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NCC audit: Restrict the definition of a short Weierstrass elliptic curve 

to base fields of characteristic greater than 3.

Signed-off-by: Daira Hopwood <daira@jacaranda.org>
This commit is contained in:
Daira Hopwood 2021-03-25 23:43:06 +00:00
parent 2e50a09e97
commit 591c7e45cc
1 changed files with 7 additions and 4 deletions
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11
protocol/protocol.tex
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@ -10309,10 +10309,11 @@ system (playing a similar rôle to \BLSPairing in \Sapling), and \Pallas for the
The \representedGroups $\GroupP$ and $\GroupV$ of points on \Pallas and \Vesta respectively
are defined in this section.
A \defining{\swEllipticCurve}, as defined for example in \cite[Definition 2.3.1]{Hisil2010}, is an
elliptic curve $E$ over a field $\GF{q}$, parameterized by $a, b \typecolon \GF{q}$ such that
$4 \mult a^3 + 27 \mult b^2 \neq 0$, with equation $E : y^2 = x^3 + a \mult x + b$. The curve has
a distinguished zero point $\Zero$, also called the \definingquotedterm{point at infinity}.
A \defining{\swEllipticCurve} over a field $\GF{q}$ of characteristic greater than $3$, as
defined for example in \cite[Definition 2.3.1]{Hisil2010}, is an elliptic curve $E$ over $\GF{q}$,
parameterized by $a, b \typecolon \GF{q}$ such that $4 \mult a^3 + 27 \mult b^2 \neq 0$, with
equation $E : y^2 = x^3 + a \mult x + b$. The curve has a distinguished zero point $\Zero$, also
called the \definingquotedterm{point at infinity}.
For \Pallas and \Vesta we have $a = 0$ and so we will omit that term below.
\begin{tabular}{@{}l@{\;}r@{\;}l}
@ -13837,6 +13838,8 @@ Peter Newell's illustration of the Jubjub bird, from \cite{Carroll1902}.
\noteCommitment is not $\bot$.
\item Correct the definition of $\PRFnf{Orchard}{}$ in \crossref{concreteprfs}
by changing $\Poseidon$ to $\PoseidonHash$.
\item Restrict the definition of a \swEllipticCurve in \crossref{pallasandvesta} to
base fields of characteristic greater than $3$.
\end{itemize}
\item Correct the description of $\lengthField$ in \crossref{unifiedpaymentaddrencoding}.
\item Correct the type signature of $\DiversifyHash{Orchard}$ in \crossref{abstracthashes}.