name twisted Edwards curves parameter a parameter d coordinate x coordinate y satisfying a x^2+y^2 = 1+d x^2 y^2 addition x = (x1 y2+y1 x2)/(1+d x1 x2 y1 y2) addition y = (y1 y2-a x1 x2)/(1-d x1 x2 y1 y2) doubling x = (x1 y1+y1 x1)/(1+d x1 x1 y1 y1) doubling y = (y1 y1-a x1 x1)/(1-d x1 x1 y1 y1) negation x = -x1 negation y = y1 neutral x = 0 neutral y = 1 toweierstrass u = (1+y)/(1-y) toweierstrass v = 2 (1+y)/(x(1-y)) a0 = 1/(a-d) a1 = 0 a2 = 4 a/(a-d)-2 a3 = 0 a4 = 1 a6 = 0 fromweierstrass x = 2 u/v fromweierstrass y = (u-1)/(u+1)