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Jan 16, 2017 at 16:52 comment added Ethan Heilman I figured out what I was doing wrong last night. I am not used to some of the quirks of EC notation. $kG$ is actually a different operation than say $kx$. Finding $G^{-1}$ would break discrete log, finding $k^{-1}$ is trivial.
Jan 16, 2017 at 8:30 comment added DrLecter @EthanHeilman Note that $(e'-e)$ can easily be inverted as it is in $\mathbb{Z}_q$. The point is that this helps us computing $x$ using the last equation above. Your equation $x=(kG)(G^{-1})$ makes no sense. Is $G$ your basepoint from an elliptic curve? What is $k$ in your equation? Anyways, let us write $G^{-1}$ as $-G$ (as you write the group additively) and what you get is: $kG-G=(k-1)G$. That doesn't help you.
Jan 15, 2017 at 21:05 comment added Ethan Heilman Doesn't finding $(e′−e)^{−1}$ s.t $x(e′−e)(e′−e)^{−1} \equiv x$ involve finding the discrete log of $x(e′−e)$. For instance if find these inverses is easy why not find $G^{-1}$ so that you can determine the secret key $x = (kG)(G^{-1})$.
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Jan 26, 2014 at 18:48 history answered DrLecter CC BY-SA 3.0