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-rw-r--r--doc/paper/figs/deposit.tex62
-rw-r--r--doc/paper/figs/keys.tex54
-rw-r--r--doc/paper/figs/refresh.tex200
-rw-r--r--doc/paper/figs/withdraw.tex49
-rw-r--r--doc/paper/taler.tex104
5 files changed, 425 insertions, 44 deletions
diff --git a/doc/paper/figs/deposit.tex b/doc/paper/figs/deposit.tex
new file mode 100644
index 00000000..101d4f70
--- /dev/null
+++ b/doc/paper/figs/deposit.tex
@@ -0,0 +1,62 @@
+
+ \begin{figure}[th]
+ \begin{minipage}[b]{0.45\linewidth}
+ \begin{center}
+ \begin{tikzpicture}[scale = 0.4,
+ transform shape,
+ msglabel/.style = { text = Black, yshift = .3cm,
+ sloped, midway },
+ okmsg/.style = { ->, color = MidnightBlue, thick,
+ >=stealth },
+ rstmsg/.style = { ->, color = BrickRed, thick,
+ >=stealth }
+ ]
+ \node[draw = MidnightBlue,
+ fill = CornflowerBlue,
+ minimum width = .3cm,
+ minimum height = 10cm
+ ] (h1) at (-4, 0) {};
+ \node[draw = MidnightBlue,
+ fill = CornflowerBlue,
+ minimum width = .3cm,
+ minimum height = 10cm
+ ] (h2) at (4, 0) {};
+ \node[above = 0cm of h1] {Merchant};
+ \node[above = 0cm of h2] {Exchange};
+
+ \path[->, color = MidnightBlue, very thick, >=stealth]
+ (-5, 4.5) edge
+ node[rotate=90, text = Black, yshift = .3cm] {Time}
+ (-5, -4.5);
+ \path[->, color = MidnightBlue, thick, >=stealth]
+ ($(h1.east)+(0,3)$) edge
+ node[text = Black, yshift = .3cm, sloped] {$S_{DK}(C), S_{c}(D)$}
+ ($(h2.west)+(0,2)$);
+ \path[->, color = MidnightBlue, thick, >=stealth]
+ ($(h2.west)+(0,0.5)$) edge
+ node[text = Black, yshift = .3cm, sloped] {200 OK: $S_{SK}(S_{c}(D))$}
+ ($(h1.east)+(0,-0.5)$);
+ \path[rstmsg]
+ ($(h2.west)+(0, -2.5)$) edge
+ node[msglabel] {409 CONFLICT: $S_{c}(D')$}
+ ($(h1.east)+(0, -3.5)$);
+ \node at (5.3, 0) {};
+ \end{tikzpicture}
+ \end{center}
+ \end{minipage}
+ \hspace{0.5cm}
+ \begin{minipage}[b]{0.45\linewidth}
+ \tiny
+ \begin{description}
+ \item[$DK$] Denomination key
+ \item[$S_{DK}()$] RSA-FDH signature using $DK$
+ \item[$c$] Private coin key, $C := cG$.
