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Clarify that Theorem 5.4.2 depends on the parameters of the Jubjub curve. 

Signed-off-by: Daira Hopwood <daira@jacaranda.org>
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Daira Hopwood 2019-06-18 22:58:14 +01:00
parent f4f4682d57
commit 847a002eff
1 changed files with 6 additions and 3 deletions
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@ -6235,9 +6235,10 @@ We show that there are no points in $\GroupJ$ with affine-ctEdwards $u$-coordina
Suppose for a contradiction that $(u, \varv) \in \GroupJ$ for $u = 1$ and some Suppose for a contradiction that $(u, \varv) \in \GroupJ$ for $u = 1$ and some
$\varv \typecolon \GF{\ParamS{r}}$. By writing the curve equation as $\varv \typecolon \GF{\ParamS{r}}$. By writing the curve equation as
$\varv^2 = (1 - \ParamJ{a} \smult u^2) / (1 - \ParamJ{d} \smult u^2)$, and noting that $\varv^2 = (1 - \ParamJ{a} \smult u^2) / (1 - \ParamJ{d} \smult u^2)$, and noting that
$1 - \ParamJ{d} \smult u^2 \neq 0$, we have $\varv^2 = (1 - \ParamJ{a}) / (1 - \ParamJ{d})$. $1 - \ParamJ{d} \smult u^2 \neq 0$ because $\ParamJ{d}$ is nonsquare,
The right-hand-side is a nonsquare in $\GF{\ParamS{r}}$, so there are no solutions for $\varv$ we have $\varv^2 = (1 - \ParamJ{a}) / (1 - \ParamJ{d})$.
(contradiction). The right-hand-side is a nonsquare in $\GF{\ParamS{r}}$ (for the \jubjubCurve parameters),
so there are no solutions for $\varv$ (contradiction).
\end{proof} \end{proof}
} %sapling } %sapling
@ -9999,6 +10000,8 @@ Peter Newell's illustration of the Jubjub bird, from \cite{Carroll1902}.
\begin{itemize} \begin{itemize}
\item Give a definition for \completeTwistedEdwardsEllipticCurves in \crossref{jubjub}. \item Give a definition for \completeTwistedEdwardsEllipticCurves in \crossref{jubjub}.
\item Clarify that \theoremref{thmnohashtouncommittedsapling} depends on the
parameters of the \jubjubCurve.
\item Ensure that this document builds correctly and without missing \item Ensure that this document builds correctly and without missing
characters on recent versions of \TeX Live. characters on recent versions of \TeX Live.
\item Update the \texttt{Makefile} to use Ghostscript for PDF optimization. \item Update the \texttt{Makefile} to use Ghostscript for PDF optimization.