Commit 04b70a7d authored by Benoit Viguier's avatar Benoit Viguier
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Using ``Reflections'' techniques (chapter 15 in \cite{CpdtJFR}), we prove
Using reflection (chapter 15 in \cite{CpdtJFR}), we prove
the functional correctness of the multiplicative inverse over \Zfield.
\begin{lemma}
\label{cor:inv_comput_field}
......
......@@ -54,7 +54,7 @@ $$E : y^2 + a_1 xy + a_3 y = x^3 + a_2 x^2 + a_4 x + a_6$$
where the $a_i$'s are in \K\ and the curve has no singular point (\ie no cusps
or self-intersections). The set of points defined over \K, written $E(\K)$, is formed by the
solutions $(x,y)$ of $E$ together with a distinguished point $\Oinf$ called point at infinity:
$$E(\K) = \{ E(x,y)~|~(x,y) \in \K \times \K\} \cup \{\Oinf\}$$
$$E(\K) = \{ (x,y) \in \K \times \K ~|~E(x,y)\} \cup \{\Oinf\}$$
\end{dfn}
\subsubsection{Short Weierstra{\ss} curves}
......@@ -317,7 +317,7 @@ Theorem opt_montgomery_ok (n m: nat) (x : K) :
forall (p : mc M), p#x0 = x ->
opt_montgomery n m x = (p *+ n)#x0.
\end{lstlisting}
The definition of \coqe{opt_montgomery} is closely related to \coqe{montgomery_rec_swap}
The definition of \coqe{opt_montgomery} is similar to \coqe{montgomery_rec_swap}
that was used in \coqe{RFC}.
We proved their equivalence, and used it in our
final proof of \coqe{Theorem RFC_Correct}.
......
\newpage
~\\
\newpage
% ~\\
% \newpage
\section{Prior reviews}
\label{appendix:past-reviews}
......
......@@ -225,7 +225,7 @@
volume = {3(2)},
pages = {1-93},
note = {\url{http://adam.chlipala.net/papers/CpdtJFR/}},
note = {\url{http://adam.chlipala.net/cpdt/}},
publisher = {University of Bologna},
}
......
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