Elliptic Curve is of the form: Y^2 = X^3 + aX + b
everything is done modulo p, for some prime p
0 denotes the "point at infinity"
Point Negation Notes:
Modulo p!!!!
Point Addition Notes:
P + Q = R
P:(x,y)
Q:(u,v)
E: Y^2 = X^3 + aX + b
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cases:
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P == 0
0 + Q = Q
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Q == 0
P + 0 = P
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Q == -P
P + (-P) = 0
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P == Q
Let L = (3x^2+a)/2y.
Then, Q: (L^2-x-x, L*(x-(L^2-x-x))-y)
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P != Q, P != -Q
Let L = (v-y)/(u-x).
Then, R: (L^2-x-u, L*(x-(L^2-x-u))-y)
Scalar Multiplication Notes:
You know how to do point addition; not sure what you're looking for here.