I recently watched this video by Computerphile, where Mike explains the mathematics of the Diffie Hellman exchange. I've been wondering, since as explained $g$, $g^a$ and $g^b$ is public, can't you just do this equation $$ \frac{1}{log_{(g^a)}(g)} = a $$ and $$ \frac{1}{log_{(g^b)}(g)} = b $$ to find their private keys? I might be dumb, please explain this.
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I believe the important part is that it is $\bmod p$ for some prime $p$, hence log won’t exactly function. – Robert Murray Feb 25 '24 at 13:49
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https://crypto.stackexchange.com/questions/12865/why-is-the-discrete-logarithm-problem-assumed-to-be-hard – Martín-Blas Pérez Pinilla Feb 25 '24 at 15:21
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Computing the discrete log is the hard part. Remember that the logarithms are taking place in the group, not the real numbers.
David Lui
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