Commit bc40eda7 authored by Benoit Viguier's avatar Benoit Viguier
Browse files

Small typos

parent 7ee3cf60
......@@ -382,10 +382,10 @@ applied (chapter 15 in \cite{CpdtJFR}).
The idea is to \emph{reflect} the goal into a decidable environment.
We show that for a property $P$, we can define a decidable Boolean property
$P_{bool}$ such that if $P_{bool}$ is \Coqe{true} then $P$ holds.
$$reify\_P : P_{bool} = true \implies P$$
By applying $reify\_P$ on $P$ our goal become $P_{bool} = true$.
$$\text{\textit{reify\_P}} : P_{bool} = \text{\textit{true}} \implies P$$
By applying \textit{reify\_P} on $P$ our goal become $P_{bool} = true$.
We then compute the result of $P_{bool}$. If the decision goes well we are
left with the tautology $true = true$.
left with the tautology $\text{\textit{true}} = \text{\textit{true}}$.
With this technique we prove the functional correctness of the inversion over \Zfield.
\begin{lemma}
......
......@@ -187,6 +187,8 @@ Definition ec_of_mc p :=
Lemma ec_of_mc_bij : bijective ec_of_mc.
\end{lstlisting}
% We use this isomorphism to derive that $(M_{a,b}(\K), + )$ is a group.
\subsubsection{Projective coordinates}
\label{subsec:ECC-projective}
......@@ -272,7 +274,7 @@ we can define a ladder similar to the one used in TweetNaCl (See \aref{alg:montg
\ENSURE{$a/c = \chi_0(n \cdot P)$ for any $P$ such that $\chi_0(P) = x$}
\STATE $(a,c) \leftarrow (1,0)$ ~~~~~~~~~~~~~~~{\color{gray}\textit{$\chi_0(\Oinf) = (1:0)$}}
\STATE $(b,d) \leftarrow (x,1)$ ~~~~~~~~~~~~~~~{\color{gray}\textit{$\chi_0(P) = (x:1)$}}
\FOR{$k$ := $m$ downto $1$}
\FOR{$k$ := $m$ \textbf{downto} $1$}
\IF{$k^{\text{th}}$ bit of $n$ is $1$}
\STATE $(a,b) \leftarrow (b,a)$
\STATE $(c,d) \leftarrow (d,c)$
......@@ -493,7 +495,7 @@ of formulas by using rewrite rules:
\qquad
\begin{split}
(a,0) \cdot (b,0) &= (a \cdot b, 0)\\
(0,a)^{-1} &= ((2\cdot a)^{-1},0)\\
(0,a)^{-1} &= (0,(2\cdot a)^{-1})\\
% (0, a)\cdot (0,b) &= (2\cdot a\cdot b, 0)\\
~\\
\end{split}
......
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