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

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I believe you are asking a question about DH exchanging key protocol. In DH, A creates a random private key of x and then will send the 𝑔𝑥mod𝑝 to B.
so nobody knows the X, although everyone can see the 𝑔𝑥mod𝑝 they cannot get the x from it, because of DLP (Discrete Logarithm Problem).

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    $\begingroup$ This does not answer the question. $\endgroup$
    – Maeher
    Dec 9, 2021 at 19:47
  • $\begingroup$ A bit more going into depth would have helped here, you could have explained that you'd need $x$ to calculate $(g^x\bmod p, g^y\bmod p) \longmapsto g^{xy}\bmod p$ I suppose. As it stands, just saying that DH is considered secure because of DLP doesn't really touch the question at hand. That said, a bit more direction could have helped instead of just downvotes and negative comments. $\endgroup$
    – Maarten Bodewes
    Dec 10, 2021 at 22:53

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