\textit{$MS_g$ = set MS to save all $\tuple{id, s_{last}}$ pairs while\r
traversing DT after a request to server (initially empty)} \\\r
\textit{SK = Secret Key} \\\r
-\textit{$SM$ = associative array of $\tuple{s, id}$ of all slots in a previous read\r
+\textit{$SM$ = associative array of $\tuple{s, id}$ of all slots in previous reads\r
(initially empty)} \\ \\\r
\textbf{Helper Functions} \\\r
$MaxSlot(SL_s)= \tuple{s, sv}$ \textit{such that} $\tuple{s, sv}\r
-\in SL_s \wedge \forall \tuple{s_s, sv_s} \in SL_s, s \geq s_s$ \\\r
+ \in SL_s \wedge \forall \tuple{s_s, sv_s} \in SL_s, s \geq s_s$ \\\r
$MinSlot(SL_s)= \tuple{s, sv}$ \textit{such that} $\tuple{s, sv} \r
-\in SL_s \wedge \forall \tuple{s_s, sv_s} \in SL_s, s \leq s_s$ \\\r
+ \in SL_s \wedge \forall \tuple{s_s, sv_s} \in SL_s, s \leq s_s$ \\\r
$Slot(SL_s,s_s)= \tuple{s, sv}$ \textit{such that} $\tuple{s, sv} \r
-\in SL_s \wedge \forall \tuple{s_s, sv_s} \in SL_s, s = s_s$ \\\r
+ \in SL_s \wedge \forall \tuple{s_s, sv_s} \in SL_s, s = s_s$ \\\r
$SeqN(\tuple{s, sv})=s$ \\\r
$SlotVal(\tuple{s, sv})=sv$ \\\r
$CreateLastSL(s,sv,id)=\tuple{s,sv,id}=sl_{last}$ \\\r
$GetCurrHmac(Dat_s = \tuple{s,id,hmac_p,DE,hmac_c})=hmac_c$ \\\r
$GetDatEnt(Dat_s = \tuple{s,id,hmac_p,DE,hmac_c})=DE$ \\\r
$GetLiveSS(SS_{live},ss_s)= ss$ \textit{such that} $ss \in SS_{live} \r
-\wedge \forall ss_s \in SS_{live}, ss = ss_s$ \\\r
+ \wedge \forall ss_s \in SS_{live}, ss = ss_s$ \\\r
$GetLiveCR(CR_{live},cr_s)= cr$ \textit{such that} $cr \in CR_{live} \r
-\wedge \forall cr_s \in CR_{live}, cr = cr_s$ \\\r
+ \wedge \forall cr_s \in CR_{live}, cr = cr_s$ \\\r
$GetLivEntLastS(LV_s,kv_s)= s$ \textit{such that} $\tuple{kv, s} \in LV_s \r
-\wedge \forall \tuple{kv_s, s_s} \in LV_s, kv_s = kv$ \\\r
+ \wedge \forall \tuple{kv_s, s_s} \in LV_s, kv_s = kv$ \\\r
$GetKV($key-value data entry$)=\tuple{k_s,v_s} = kv_s$ \\\r
$GetSS($slot-sequence data entry$)=\tuple{id_s,s_{s_{last}}} = ss_s$ \\\r
$GetQS($queue-state data entry$)=qs_s$ \\\r
$GetS(cr = \tuple{s, id})=s$ \\\r
$GetId(cr = \tuple{s, id})=id$ \\\r
$GetKeyVal(DT_s,k_s)= \tuple{k, v}$ \textit{such that} $\tuple{k, v} \r
-\in DT_s \wedge \forall \tuple{k_s, v_s} \in DT_s, k = k_s$ \\\r
+ \in DT_s \wedge \forall \tuple{k_s, v_s} \in DT_s, k = k_s$ \\\r
$MaxLastSeqN(MS_s)= s_{last}$ \textit{such that} $\tuple{id, s_{last}} \in MS_s \r
