Commit bc40eda7 by Benoit Viguier

### 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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