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Specify (as a note in \crossref{actionstatement}) the encoding of primary inputs to the action circuit. 

This uses new helper functions $\Selectx$ and $\Selecty$ defined in \crossref{concreteextractorpallas}.
The specification of Extract_P has also been refactored to use $\Selectx$ (this does not change the Orchard protocol).

Signed-off-by: Daira Hopwood <daira@jacaranda.org>
This commit is contained in:
Daira Hopwood 2021-06-04 20:55:23 +01:00
parent 6a0c15df29
commit 5fa8a60b08
1 changed files with 28 additions and 4 deletions
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32
protocol/protocol.tex
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@ -2077,6 +2077,8 @@ electronic commerce and payment, financial privacy, proof of work, zero knowledg
\newcommand{\Generator}{\mathcal{P}}
\newcommand{\Selectu}{\scalebox{1.53}{$u$}}
\newcommand{\Selectv}{\scalebox{1.53}{$\varv$}}
\newcommand{\Selectx}{\scalebox{1.53}{$x$}}
\newcommand{\Selecty}{\scalebox{1.53}{$y$}}
\newcommand{\subgroupr}{(\kern-0.075emr\kern-0.075em)}
\newcommand{\Extract}{\mathsf{Extract}}
\newcommand{\GroupHash}{\mathsf{GroupHash}}
@ -6957,10 +6959,10 @@ Let $\ValueCommitAlg{Orchard}$, $\NoteCommitAlg{Orchard}$, and $\CommitIvkAlg$ b
Let $\SpendAuthSig{Orchard}$ be as defined in \crossref{concretespendauthsig}.
\vspace{-0.25ex}
Let $\GroupP$, $\GroupPstar$, $\GroupPx$, $\reprP$, $\ParamP{q}$, and $\ParamP{r}$ be as defined in \crossref{pallasandvesta}.
Let $\GroupP$, $\GroupPstar$, $\reprP$, $\ParamP{q}$, and $\ParamP{r}$ be as defined in \crossref{pallasandvesta}.
\vspace{-0.25ex}
Let $\ExtractP$ and $\ExtractPbot$ be as defined in \crossref{concreteextractorpallas}.
Let $\Selectx$, $\Selecty$, $\GroupPx$, $\ExtractP$, and $\ExtractPbot$ be as defined in \crossref{concreteextractorpallas}.
\vspace{-0.25ex}
Let $\DeriveNullifierAlg$ be as defined in \crossref{commitmentsandnullifiers}.
@ -7055,6 +7057,13 @@ $\vNew{} = 0$ or $\enableOutputs = 1$.
For details of the form and encoding of \actionStatement proofs, see \crossref{halo2}.
\begin{pnotes}
\item The \primaryInputs are encoded as the following sequence of type $\typeexp{\GF{\ParamP{q}}}{8}$: \\
$\big[\,\rt{Orchard} \pmod{\ParamP{q}}, \Selectx\Of{\cvNet{}}, \Selecty\Of{\cvNet{}},
\nfOld{} \pmod{\ParamP{q}}, \Selectx\Of{\AuthSignRandomizedPublic}, \Selecty\Of{\AuthSignRandomizedPublic},
\cmX \!\pmod{\ParamP{q}}, \mathsf{flagsOrchard} \pmod{\ParamP{q}} \,\big]$, \\[0.5ex]
where $\mathsf{flagsOrchard} = 2 \mult \enableOutputs + \enableSpends$. \\[1ex]
(Recall from \crossref{notation} that ``$\!\!\pmod{\ParamP{q}}$'' converts an integer into a $\GF{\ParamP{q}}$
element in the obvious way.)
\item \xPrimary and \auxiliaryInputs \MUST be constrained to have the types specified.
In particular, $\DiversifiedTransmitBaseOld$ cannot be $\ZeroP$.
The $\ValueCommitOutput{Orchard}$ and $\SpendAuthSigPublic{Orchard}$ types represent
@ -10795,6 +10804,16 @@ $\abstG{}\Of{P\Repr}$ is computed as follows:
\vspace{-1ex}
Let $\GroupP$, $\ZeroP$, $\ParamP{q}$, and $\ParamP{b}$ be as defined in \crossref{pallasandvesta}.
Define $\Selectx \typecolon \GroupP \rightarrow \GF{\ParamP{q}}$ and $\Selecty \typecolon \GroupP \rightarrow \GF{\ParamP{q}}$ such that:
\vspace{-1ex}
\begin{formulae}
\item $\Selectx\big(\ZeroP\big) = 0$
\item $\Selectx\big((x, y)\big) = x$
\item $\Selecty\big(\ZeroP\big) = 0$
\item $\Selecty\big((x, y)\big) = y$.
\end{formulae}
Define $\GroupPstarx$ as the set of $x$-coordinates (as integers) of points on the \pallasCurve, i.e.
\vspace{-1ex}
@ -10810,8 +10829,7 @@ Define $\ExtractP \typecolon \GroupP \rightarrow \GroupPx$ such that
\vspace{-1ex}
\begin{formulae}
\item $\ExtractP\big(\ZeroP\big) = 0$
\item $\ExtractP\big((x, y)\big) = x \bmod \ParamP{q}$.
\item $\ExtractP(P) = \Selectx(P) \bmod \ParamP{q}$.
\end{formulae}
\vspace{-1ex}
@ -14337,6 +14355,12 @@ Peter Newell's illustration of the Jubjub bird, from \cite{Carroll1902}.
\historyentry{2021.2.3}{}
\begin{itemize}
\nufive{
\item Specify (as a note in \crossref{actionstatement}) the encoding of \primaryInputs
to the \actionCircuit. This uses new helper functions $\Selectx$ and $\Selecty$ defined
in \crossref{concreteextractorpallas}. The specification of $\ExtractP$ has also been
refactored to use $\Selectx$ (this does not change the \Orchard protocol).
} %nufive
\item Move the section on abstraction (previously section 5.1) to \crossref{abstractprotocol}.
Section 5.2 has been split into two (\crossref{endian} and \crossref{bitlayout}) to
avoid renumbering later subsections.