Add accumulator to snapshot

As close to cardano-scaling/hydra#2324 as possible

Author: vrom911

src/Hydra/Protocol/Figures/offchain-protocol.tex

@@ -48,7 +48,7 @@
 							$\Uinit \gets \bigcup_{j=1}^{n} U_j$ \;
 							% $\Out~(\hpSnap,(0,U_0))$ \;
 							$\hatmL \gets \Uinit$ \;
-							$\bar{\mc S} \gets \Sno(0, 0, [], \Uinit, \emptyset , \emptyset)$ \;
+							$\bar{\mc S} \gets \Sno(0, 0, [], \Uinit, \emptyset , \emptyset, \textcolor{red}{\accUTxO(\Uinit)})$ \;
 							$\hatv, \hats \gets 0$ \;
 							$\hatmT \gets \emptyset$ \;
 							$\tx_\omega \gets \bot$ \;
@@ -165,17 +165,18 @@
 									$\msCSig \gets \msComb(\hydraKeys^{setup}, \hatSigma)$ \;
 
 									% TODO: DRY message creation
-									\textcolor{red}{$\eta \gets \accUTxO(\hatmU)$} \;
+									\textcolor{red}{$A \gets \bar{\mc S}.A$} \;
+									\textcolor{red}{$\eta \gets \bar{\mc S}.U$} \;
 
-									\textcolor{red}{$\eta_\alpha \gets \accUTxO(U_\alpha)$} \;
+									\textcolor{red}{$\eta_\alpha \gets \bar{\mc S}.U_\alpha$} \;
 									$U_\omega \gets \mathsf{outputs}(\tx_\omega)$ \;
-									\textcolor{red}{$\eta_\omega \gets \accUTxO(U_\omega)$} \;
+									\textcolor{red}{$\eta_\omega \gets \bar{\mc S}.U_\omega$} \;
 									% NOTE: Implementation differs here and
 									% below as it stores seen version in seen
 									% snapshot and uses that to verify
 									\Req{} $\msVfy(\hydraKeysAgg, (\cid || \hatv || \hats || \eta || \eta_\alpha || \eta_\omega), \msCSig)$ \;
 									% create confirmed snapshot for later reference
-									$\bar{\mc S} \gets \Sno(\hatv, \hats, \hatmT, \hatmU, U_\alpha, U_\omega)$ \;
+									$\bar{\mc S} \gets \Sno(\hatv, \hats, \hatmT, \hatmU, U_\alpha, U_\omega, \bar{\mc S}.A)$ \;
 									$\bar{\mc S}.\sigma \gets \msCSig$ \;
 									%$\Out~(\hpSnap,(\bar{\mc S}.s,\bar{\mc S}.U))$ \;
 									$\forall \tx \in \mT_{\mathsf{req}} : \Out (\hpConf,\tx)$ \;
@@ -261,9 +262,9 @@
 				\begin{walgo}{0.6}
 					% CLOSE from client
 					\On{$(\hpClose)$ from client}{
-						\textcolor{red}{$\eta \gets \accUTxO(\bar{\mc S}.U)$} \;
-						\textcolor{red}{$\eta_\alpha \gets \accUTxO(\bar{\mc S}.U_\alpha$)} \;
-						\textcolor{red}{$\eta_\omega \gets \accUTxO(\bar{\mc S}.U_\omega)$} \;
+						\textcolor{red}{$\eta \gets \hash(\bar{\mc S}.A)$} \;
+						\textcolor{red}{$\eta_\alpha \gets \hash(\accUTxO(\bar{\mc S}.U_\alpha))$} \;
+						\textcolor{red}{$\eta_\omega \gets \hash(\accUTxO(\bar{\mc S}.U_\omega))$} \;
 						$\xi \gets \bar{\mc S}.\sigma$ \;
 						% XXX: \hatv needed to distinguish between CloseType redeemer, explain how exactly?
 						$\PostTx{}~(\mtxClose, \hatv, \bar{\mc S}.v, \bar{\mc S}.s, \eta , \eta_\alpha, \eta_\omega, \xi)$ \;
@@ -275,9 +276,9 @@
 					% CLOSE TX
 					\On{$(\gcChainClose, \eta) \lor (\gcChainContest, s_{c}, \eta)$ from chain}{
 						\If{$\bar{\mc S}.s > s_{c}$}{
-							\textcolor{red}{$\eta \gets \accUTxO(\bar{\mc S}.U)$} \;
-							\textcolor{red}{$\eta_\alpha \gets \accUTxO(\bar{\mc S}.U_\alpha$)} \;
-							\textcolor{red}{$\eta_\omega \gets \accUTxO({\bar{\mc S}.U_\omega})$} \;
+							\textcolor{red}{$\eta \gets \hash(\bar{\mc S}.A)$} \;
+							\textcolor{red}{$\eta_\alpha \gets \hash(\accUTxO(\bar{\mc S}.U_\alpha))$} \;
+							\textcolor{red}{$\eta_\omega \gets \hash(\accUTxO(\bar{\mc S}.U_\omega))$} \;
 							$\xi \gets \bar{\mc S}.\sigma$ \;
 							% XXX: \hatv needed to distinguish between CloseType redeemer, explain how exactly?
 							$\PostTx{}~(\mtxContest, \hatv, \bar{\mc S}.v, \bar{\mc S}.s, \eta , \eta_\alpha, \eta_\omega , \xi)$ \;

