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I was reading about elliptic curves in this pdf. Page 55 of the pdf states that if number of points on elliptic curve #$E(F_p) = p$, then there exists a p-adic logarithmic map that homomorphically maps points in $E(F_p)$ to $F_p$. Now, solving for discrete logarithm on $E(F_p)$ reduces to solving for discrete logarithm in $F_p$.

Can anyone please explain what is p-adic logarithmic map and how to compute it? Does the technique extend to $E(F_{p^k})$?

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  • $\begingroup$ For future reference: In SO, cross-posting on two different sites is not a good etiquette. Select one, and give the community a chance to answer. $\endgroup$ – kelalaka Dec 2 '18 at 11:15
  • $\begingroup$ Sorry about that. Didn't know where to post. Won't repeat it again. $\endgroup$ – satya Dec 2 '18 at 13:47

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