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How does FHE handle, say, a quantum cracker?



I assume you're talking about the quantum resistance of the underlying schemes in use? My understanding is that all the current schemes of practical interest rely on the hardness of (variants of) LWE (https://en.wikipedia.org/wiki/Learning_with_errors), which is believed to be hard even if you have a quantum computer.


Shortest lattice vector is currently thought to be quantum-resistant.




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