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Polish
fgrieu
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Why is it hard to compute $g^{xy}\bmod p$ from $g^x\bmod p$ and $g^y\bmod p$?

Why is it hard to compute $$(g^x\bmod p, g^y\bmod p) \longmapsto g^{xy}\bmod p $$ when can we quickly compute $$x \longmapsto g^x\bmod p$$ ?