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The notation you are seeing is for symmetric crypto. Garbled circuits typically use symmetric crypto since it can and symmetric crypto is fast. You may be able to do garbled circuits with asymmetric crypto, but it is definitely non-standard and may have subtle issues.


One of the security guarantees of garbled circuits is that the evaluator doesn't learn anything about the circuit beyond the output on the given input. Executing more than one input string will break this property. For instance, if you allow him to evaluate two inputs, $0^n$ and $1^n$, then he can "mix and match" bits on each gate to determine what kind of ...

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