name binary Edwards curves parameter d1 parameter d2 coordinate x coordinate y satisfying d1(x+y)+d2(x^2+y^2) = (x+x^2)(y+y^2) addition x = (d1(x1+x2)+d2(x1+y1)(x2+y2)+(x1+x1^2)(x2(y1+y2+1)+y1 y2)) / (d1+(x1+x1^2)(x2+y2)) addition y = (d1(y1+y2)+d2(x1+y1)(x2+y2)+(y1+y1^2)(y2(x1+x2+1)+x1 x2)) / (d1+(y1+y1^2)(x2+y2)) doubling x = (d1(x1+x1)+d2(x1+y1)(x1+y1)+(x1+x1^2)(x1(y1+y1+1)+y1 y1)) / (d1+(x1+x1^2)(x1+y1)) doubling y = (d1(y1+y1)+d2(x1+y1)(x1+y1)+(y1+y1^2)(y1(x1+x1+1)+x1 x1)) / (d1+(y1+y1^2)(x1+y1)) negation x = y1 negation y = x1 toweierstrass u = d1(d1^2+d1+d2)(x+y)/(x y+d1(x+y)) toweierstrass v = d1(d1^2+d1+d2)(x/(x y+d1(x+y))+d1+1) a0 = 1 a1 = 1 a2 = d1^2+d2 a3 = 0 a4 = 0 a6 = d1^4(d1^4+d1^2+d2^2) fromweierstrass x = d1(u+d1^2+d1+d2)/(u+v+(d1^2+d1)(d1^2+d1+d2)) fromweierstrass y = d1(u+d1^2+d1+d2)/(v+(d1^2+d1)(d1^2+d1+d2))