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Remove the check that Merkle roots are not ⊥ for Orchard #530

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Remove the check that Merkle roots are not ⊥ for Orchard #530

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717a46b
Delete the consensus rule in \crossref{transactions} that required ch…
daira Jun 30, 2021
05ba3a1
Change the type of MerkleCRH^Orchard to have MerkleHash^Orchard in pl…
daira Jun 30, 2021
ce1529d
Allow the Merkle path validity check in the Action circuit to pass if…
daira Jun 30, 2021
1ce9739
Fix a typo in the Security Requirements for \crossref{orchardmerklecr…
daira Jun 30, 2021
cc3b523
Regenerate protocol.pdf.
daira Jun 30, 2021
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128 changes: 80 additions & 48 deletions protocol/protocol.tex
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Original file line number Diff line number Diff line change
Expand Up @@ -1894,6 +1894,7 @@
\newcommand{\MerkleHash}[1]{\bitseq{\MerkleHashLength{#1}}}
\newcommand{\MerkleHashOrchard}{\GroupPx}
\newcommand{\MerkleLayer}[1]{\range{0}{\MerkleDepth{#1}-1}}
\newcommand{\hash}{\mathsf{hash}}
\newcommand{\layerInput}{\mathsf{layer}}
\newcommand{\layerRepr}{{l\Repr}}
\newcommand{\leftInput}{\mathsf{left}}
Expand Down Expand Up @@ -3388,17 +3389,6 @@
\sapling{There is no equivalent of interstitial \treestates for \Sapling\nufive{ or
for \Orchard}.}

\nufive{
\vspace{1ex}
$\MerkleCRH{Orchard}$ can produce $\bot$ as output (with insignificant probability).
If either input is $\bot$, this is propagated to the output, and so if any \merkleNode
of a \noteCommitmentTree is $\bot$, then the \merkleRoot of that tree will be $\bot$.

\vspace{-1ex}
\consensusrule{The \merkleRoot of the \Orchard \noteCommitmentTree \MUSTNOT be $\bot$
in any (intermediate or output) \treestate created by a \block.}
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Note that after this change, the Orchard Merkle root in a final treestate (not just an intermediate treestate) is allowed to be 0. There's no advantage in making a distinction between intermediate and final roots, even if the latter is cheaper to check.

} %nufive


\lsubsection{JoinSplit Transfers and Descriptions}{joinsplit}

Expand Down Expand Up @@ -3767,13 +3757,12 @@
\begin{tabular}{@{\hskip 2em}l@{\;}l@{\;}l@{\;}l@{\;}l}
$\MerkleCRH{Sprout}$ &$\typecolon\, \MerkleLayer{Sprout}$ &$\times\; \MerkleHash{Sprout}$ &$\times\; \MerkleHash{Sprout}$ &$\rightarrow \MerkleHash{Sprout}$ \\
\setsapling $\MerkleCRH{Sapling}$ &\setsapling $\typecolon\, \MerkleLayer{Sapling}$ &\setsapling $\times\; \MerkleHash{Sapling}$ &\setsapling $\times\; \MerkleHash{Sapling}$ &\setsapling $\rightarrow \MerkleHash{Sapling}$\notbeforenufive{ \\
\setnufive $\MerkleCRH{Orchard}$ &\setnufive $\typecolon\, \MerkleLayer{Orchard}$ &\setnufive $\times\; \maybe{\MerkleHashOrchard}$ &\setnufive $\times\; \maybe{\MerkleHashOrchard}$ &\setnufive $\rightarrow \maybe{\MerkleHashOrchard}$}.
\setnufive $\MerkleCRH{Orchard}$ &\setnufive $\typecolon\, \MerkleLayer{Orchard}$ &\setnufive $\times\; \MerkleHashOrchard$ &\setnufive $\times\; \MerkleHashOrchard$ &\setnufive $\rightarrow \MerkleHashOrchard$}.
\end{tabular}

$\MerkleCRH{Sprout}$ is \collisionResistant except on its first argument.
\sapling{$\MerkleCRH{Sapling}$\notnufive{ is}\nufive{ and $\MerkleCRH{Orchard}$ are}
\collisionResistant on all\notnufive{ its}\nufive{ their} arguments\nufive{ (restricted
to non-$\bot$ inputs in the case of $\MerkleCRH{Orchard}$)}.}
\collisionResistant on all\notnufive{ its}\nufive{ their} arguments.}

These functions are instantiated in \crossref{merklecrh}.

