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How is that weaker (or any different) from the obfuscator that was proven to not exist? Namely, an obfuscator that preserves functionality and has the black box property.

I think the key point is the effienctly compute in the defintion. It seems that the black box property means C() and an oracle version of A() must be completely indistinguishable, including things like runtime and memory usage.

The weaker obfuscator has no guarantee about that.

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