diff --git a/misc/ecc-formulas.tex b/misc/ecc-formulas.tex index eb69c7c73fff7df2a54746c1af6d1c439c8467af..1b21dea730c6c754b1289eb47e1e5bbcd9caa3c1 100644 --- a/misc/ecc-formulas.tex +++ b/misc/ecc-formulas.tex @@ -138,20 +138,20 @@ coordinate $T$, with $Z T = X Y$ (see According to djb, the formulas in Section 3.1 are the once to use, because they are complete. See -\url{http://www.hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html#addition-add-2008-hwcd}, +\url{http://www.hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html#addition-add-2008-hwcd-3}, \begin{align*} - A &= x_1 x_2 \\ - B &= y_1 y_2 \\ - C &= t_1 d' t_2 \\ - D &= z_1 z_2 \\ - E &= (x_1+y_1) (x_2+y_2)-A-B \\ - F &= D-C \\ - G &= D+C \\ - H &= B-a A \\ - x_3 &= E*F \\ - y_3 &= G*H \\ - t_3 &= E*H \\ - z_3 &= F*G + A &= (y_1 - x_1)(y_2 - x_2) \\ + B &= (y_1 + x_1)(y_2 + x_2) \\ + C &= 2 t_1 d' t_2 \\ + D &= 2 z_1 z_2 \\ + E &= B - A \\ + F &= D - C \\ + G &= D + C \\ + H &= B + A \\ + x_3 &= E F \\ + y_3 &= G H \\ + t_3 &= E H \\ + z_3 &= F G \end{align*} In our notation $a = -1$, and the $d'$ above is $-d$.