+ \item[$S_{C}()$] EdDSA signature using $c$
+ \item[$D$] Deposit details
+ \item[$SK$] Exchange's signing key
+ \item[$S_{SK}()$] EdDSA signature using $SK$
+ \item[$D'$] Conficting deposit details $D' \not= D$
+ \end{description}
+ \end{minipage}
+ \end{figure}
+
diff --git a/doc/paper/figs/keys.tex b/doc/paper/figs/keys.tex
new file mode 100644
index 00000000..839c273f
--- /dev/null
+++ b/doc/paper/figs/keys.tex
@@ -0,0 +1,54 @@
+ \begin{figure}[th]
+ \begin{minipage}[b]{0.45\linewidth}
+ \begin{center}
+ \begin{tikzpicture}[scale = 0.4,
+ transform shape,
+ msglabel/.style = { text = Black, yshift = .3cm,
+ sloped, midway },
+ okmsg/.style = { ->, color = MidnightBlue, thick,
+ >=stealth },
+ rstmsg/.style = { ->, color = BrickRed, thick,
+ >=stealth }
+ ]
+ \node[draw = MidnightBlue,
+ fill = CornflowerBlue,
+ minimum width = .3cm,
+ minimum height = 10cm
+ ] (h1) at (-4, 0) {};
+ \node[draw = MidnightBlue,
+ fill = CornflowerBlue,
+ minimum width = .3cm,
+ minimum height = 10cm
+ ] (h2) at (4, 0) {};
+ \node[above = 0cm of h1] {Wallet};
+ \node[above = 0cm of h2] {Exchange};
+
+ \path[->, color = MidnightBlue, very thick, >=stealth]
+ (-5, 4.5) edge
+ node[rotate=90, text = Black, yshift = .3cm] {Time}
+ (-5, -4.5);
+ \path[->, color = MidnightBlue, thick, >=stealth]
+ ($(h1.east)+(0,3)$) edge
+ node[text = Black, yshift = .3cm, sloped] {GET {\tt /keys}}
+ ($(h2.west)+(0,2)$);
+ \path[->, color = MidnightBlue, thick, >=stealth]
+ ($(h2.west)+(0,0.5)$) edge
+ node[text = Black, yshift = .3cm, sloped] {200 OK: $S_T(DK,A_{DK},M), S_M(SK)$}
+ ($(h1.east)+(0,-0.5)$);
+ \node at (5.3, 0) {};
+ \end{tikzpicture}
+ \end{center}
+ \end{minipage}
+ \hspace{0.4cm}
+ \begin{minipage}[b]{0.45\linewidth}
+ \tiny
+ \begin{description}
+ \item[$T$] financial regulator key Necessarily pinned
+ \item[$DK$] RSA public key (``denomination key'')
+ \item[$A_{DK}$] Value of coins signed by $DK$
+ \item[$M$] Offline master key of exchange
+ \item[$SK$] Online signing key of exchange
+ \end{description}
+ \end{minipage}
+ \end{figure}
+
diff --git a/doc/paper/figs/refresh.tex b/doc/paper/figs/refresh.tex
new file mode 100644
index 00000000..6908527e
--- /dev/null
+++ b/doc/paper/figs/refresh.tex
@@ -0,0 +1,200 @@
+\begin{frame}{Taler {\tt /refresh/melt}}
+ \begin{figure}[th]
+ \begin{minipage}[b]{0.45\linewidth}
+ \begin{center}
+ \begin{tikzpicture}[scale = 0.4,
+ transform shape,
+ msglabel/.style = { text = Black, yshift = .3cm,
+ sloped, midway },
+ okmsg/.style = { ->, color = MidnightBlue, thick,
+ >=stealth },
+ rstmsg/.style = { ->, color = BrickRed, thick,
+ >=stealth }
+ ]
+ \node[draw = MidnightBlue,
+ fill = CornflowerBlue,
+ minimum width = .3cm,
+ minimum height = 10cm
+ ] (h1) at (-4, 0) {};
+ \node[draw = MidnightBlue,
+ fill = CornflowerBlue,
+ minimum width = .3cm,
+ minimum height = 10cm
+ ] (h2) at (4, 0) {};
+ \node[above = 0cm of h1] {Customer};
+ \node[above = 0cm of h2] {Exchange};
+
+ \path[->, color = MidnightBlue, very thick, >=stealth]
+ (-5, 4.5) edge
+ node[rotate=90, text = Black, yshift = .3cm] {Time}
+ (-5, -4.5);
+ \path[->, color = MidnightBlue, thick, >=stealth]
+ ($(h1.east)+(0,3)$) edge
+ node[text = Black, yshift = .3cm, sloped] {POST {\tt /refresh/melt} $S_{DK}(C), S_c({\cal DK}, {\cal T},{\cal B})$}
+ ($(h2.west)+(0,2)$);
+ \path[->, color = MidnightBlue, thick, >=stealth]
+ ($(h2.west)+(0,0.5)$) edge
+ node[text = Black, yshift = .3cm, sloped] {200 OK: $S_{SK}(H({\cal T}, {\cal B}),\gamma)$}
+ ($(h1.east)+(0,-0.5)$);
+ \path[rstmsg]
+ ($(h2.west)+(0, -2.5)$) edge
+ node[msglabel] {409 CONFLICT: $S_{C}(X), \ldots$}
+ ($(h1.east)+(0, -3.5)$);
+ \node at (5.3, 0) {};
+ \end{tikzpicture}
+ \end{center}
+ \end{minipage}
+ \hspace{0.5cm}
+ \begin{minipage}[b]{0.45\linewidth}
+ \tiny
+ \begin{description}
+ \item[$\kappa$] System-wide security parameter, usually 3.
