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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?

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    $\begingroup$ A chain is only as strong as its weakest link $\endgroup$ – CodesInChaos Mar 17 '18 at 21:39
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    $\begingroup$ @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 Orbit Mar 18 '18 at 4:32
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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.

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  • $\begingroup$ But what if I use SHA-3 and floss each day? $\endgroup$ – Q-Club Mar 18 '18 at 2:35

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