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As the title says, we have an elliptic curve, doesn't matter which one, say p256. We choose any scalar.

Can the multiplication of a point on curve with the scalar result in a point that is not on curve? There would be a case where you get the infinity point as result and which is not considered to be on the curve, but is there any other case? Thank you!

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Can the multiplication of a point on curve with the scalar result in a point that is not on curve? There would be a case where you get the infinity point as result and which is not considered to be on the curve, but is there any other case?

No. Addition on points of elliptic curves with the point at infinity forms a group. Groups have to be closed, i.e. adding two elements from the group must yield another element from the group. Therefore, repeated addition - which is what scalar multiplication is - will not get you out of the group of the points.

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  • $\begingroup$ that was what I also thought, but just wanted to make sure. Thank you! $\endgroup$ Jul 21 at 12:57

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