+ \\ \smallskip
+ \item[$\cal DK$] $:= [DK^{(i)}]_i$ \\ List of denomination keys \\
+ $D + \sum_i A_{DK^{(i)}} < A_{DK}$
+ \item[$t_j$] Random scalar for $j<\kappa$
+ \item[${\cal T}$] $:= [T_j]_\kappa$ where $T_j = t_j G$
+ \item[$k_j$] $:= c T_j = t_j C$ is an ECDHE
+ \item[$b_j^{(i)}$] $:= \texttt{KDFb}(k_j,i)$ % blinding factor
+ \item[$c_j^{(i)}$] $:= \texttt{KDFc}(k_j,i)$ % coin secret keys
+ \item[$C_j^{(i)}$] $: = c_j^{(i)} G$ % new coin publics % keys
+ \item[${\cal B}$] $:= [H( \beta_j )]_\kappa$ where \\
+ $\beta_j := \left[ B_{b_j^{(i)}}(C_j^{(i)}) \right]_i$
+ \\ \smallskip
+ \item[$\gamma$] Random value in $[0,\kappa)$
+% \\ \smallskip
+% \item[$X$] Deposit or refresh
+ \end{description}
+ \end{minipage}
+ \end{figure}
+\end{frame}
+
+
+\begin{frame}{Taler {\tt /refresh/reveal}}
+ \begin{figure}[th]
+ \begin{minipage}[b]{0.45\linewidth}
+ \begin{center}
+ \begin{tikzpicture}[scale = 0.4,
+ transform shape,
+ msglabel/.style = { text = Black, yshift = .3cm,
+ sloped, midway },
+ okmsg/.style = { ->, color = MidnightBlue, thick,
+ >=stealth },
+ rstmsg/.style = { ->, color = BrickRed, thick,
+ >=stealth }
+ ]
+ \node[draw = MidnightBlue,
+ fill = CornflowerBlue,
+ minimum width = .3cm,
+ minimum height = 10cm
+ ] (h1) at (-4, 0) {};
+ \node[draw = MidnightBlue,
+ fill = CornflowerBlue,
+ minimum width = .3cm,
+ minimum height = 10cm
+ ] (h2) at (4, 0) {};
+ \node[above = 0cm of h1] {Customer};
+ \node[above = 0cm of h2] {Exchange};
+
+ \path[->, color = MidnightBlue, very thick, >=stealth]
+ (-5, 4.5) edge
+ node[rotate=90, text = Black, yshift = .3cm] {Time}
+ (-5, -4.5);
+ \path[->, color = MidnightBlue, thick, >=stealth]
+ ($(h1.east)+(0,3)$) edge
+ node[text = Black, yshift = .3cm, sloped] {POST {\tt /refresh/reveal} $H({\cal T}, {\cal B}), {\tilde{\cal T}}, \beta_\gamma$}
+ ($(h2.west)+(0,2)$);
+ \path[->, color = MidnightBlue, thick, >=stealth]
+ ($(h2.west)+(0,0.5)$) edge
+ node[text = Black, yshift = .3cm, sloped] {200 OK: $\cal S$}
+ ($(h1.east)+(0,-0.5)$);
+ \path[rstmsg]
+ ($(h2.west)+(0, -2.5)$) edge
+ node[msglabel] {400 BAD REQUEST: $Z$}
+ ($(h1.east)+(0, -3.5)$);
+ \node at (5.3, 0) {};
+ \end{tikzpicture}
+ \end{center}
+ \end{minipage}
+ \hspace{0.5cm}
+ \begin{minipage}[b]{0.45\linewidth}
+ \tiny
+ \begin{description}
+ \item[$\cal DK$] $:= [DK^{(i)}]_i$
+ \item[$t_j$] .. \\ \smallskip
+
+ \item[$\tilde{\cal T}$] $:= [t_j | j \in \kappa, j \neq \gamma]$ \\ \smallskip
+
+ \item[$k_\gamma$] $:= c T_\gamma = t_\gamma C$
+ \item[$b_\gamma^{(i)}$] $:= \texttt{KDFb}(k_\gamma,i)$
+ \item[$c_\gamma^{(i)}$] $:= \texttt{KDFc}(k_\gamma,i)$
