My understanding is that an important result used in ECC is that any point $P$ $\in E(F_p)$ (where $E(F_p)$ is the group of points on an elliptic curve over the finite field $F_p$) is the generator of a subgroup of $E(F_p)$. Is there a simple way of showing this? Am I over looking something?
Proof of Points on an elliptic curve over a finite field being generators of subgroups.
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group-theory
elliptic-curves
cryptography
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2Any element $g$ of a group $G$ is a generator of the subgroup $\{g^n:n\in\mathbb Z\}$ of $G$. – 2017-02-01
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0@TonyK Ah I see good point. – 2017-02-01