diff --git a/protocol/protocol.tex b/protocol/protocol.tex index 4a06a7bf..1d8371b6 100644 --- a/protocol/protocol.tex +++ b/protocol/protocol.tex @@ -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 $\varv \typecolon \GF{\ParamS{r}}$. By writing the curve equation as $\varv^2 = (1 - \ParamJ{a} \smult u^2) / (1 - \ParamJ{d} \smult u^2)$, and noting that -$1 - \ParamJ{d} \smult u^2 \neq 0$, we have $\varv^2 = (1 - \ParamJ{a}) / (1 - \ParamJ{d})$. -The right-hand-side is a nonsquare in $\GF{\ParamS{r}}$, so there are no solutions for $\varv$ -(contradiction). +$1 - \ParamJ{d} \smult u^2 \neq 0$ because $\ParamJ{d}$ is nonsquare, +we have $\varv^2 = (1 - \ParamJ{a}) / (1 - \ParamJ{d})$. +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} } %sapling @@ -9999,6 +10000,8 @@ Peter Newell's illustration of the Jubjub bird, from \cite{Carroll1902}. \begin{itemize} \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 characters on recent versions of \TeX Live. \item Update the \texttt{Makefile} to use Ghostscript for PDF optimization.