+ \item[$C_\gamma^{(i)}$] $: = c_\gamma^{(i)} G$
+
+ \item[$B_\gamma^{(i)}$] $:= B_{b_\gamma^{(i)}}(C_\gamma^{(i)})$
+ \item[$\beta_\gamma$] $:= \big[ B_\gamma^{(i)} \big]_i$
+ \item[$\cal S$] $:= \left[ S_{DK^{(i)}}( B_\gamma^{(i)} ) \right]_i$ \\ \smallskip
+
+ \item[$Z$] Cut-and-choose missmatch information
+ \end{description}
+ \end{minipage}
+ \end{figure}
+\end{frame}
+
+
+\begin{frame}{Taler {\tt /refresh/link}}
+ \begin{figure}[th]
+ \begin{minipage}[b]{0.45\linewidth}
+ \begin{center}
+ \begin{tikzpicture}[scale = 0.4,
+ transform shape,
+ msglabel/.style = { text = Black, yshift = .3cm,
+ sloped, midway },
+ okmsg/.style = { ->, color = MidnightBlue, thick,
+ >=stealth },
+ rstmsg/.style = { ->, color = BrickRed, thick,
+ >=stealth }
+ ]
+ \node[draw = MidnightBlue,
+ fill = CornflowerBlue,
+ minimum width = .3cm,
+ minimum height = 10cm
+ ] (h1) at (-4, 0) {};
+ \node[draw = MidnightBlue,
+ fill = CornflowerBlue,
+ minimum width = .3cm,
+ minimum height = 10cm
+ ] (h2) at (4, 0) {};
+ \node[above = 0cm of h1] {Customer};
+ \node[above = 0cm of h2] {Exchagne};
+
+ \path[->, color = MidnightBlue, very thick, >=stealth]
+ (-5, 4.5) edge
+ node[rotate=90, text = Black, yshift = .3cm] {Time}
+ (-5, -4.5);
+ \path[->, color = MidnightBlue, thick, >=stealth]
+ ($(h1.east)+(0,3)$) edge
+ node[text = Black, yshift = .3cm, sloped] {POST {\tt /refresh/link} $C$}
+ ($(h2.west)+(0,2)$);
+ \path[->, color = MidnightBlue, thick, >=stealth]
+ ($(h2.west)+(0,0.5)$) edge
+ node[text = Black, yshift = .3cm, sloped] {200 OK: $T_\gamma$}
+ ($(h1.east)+(0,-0.5)$);
+ \path[rstmsg]
+ ($(h2.west)+(0, -2.5)$) edge
+ node[msglabel] {404 NOT FOUND}
+ ($(h1.east)+(0, -3.5)$);
+ \node at (5.3, 0) {};
+ \end{tikzpicture}
+ \end{center}
+ \end{minipage}
+ \hspace{0.5cm}
+ \begin{minipage}[b]{0.45\linewidth}
+ \tiny
+ \begin{description}
+ \item[$C$] Old coind public key \\ \smallskip
+ \item[$T_\gamma$] Linkage data $\cal L$ at $\gamma$
+ \end{description}
+ \end{minipage}
+ \end{figure}
+\end{frame}
+
diff --git a/doc/paper/figs/withdraw.tex b/doc/paper/figs/withdraw.tex
new file mode 100644
index 00000000..8fc1ded3
--- /dev/null
+++ b/doc/paper/figs/withdraw.tex
@@ -0,0 +1,49 @@
+\begin{SCfigure}
+ \begin{minipage}[b]{0.45\linewidth}
+ \begin{tikzpicture}[scale = 0.4,
+ transform shape,
+ msglabel/.style = { text = Black, yshift = .3cm,
+ sloped, midway },
+ okmsg/.style = { ->, color = MidnightBlue, thick,
+ >=stealth },
+ rstmsg/.style = { ->, color = BrickRed, thick,
+ >=stealth }
+ ]
+ \node[draw = MidnightBlue,
+ fill = CornflowerBlue,
+ minimum width = .3cm,
+ minimum height = 10cm
+ ] (h1) at (-4, 0) {};
