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In one of my assignments I need to solve the problem below:

For a Montgomery curve $3v^2 = u^3+u^2+u$ over ${\mathbb{F}}_{11}$ and point $P = (9,8)$, compute the $x$ coordinate of $3P$ using the Montgomery ladder.

I just need a hint to get an idea and not the whole answer. if anyone with some useful links would also be appreciable. As I tried to search google for this but was not able to get any idea.


Is it that I need to find it as $3P = 2P + P $ because I found one question about scalar multiplication here. but then I think it is not the correct way to use the Montgomery ladder.

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  • $\begingroup$ Do you know what the Montgomery ladder algorithm is? $\endgroup$ – poncho Jan 16 '16 at 1:57
  • $\begingroup$ Yes I have read about it and I know that we double when we have bit 1 and we add if bit 0. But I am not able to apply here. Or otherwise I haven't that much knowledge about it. $\endgroup$ – TechJ Jan 16 '16 at 1:59
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    $\begingroup$ See en.wikipedia.org/wiki/… $\endgroup$ – poncho Jan 16 '16 at 4:58

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