-\wedge \forall \tuple{id_s, s_{s_{last}}} \in MS_s, s_{last} \geq s_{s_{last}}$ \\\r
+ \wedge \forall \tuple{id_s, s_{s_{last}}} \in MS_s, s_{last} \geq s_{s_{last}}$ \\\r
$MinLastSeqN(MS_s)= s_{last}$ \textit{such that} $\tuple{id, s_{last}} \in MS_s \r
-\wedge \forall \tuple{id_s, s_{s_{last}}} \in MS_s, s_{last} \leq s_{s_{last}}$ \\\r
+ \wedge \forall \tuple{id_s, s_{s_{last}}} \in MS_s, s_{last} \leq s_{s_{last}}$ \\\r
+$MinCRSeqN(CR_s)= s$ \textit{such that} $\tuple{s, id} \in CR_s \r
+ \wedge \forall \tuple{s_s, id_s} \in CR_s, s \leq s_s$ \\\r
\r
\begin{algorithmic}[1]\r
\Procedure{Error}{$msg$}\r
\end{algorithmic}\r
\r
\begin{algorithmic}[1]\r
-\Function{AddCRLivEnt}{$CR_{s_{live}},de_s$}\r
-\State $cr_s \gets GetCR(de_s)$\r
+\Function{AddCRLivEnt}{$CR_{s_{live}},cr_s$}\r
+%\State $cr_s \gets GetCR(de_s)$\r
\State $cr_t \gets GetLiveCR(CR_{s_{live}},cr_s)$\r
\If{$cr_t = \emptyset$}\r
\State $CR_{s_{live}} \gets CR_{s_{live}} \cup \{cr_s\}$\Comment{First occurrence}\r
\EndFunction\r
\end{algorithmic}\r
\r
+\begin{algorithmic}[1]\r
+\Function{UpdateSM}{$SM_s,CR_s$}\Comment{Remove if dead}\r
+\State $s_{cr_{min}} \gets MinCRSeqN(CR_s)$\r
+ \State $SM_s \gets SM_s - \{\tuple{s_s,id_s} \mid \tuple{s_s,id_s}\r
+ \in SM_s \wedge s_s < s_{cr_{min}}\}$\r
+\State \Return{$CR_{s_{live}}$}\r
+\EndFunction\r
+\end{algorithmic}\r
+\r
\begin{algorithmic}[1]\r
\Procedure{CheckLastSeqN}{$MS_s,MS_t$}\r
\For {$\tuple{id, s_t}$ in $MS_t$}\Comment{Check $MS_t$ based on the newer $MS_s$}\r
\State $id_s \gets GetId(cr_s)$\r
\State $s_{s_{last}} \gets GetLastSeqN(MS_s,id_s)$\r
\If{$s_{s_{last}} < s_s$}\r
- \State $\Call{CheckColRes}{SM_s,cr_s}$\r
+ \State $id_t \gets SM_s[s_s]$\r
+ \If{$id_s \neq id_t$}\r
+ \State \Call{Error}{'Invalid $id$ for this slot update'}\r
+ \EndIf\r
\EndIf\r
\EndIf\r
\EndProcedure\r
\end{algorithmic}\r
\r
-\begin{algorithmic}[1]\r
-\Procedure{CheckColRes}{$SM_s,cr_t$}\Comment{Check $id_s$ in $SM_s$}\r
-\State $s_t \gets GetS(cr_t)$\r
-\State $id_s \gets SM_s[s_t]$\r
-\If{$id_s \neq id_t$}\r
- \State \Call{Error}{'Invalid $id$ for this slot update'}\r
-\EndIf\r
-\EndProcedure\r
-\end{algorithmic}\r
-\r
\begin{algorithmic}[1]\r
\Function{StoreLastSlot}{$MS_s,sl_l,s_s,sv_s,id_s$}\r
\State $s_{min} \gets MinLastSeqN(MS_s)$\r
\begin{algorithmic}[1]\r
\Procedure{ProcessSL}{$SL_g$}\r
\State $MS_g \gets \emptyset$\r
