name Montgomery curves parameter a parameter b coordinate x coordinate y satisfying b y^2 = x^3 + a x^2 + x addition x = b (y2-y1)^2/(x2-x1)^2-a-x1-x2 addition y = (2 x1+x2+a) (y2-y1)/(x2-x1)-b (y2-y1)^3/(x2-x1)^3-y1 doubling x = b (3 x1^2+2 a x1+1)^2/(2 b y1)^2-a-x1-x1 doubling y = (2 x1+x1+a) (3 x1^2+2 a x1+1)/(2 b y1)-b (3 x1^2+2 a x1+1)^3/(2 b y1)^3-y1 negation x = x1 negation y = -y1 toweierstrass weierx = x toweierstrass weiery = y a0 = b a1 = 0 a2 = a a3 = 0 a4 = 1 a6 = 0 fromweierstrass x = weierx fromweierstrass y = weiery