Commit 66856523 by Benoit Viguier

 ... ... @@ -38,11 +38,10 @@ We consider \xcoord-only operations. Throughout the computation, these $x$-coordinates are kept in projective representation $(X : Z)$, with $x = X/Z$; the point at infinity is represented as $(1:0)$. See \sref{subsec:ECC-projective} for more details. We define two operations: We define the opperation: \begin{align*} \texttt{xADD} &: (x_{Q-P}, (X_P:Z_P), (X_Q:Z_Q)) \mapsto \\ &(X_{P + Q}:Z_{P + Q})\\ \texttt{xDBL} &: (X_P:Z_P) \mapsto (X_{2 \cdot P}:Z_{2 \cdot P}) \texttt{xladderstep} &: (x_{Q-P}, (X_P:Z_P), (X_Q:Z_Q)) \mapsto \\ &((X_{2 \cdot P}:Z_{2 \cdot P}), (X_{P + Q}:Z_{P + Q})) \end{align*} In the Montgomery ladder, % notice that the arguments of \texttt{xADD} and \texttt{xDBL} ... ... @@ -64,8 +63,9 @@ computing a \xcoord-only scalar multiplication (see \aref{alg:montgomery-ladder} \STATE $R = (X_R:Z_R) \leftarrow (x_P:1)$ \FOR{$k$ := $m$ down to $1$} \STATE $(Q,R) \leftarrow \texttt{CSWAP}((Q,R), k^{\text{th}}\text{ bit of }n)$ \STATE $Q \leftarrow \texttt{xDBL}(Q)$ \STATE $R \leftarrow \texttt{xADD}(x_P,Q,R)$ % \STATE $Q \leftarrow \texttt{xDBL}(Q)$ % \STATE $R \leftarrow \texttt{xADD}(x_P,Q,R)$ \STATE $(Q,R) \leftarrow \texttt{xladderstep}(x_P,Q,R)$ \STATE $(Q,R) \leftarrow \texttt{CSWAP}((Q,R), k^{\text{th}}\text{ bit of }n)$ \ENDFOR \RETURN $X_Q/Z_Q$ ... ...