-\State $SM_{curr} \gets \emptyset$\r
+%\State $SM_{curr} \gets \emptyset$\r
\State $\tuple{s_{g_{min}},sv_{g_{min}}} \gets MinSlot(SL_g)$\r
\State $\tuple{s_{g_{max}},sv_{g_{max}}} \gets MaxSlot(SL_g)$\r
\For{$s_g \gets s_{g_{min}}$ \textbf{to} $s_{g_{max}}$}\Comment{Process slots \r
in $SL_g$ in order}\r
\State $\tuple{s_g,sv_g} \gets Slot(SL_g,s_g)$\r
- \State $SM_{curr} \gets SM_{curr} \cup \{\tuple{s_g,sv_g}\}$\r
\State $Dat_g \gets Decrypt(SK,sv_g)$\r
+ \State $id_g \gets GetMacId(Dat_g)$\r
+ %\State $SM_{curr} \gets SM_{curr} \cup \{\tuple{s_g,id_g}\}$\r
+ \State $SM \gets SM \cup \{\tuple{s_g,id_g}\}$\r
\State $s_{g_{in}} \gets GetSeqN(Dat_g)$\r
\If{$s_g \neq s_{g_{in}}$}\r
\State \Call{Error}{'Invalid sequence number'}\r
\ForAll{$de_{g_{cr}} \in DE_{g_{cr}}$}\r
\State $cr_g \gets GetCR(de_{g_{cr}})$\r
\State $\Call{CheckCollision}{MS,SM,cr_g}$\r
- \State $CR_{live} \gets \Call{AddCRLivEnt}{CR_{live},de_{g_{cr}}}$\r
+ %\State $CR_{live} \gets \Call{AddCRLivEnt}{CR_{live},de_{g_{cr}}}$\r
+ \State $CR_{live} \gets \Call{AddCRLivEnt}{CR_{live},cr_g}$\r
\EndFor\r
\EndIf\r
\State $sl_{last} \gets \Call{StoreLastSlot}{MS,sl_{last},s_g,sv_g,id_g}$\r
\State $DT \gets \Call{UpdateDT}{DT,DE_g,LV,s_g}$\r
\EndFor\r
-\State $SM \gets SM_{curr}$\r
+%\State $SM \gets SM_{curr}$\r
\If{$m + |SL_g| \leq max_g$}\Comment{Check actual size against $max_g$}\r
\State $m \gets m + |SL_g|$\r
\Else\r
\State $\Call{CheckLastSeqN}{MS_g,MS}$\r
\State $\Call{UpdateSSLivEnt}{SS_{live},MS}$\r
\State $\Call{UpdateCRLivEnt}{CR_{live},MS}$\r
+\State $\Call{UpdateSM}{SM,CR_{live}}$\r
\EndProcedure\r
\end{algorithmic}\r
\r
\item Case 2.2.1: Some message in $\mathsf{X}$ was accepted. Let $\mathsf{s_{w_J}}$ \r
be the greatest sequence number of the messages that client $\mathsf{J}$ sent in \r
the path of message $\mathsf{w}$. In this case, before sending $\mathsf{p}$, \r
-$\mathsf{J}$'s value in $\mathsf{SM_J}$ for its own latest sequence number would \r
+$\mathsf{J}$'s value in $\mathsf{MS_J}$ for its own latest sequence number would \r
be strictly greater than $\mathsf{s_{q_J}}$. If there is a sequence of messages with \r
contiguous sequence numbers that $\mathsf{J}$ receives between $\mathsf{r_1}$ and \r
$\mathsf{p}$, $\mathsf{J}$ throws an error for a similar reason as Case 1.1. Otherwise, \r
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