Expand Down Expand Up @@ -5938,22 +5927,31 @@
$\MerkleNode{\MerkleDepth{}}{i}$ is in a tree with a given \merkleRoot $\rt{} = \MerkleNode{0}{0}$.

\sapling{
\pnote{
For \Sapling, Merkle \merkleHashes are specified to be encoded as bit sequences, but the
\merkleRoot $\rt{Sapling}$ is encoded for the \primaryInput of a \spendProof as an element
of $\GF{\ParamJ{q}}$, as specified in \crossref{cctsaplingspend}. The \spendCircuit allows
inputs to $\MerkleCRH{Sapling}$ at each \merkleNode to be \nonCanonicallyFieldElement encoded,
as specified in \crossref{cctmerklepath}.
} %pnote
} %sapling

\begin{pnotes}
\item For \Sapling, Merkle \merkleHashes are specified to be encoded as bit sequences, but the
\merkleRoot $\rt{Sapling}$ is encoded for the \primaryInput of a \spendProof as an element
of $\GF{\ParamJ{q}}$, as specified in \crossref{cctsaplingspend}. The \spendCircuit allows
inputs to $\MerkleCRH{Sapling}$ at each \merkleNode to be \nonCanonicallyFieldElement encoded,
as specified in \crossref{cctmerklepath}.
Comment on lines +5931 to +5935
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This is just moving the existing note for formatting reasons.

\nufive{
\pnote{
For \Orchard, Merkle \merkleHashes have type $\MerkleHashOrchard$ as defined in
\crossref{concreteextractorpallas}. Similarly to \Sapling, the \actionCircuit allows inputs
to $\MerkleCRH{Orchard}$ at each \merkleNode to be \nonCanonicallyFieldElement encoded.
} %pnote
\item For \Orchard, Merkle \merkleHashes have type $\MerkleHashOrchard$ as defined in
\crossref{concreteextractorpallas}. Similarly to \Sapling, the \actionCircuit allows
inputs to $\MerkleCRH{Orchard}$ at each \merkleNode to be \nonCanonicallyFieldElement
encoded.
Comment on lines +5937 to +5940
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Similarly, this is just moving the existing note into a list.

\item The \actionCircuit is permitted to be implemented in such a way that the \merklePath
validity check can pass if any \merkleHash on the path, including the \merkleRoot, is
$0$. This can only happen if $\SinsemillaHash$ returned $\bot$ for that hash, because
$0$ is not the $x$-coordinate of any point on the \pallasCurve (as shown in a note at
\crossref{concreteextractorpallas}), and $\SinsemillaHashToPoint$ cannot return
$\ZeroP$. Allowing the validity check to pass in that case models the fact that
incomplete addition is used to implement Sinsemilla in the circuit. As proven in
\theoremref{thmsinsemillaex}, a $\bot$ output from $\SinsemillaHash$ yields a
nontrivial discrete logarithm relation. Since we assume finding such a relation to be
infeasible, we can argue that it is safe to allow an adversary to create a proof that
passes the Merkle validity check in such a case.
} %nufive
\end{pnotes}
} %sapling