+ \node[draw = MidnightBlue,
+ fill = CornflowerBlue,
+ minimum width = .3cm,
+ minimum height = 10cm
+ ] (h2) at (4, 0) {};
+ \node[above = 0cm of h1] {Wallet};
+ \node[above = 0cm of h2] {Exchange};
+
+ \path[->, color = MidnightBlue, very thick, >=stealth]
+ (-5, 4.5) edge
+ node[rotate=90, text = Black, yshift = .3cm] {Time}
+ (-5, -4.5);
+ \path[okmsg, dashed]
+ ($(h1.east)+(0, 4.0)+(0, -1.0)$) edge
+ node[msglabel] {SEPA(RK,A)}
+ ($(h2.west)+(0, 3.5)+(0, -1.0)$);
+ \path[okmsg]
+ ($(h1.east)+(0, -1.0)$) edge
+ node[msglabel] {$S_{RK}(DK, B_b(C))$}
+ ($(h2.west)+(0, -1.5)$);
+ \path[okmsg]
+ ($(h2.west)+(0, -2.0)$) edge
+ node[msglabel] {200 OK: $S_{DK}(B_b(C))$)}
+ ($(h1.east)+(0, -2.5)$);
+ \path[rstmsg]
+ ($(h2.west)+(0, -3.5)$) edge
+ node[msglabel] {402 PAYMENT REQUIRED: $S_{RK}(DK, B_b(C))$)}
+ ($(h1.east)+(0, -4)$);
+ \node at (5.3, 0) {};
+ \end{tikzpicture}
+ \end{minipage}
+\end{SCfigure}
+
diff --git a/doc/paper/taler.tex b/doc/paper/taler.tex
index 8e7ae606..79272cb4 100644
--- a/doc/paper/taler.tex
+++ b/doc/paper/taler.tex
@@ -26,15 +26,18 @@
\usepackage{palatino}
\usepackage{xspace}
\usepackage{microtype}
-\usepackage{tikz,eurosym}
-\usepackage{amsmath,amssymb}
-\usepackage{enumitem}
+\usepackage{amsmath,amssymb,eurosym}
+\usepackage[dvipsnames]{xcolor}
+\usepackage{tikz}
\usetikzlibrary{shapes,arrows}
\usetikzlibrary{positioning}
\usetikzlibrary{calc}
+% \usepackage{enumitem}
\usepackage{caption}
\usepackage{subcaption}
\usepackage{subfig}
+% \usepackage{sidecap}
+% \usepackage{wrapfig}
% Relate to:
% http://fc14.ifca.ai/papers/fc14_submission_124.pdf
@@ -607,7 +610,6 @@ We use RSA for denomination keys and EdDSA over some eliptic curve
$\mathbb{E}$ for all other keys. Let $G$ denote the generator of
our elliptic curve $\mathbb{E}$.
-
\subsection{Withdrawal}
To withdraw anonymous digital coins, the customer first selects an
@@ -624,23 +626,28 @@ Now the customer carries out the following interaction with the exchange:
% It does create some confusion, like is a withdrawal key semi-ephemeral
% like a linking key?
-\begin{enumerate}
- \item The customer randomly generates:
+\begin{description}
+ \item[Setup] The customer randomly generates:
\begin{itemize}
\item withdrawal key $W := (w_s,W_p)$ with private key $w_s$ and public key $W_p$,
\item coin key $C := (c_s,C_p)$ with private key $c_s$ and public key $C_p := c_s G$,
\item blinding factor $b$, and commits $\langle W, C, b \rangle$ to disk.
\end{itemize}
- \item The customer transfers an amount of money corresponding to at least $K_v$
- to the exchange, with $W_p$ in the subject line of the transaction.
