diff --git a/prelim.tex b/prelim.tex index aa4e2d37a16705fafadd86abba1a7c5fc3d03fce..4005f2154ea6ca0376af07d20b2570c474c10d31 100644 --- a/prelim.tex +++ b/prelim.tex @@ -73,7 +73,7 @@ The algorithm used to compute the addition (\Add{}) is listed in \Cref{alg:add}. \begin{algorithm}[h] \caption{Renes-Costello-Batina formula for $a=-3$. Used for exception-free addition on Barreto's curve.}\label{alg:add} \begin{algorithmic} -\Procedure{Add}{$(X_1 : Y_1 : Z_1)$, $(X_2 : Y_2 : Z_2)$}\\ +\Procedure{Add}{$(X_1 : Y_1 : Z_1)$, $(X_2 : Y_2 : Z_2)$} % \Comment{Compute $(X_1 : Y_1 : Z_1)+(X_2 : Y_2 : Z_2)$} \vspace{-0.5em} \begin{multicols}{3} @@ -87,7 +87,7 @@ The algorithm used to compute the addition (\Add{}) is listed in \Cref{alg:add}. \par $v_{ 9} \gets Y_1 + Z_1$ \par $v_{10} \gets Y_2 + Z_2$ \par $v_{11} \gets v_{ 9} \cdot v_{10}$ -\par $v_{13} \gets v_{11} - v_{12}$ +\par $v_{13} \gets v_{11} - v_{12}$ \par $v_{14} \gets X_1 + Z_1$ \par $v_{15} \gets X_2 + Z_2$ \par $v_{16} \gets v_{14} \cdot v_{15}$ @@ -144,6 +144,8 @@ The cost of the doubling formulas is $8\mathbf{M} + 3\mathbf{S} + 2\mathbf{m_b} \begin{algorithmic} \Procedure{Double}{$(X : Y : Z)$} % \Comment{Compute $[2](X : Y : Z)$} +\vspace{-0.5em} + \begin{multicols}{3} \par $v_{ 1} \gets X \cdot X$ \par $v_{ 2} \gets Y \cdot Y$