\lsubsection{SIGHASH Transaction Hashing}{sighash}
Expand Down Expand Up @@ -7085,6 +7083,9 @@
\item In the Merkle path validity check, each \merkleLayer does \emph{not} check that its
input bit sequence is a canonical encoding (in $\range{0}{\ParamP{q}-1}$) of the integer
from the previous \merkleLayer.
\item As specified in \crossref{merklepath}, the validity check is permitted to be implemented in
such a way that it can pass if any $\MerkleCRH{Orchard}$ hash on the \merklePath outputs $0$.
This allows nondeterministic, incomplete addition to be used in the circuit for $\SinsemillaHash$.
\item It is \emph{not} checked that $\ValueCommitRand{} < \ParamP{r}$ or that $\NoteCommitRandOld{} < \ParamP{r}$
or that $\NoteCommitRandNew{} < \ParamP{r}$.
\item $\SpendAuthSigRandomizePublic{Orchard}(\AuthSignRandomizer, \AuthSignPublicPoint) =
Expand Down Expand Up @@ -8139,29 +8140,29 @@
\vspace{-2ex}
Let $\SinsemillaHash$ be as specified in \crossref{concretesinsemillahash}.

$\MerkleCRH{Orchard} \typecolon \MerkleLayer{Orchard} \times \maybe{\MerkleHashOrchard} \times \maybe{\MerkleHashOrchard}
\rightarrow \maybe{\MerkleHashOrchard}$ is defined as follows:
$\MerkleCRH{Orchard} \typecolon \MerkleLayer{Orchard} \times \MerkleHashOrchard \times \MerkleHashOrchard
\rightarrow \MerkleHashOrchard$ is defined as follows:

\begin{formulae}
\item $\MerkleCRH{Orchard}(\layerInput, \leftInput, \rightInput) := \begin{cases}
\bot, &\caseif \leftInput = \bot \text{ or } \rightInput = \bot \\
\Longunderstack[l]{$\SinsemillaHash(\ascii{z.cash:Orchard-MerkleCRH},$ \\
$\hspace{6.7em} \layerRepr \bconcat \leftRepr \bconcat \rightRepr),$} &\Longunderstack{\\ \squash otherwise}
0, &\caseif \hash = \bot \\
\hash, &\caseotherwise
\end{cases}$
\item \begin{tabular}{l@{\;}r@{\;}l}
where &$\layerRepr$ &$= \ItoLEBSP{10}\big(\MerkleDepth{Orchard} - 1 - \layerInput\big)$ \\
&$\leftRepr$ &$= \ItoLEBSP{\MerkleHashLength{Orchard}}\big(\leftInput\big)$ when $\leftInput \neq \bot$ \\
&$\rightRepr$ &$= \ItoLEBSP{\MerkleHashLength{Orchard}}\big(\rightInput\big)$ when $\rightInput \neq \bot$.
\item \begin{tabular}{@{}l@{\;}r@{\;}l}
where &$\hash$ &$= \SinsemillaHash(\ascii{z.cash:Orchard-MerkleCRH},\, \layerRepr \bconcat \leftRepr \bconcat \rightRepr)$ \\
&$\layerRepr$ &$= \ItoLEBSP{10}\big(\MerkleDepth{Orchard} - 1 - \layerInput\big)$ \\
&$\leftRepr$ &$= \ItoLEBSP{\MerkleHashLength{Orchard}}\big(\leftInput\big)$ \\
&$\rightRepr$ &$= \ItoLEBSP{\MerkleHashLength{Orchard}}\big(\rightInput\big)$.
\end{tabular}
\end{formulae}

\begin{securityrequirements}
\item $\SinsemillaHash$ must be \collisionResistant, when restricted to non-$\bot$ inputs.
\item It must be infeasible to find a input of length $6 + 2 \mult \MerkleHashLength{Orchard}$
to $\SinsemillaHash$ that yields output $\bot$.
\item $\SinsemillaHash$ must be \collisionResistant.
\item It must be infeasible to find a input of length $10 + 2 \mult \MerkleHashLength{Orchard}$
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This was an independent typo.

bits to $\SinsemillaHash$ that yields output $\bot$.
\end{securityrequirements}

\pnote{The prefix $l$ provides domain separation between inputs at different layers of the
\pnote{The prefix $\layerRepr$ provides domain separation between inputs at different layers of the
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Similarly, an independent fix.

