Using the NetBeans environment and relying on the examples already seen, we try to implement the addition of points and the multiplication of a point by a scalar following the algorithms below

Algorithm for summation of two points, P, Q, of the elliptic curve

Algorithm for adding a point P with itself times Using this algorithm, the number of additions to be performed is of the order of the binary logarithm of n, while adding directly, the number of additions is n

\begin{tabular}{l} \hline ENTRADA: Dos puntos de la curva: P=(xP,yP,zP),Q=(xQ,yQ,zQ) \\ SALIDA: Punto suma R=(xR,yR,zR) \\ \hline 00: add (P,Q){ \\ 01: if (zP==0) return Q \\ 02: if (zQ==0) return P \\ 03: if (xP==xQ){ \\ 04: if (yP+yQ==0) return (0,1,0) \\ 05:=(3xP2+a)/(2yP) \\ 06:} else \{ \\ 07:=(yQyP)/(xQxP) \\ 08:xR=2xPxQ \\ 09: return (xR,(xPxR)yP,1) \\ 10:11:l \end{tabular} ENTRADA: Un punto de la curva P=(xP,yP,zP) y un valor n entero SALIDA: Punto suma R=nP