Re: Addition Law and K*P for Montgomery-form Curves

On Tue, 20 Dec 2005 07:53:36 +0100, "¬a\\/b" <al@xxx> wrote:
>I have found this
>"
>1 Let
>k = k0 + k1*2 + k2*2^2 + ... + kr*2^r; ki in [0; 1]; k0 = kr = 1
>be the binary representation of k.
>
>2) Let S = P, T = 2P, U = -P.
>3) For i = 1..r do the following:
> when ki = 1
> S := S + T (using U); T := 2T (U is unchanged);
> when ki = 0
> U := U - T (using S); T := 2T (S is unchanged):
>4) Then we have S = kP.
>"
>but if k0==1 than k is odd: and for k even?
>There is someone that can post this algo in "coodinates form"
>or can explain what does it mean "using U" or -P in a Montgomery-form
>Curve
>Thanks

if P(x, 1, z) is a point in the Montgomery-form Curve
E: b*Z*Y^2 = X^3 + a*Z*X^2+ X*Z^2
what are the coodinates for -P ?
Thank you
.

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