantum computers, but since there is post-quantum hash function SHA-3, does not this make the digital signature resistant to them?
2$\begingroup$ A chain is only as strong as its weakest link $\endgroup$– CodesInChaosMar 17, 2018 at 21:39
1$\begingroup$ @CodesInChaos: But a chain locked in a box is as strong as the box. You need to know which metaphor is appropriate to a situation, before applying it to reach a conclusion. (As it happens, yours is in this case...) $\endgroup$– Lightness Races in OrbitMar 18, 2018 at 4:32
No. Anyone who can compute elliptic-curve discrete logs, such as an adversary with a quantum computer powerful enough to run Shor's algorithm, can immediately recover an ECDSA private key and forge arbitrary signatures of their choice. It doesn't matter if you use SHA-3 or floss each day.