Addition Law and K*P for Montgomery-form elliptic Curves

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
elliptic Curve

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
Received on Fri Dec 23 20:11:15 2005