src/Hydra/Protocol/OffChain.tex

@@ -143,12 +143,13 @@ \subsection{Variables}
             $\bar{\mc S}.U$         & snapshotted UTxO set \\ \hline
             $\bar{\mc S}.U_\alpha$ & pending UTxO to increment \\ \hline
             $\bar{\mc S}.U_\omega$       & pending UTxO to decrement \\ \hline
+            \textcolor{red}{$\bar{\mc S}.A$}         & \textcolor{red}{BLS accumulator of the UTxO set} \\ \hline
             $\bar{\mc S}.\sigma$         & multisignature \\ \hline
           \end{tabular}
         \end{center}
 \end{itemize}
 
-where constructor $\text{snObj}(v, n, T, U, U_\alpha, U_\omega)$ initializes a
+where constructor $\text{snObj}(v, n, T, U, U_\alpha, U_\omega, \textcolor{red}{A})$ initializes a
 new snapshot object with $\bar{\mathcal{S}}.\sigma = \emptyset$. \\
 
 Additionally, deposit objects are created using
@@ -191,7 +192,7 @@ \subsubsection{Initializing the head}
 $\hatv = 0$, as well as snapshot number $\hats = 0$. No deposit transaction
 $\tx_{\alpha} = \bot$ and no decrement transaction $\tx_{\omega} = \bot$ are
 pending, and the last confirmed snapshot is initialized accordingly
-$\bar{\mc S} \gets \blue{\Sno(0, 0, [], \Uinit, \emptyset, \emptyset)}$.
+$\bar{\mc S} \gets \blue{\Sno(0, 0, [], \Uinit, \emptyset, \emptyset, \accUTxO(\Uinit))}$.
 
 \subsubsection{Processing transactions off-chain}
 
@@ -287,8 +288,8 @@ \subsubsection{Processing transactions off-chain}
 multisignature $\msCSig$ and $\Req$ it to be valid (constructing the signed
 message as in $\hpRS$). If everything is fine, the snapshot can be considered
 confirmed by creating the snapshot object
-$\bar{\mc S} \gets \Sno(\hatv, \hats, \hatmT, \hatmU, U_{\alpha}, \mathsf{outputs}(\tx_{\omega}))$
-and storing the multi-signature $\msCSig$ in it for later reference. In case
+$\bar{\mc S} \gets \Sno(\hatv, \hats, \hatmT, \hatmU, U_{\alpha}, \mathsf{outputs}(\tx_{\omega}), \textcolor{red}{A})$
+where \textcolor{red}{$A = \accUTxO(\hatmU)$ is the accumulator of the UTxO set}, and storing the multi-signature $\msCSig$ in it for later reference. In case
 there is a pending decommit, any participant can now submit a \mtxDecrement{}
 transaction by providing the just confirmed snapshot with its digests of the
 active UTxO set $\eta$ and the to be removed UTxO set $\eta_{\omega}$. If, however, there