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What happens when quantum-resistant cryptography is implemented using a quantum computer?

Give the whole deal with the qubits, is this even a worthy action?

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    $\begingroup$ Quantum computers can simulate classical computers in polynomial time. So nothing special happens? $\endgroup$ – SEJPM Sep 12 '18 at 14:44
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What happens when quantum-resistant cryptography is implemented using a quantum computer?

You may want to note that "quantum-resistant" doesn't mean "the quantum computer will blow up when trying to decrypt this" nor "the quantum computer will error out when decrypting this". It means that an adversary who has access to a quantum computer has no significant advantage over an adversary who doesn't when it comes to breaking security guarantees.

Now if you implement post-quantum cryptography on a quantum computer, which you can because it runs on classical computers and quantum computers can simulate classical computers in polynomial time, then you're essentially at the same situation as with classical cryptography on classical computers, that is an adversary who uses the same kind of computing as you do to apply the primitive can't easily break it.

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