\noteCommitmentTree.}
} %nufive

Expand Down Expand Up @@ -10183,10 +10184,12 @@
\end{proof}

\vspace{-2ex}
\nnote{There are also no points in $\GroupP$ with \affineSW $x$-coordinate $0 \pmod{\ParamP{q}}$.
We do not choose $\Uncommitted{Orchard} = 0$ because we define $\ExtractPbot\Of{\ZeroP} = 0$.
Although $\SinsemillaCommitAlg{}$ cannot return $\ZeroP$ (the incomplete addition would return
$\bot$ instead), it would arguably be confusing to rely on that.}
\nnote{There are also no points in $\GroupP$ with \affineSW $x$-coordinate
$0 \pmod{\ParamP{q}}$, as shown in a note at \crossref{concreteextractorpallas}.
We do not choose $\Uncommitted{Orchard} = 0$ because $\MerkleCRH{Orchard}$ returns $0$
in exceptional cases. Although the \merkleHashes of \merkleLeafNodes are separated from
the \merkleHashes at other \merkleLayers by the $\layerInput$ input to $\MerkleCRH{Orchard}$,
it would arguably be confusing to rely on that.}
} %nufive


Expand Down Expand Up @@ -10868,9 +10871,13 @@
\item $\ExtractPbot\big(P \typecolon \GroupP\big) = \ExtractP(P)$.
\end{formulae}

\vspace{-3ex}
\nnote{$\ExtractP$ returns the type $\GroupPx$ which is precise for its range, unlike $\ExtractJ$
which returns a bit sequence.}
\vspace{-2ex}
\begin{pnotes}
\item There is no solution to $y^2 = 0^3 + 5$ in $\GF{\ParamP{q}}$, and so $\ExtractP(P)$
can only be $0$ when $P = \ZeroP$.
Comment on lines +10876 to +10877
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We need to say this in order to argue that MerkleCRHOrchard only returns 0 for the exceptional case that we proved would yield a discrete log.

\item $\ExtractP$ returns the type $\GroupPx$ which is precise for its range, unlike $\ExtractJ$
which returns a bit sequence.
\end{pnotes}
} %nufive

\nufive{
Expand Down Expand Up @@ -14426,6 +14433,31 @@
\lsection{Change History}{changehistory}


\historyentry{2021.2.9}{}
\begin{itemize}
\nufive{
\item Delete the consensus rule in \crossref{transactions} that required checking
that each intermediate \merkleRoot of the \noteCommitmentTree is not $\bot$.
Checking this rule would have imposed a significant performance penalty,
since intermediate roots do not otherwise need to be computed.
\item Change the type of $\MerkleCRH{Orchard}$ to have $\MerkleHashOrchard$ in place
of $\maybe{\MerkleHashOrchard}$ for the inputs and output, and map a $\bot$
output from $\SinsemillaHash$ to $0$. (We retain the original definitions
of $\SinsemillaHash$ and $\SinsemillaHashToPoint$ both because it would be
disruptive to change them at this point in the Network Upgrade Process, and
because it is necessary to track $\bot$ outputs in order to correctly model
non-determinism in the \actionCircuit.)
\item Allow the Merkle path validity check in the \actionCircuit to pass if any
output of $\MerkleCRH{Orchard}$ is $0$, and add a note in \crossref{merklepath}
arguing that this is safe.
\item Fix a typo in the Security Requirements for \crossref{orchardmerklecrh}: the
length of the input to $\SinsemillaHash$ is $10 + 2 \mult \MerkleHashLength{Orchard}$
bits, not $6 + 2 \mult \MerkleHashLength{Orchard}$ bits.
} % nufive
\item No changes before \NUFive.
\end{itemize}


\historyentry{2021.2.8}{2021-06-29}
\begin{itemize}
\nufive{
Expand Down