- \item The exchange receives the transaction and credits the $W_p$ reserve with
- the respective amount in its database.
- \item The customer sends $S_W(B)$ where $B := B_b(\FDH_K(C_p))$ to the exchange
- to request withdrawal of $C$; here, $B_b$ denotes Chaum-style blinding with
- blinding factor $b$.
- \item The exchange checks if the same withdrawal request was issued before;
- in this case, it sends $S_K(B)$ to the customer.%
-\footnote{$S_K$ denotes a Chaum-style blind signature with private key $K_s$.}
+ \item[SEPA Send]
+ The customer transfers an amount of money corresponding to
+ at least $K_v$ to the exchange, with $W_p$ in the subject line
+ of the transaction.
+ \item[SEPA Recieve]
+ The exchange receives the transaction and credits the reserve $W_p$
+ with the respective amount in its database.
+ \item[POST {\tt /withdraw/sign}]
+ The customer sends $S_W(B)$ where $B := B_b(\FDH_K(C_p))$ to
+ the exchange to request withdrawal of $C$; here, $B_b$ denotes
+ Chaum-style blinding with blinding factor $b$.
+ \item[200 OK / 402 PAYMENT REQUIRED]
+ The exchange checks if the same withdrawal request was issued before;
+ in this case, it sends a Chaum-style blind signature $S_K(B)$ with
+ private key $K_s$ to the customer. \\
If this is a fresh withdrawal request, the exchange performs the following transaction:
\begin{enumerate}
\item checks if the reserve $W_p$ has sufficient funds
@@ -656,11 +663,11 @@ Now the customer carries out the following interaction with the exchange:
Assuming the signature was valid, this would involve showing the transaction
history for the reserve.
% FIXME: Is it really the whole history?
- \item The customer computes and verifies the unblinded signature
+ \item[Done] The customer computes and verifies the unblinded signature
$S_K(\FDH_K{C_p}) = U_b(S_K(B))$.
Finally the customer saves the coin $\langle S_K(\FDH_K(C_p)), c_s \rangle$
to their local wallet on disk.
-\end{enumerate}
+\end{description}
\subsection{Exact and partial spending}
@@ -681,11 +688,13 @@ with signature $\widetilde{C} := S_K(\FDH_K(C_p))$
% FIXME: Again, these steps occur at different points in time, maybe
% that's okay, but refresh is slightly different.
-\begin{enumerate}
-\item\label{contract}
+\begin{description}
+\item[Merchant Setup] % \label{contract}
Let $\vec{X} := \langle X_1, \ldots, X_n \rangle$ denote the list of
exchanges accepted by the merchant where each $X_j$ is a exchange's
- public key. The merchant creates a digitally signed contract
+ public key.
+\item[Proposal]
+ The merchant creates a digitally signed contract
$\mathcal{A} := S_M(m, f, a, H(p, r), \vec{X})$
where $m$ is an identifier for this transaction, $a$ is data relevant
to the contract indicating which services or goods the merchant will
@@ -693,26 +702,30 @@ with signature $\widetilde{C} := S_K(\FDH_K(C_p))$
$p$ is the merchant's payment information (e.g. his IBAN number), and
$r$ is a random nonce. The merchant commits $\langle \mathcal{A} \rangle$
to disk and sends $\mathcal{A}$ to the customer.
-\item\label{deposit}
+\item[Customer Setup] % \label{deposit}
The customer should already possess a coin issued by a exchange that is
accepted by the merchant, meaning $K$ should be publicly signed by
some $X_j$ from $\vec{X}$, and has a value $\geq f$.
-\item The customer generates a \emph{deposit-permission} $\mathcal{D} :=
- S_c(\widetilde{C}, m, f, H(a), H(p,r), M_p)$
+\item[POST {\tt /???}]
+ The customer generates a \emph{deposit-permission}
+ $\mathcal{D} := S_c(\widetilde{C}, m, f, H(a), H(p,r), M_p)$
and sends $\langle \mathcal{D}, X_j\rangle$ to the merchant,
where $X_j$ is the exchange which signed $K$.
-\item The merchant gives $(\mathcal{D}, p, r)$ to the exchange, thereby
+\item[POST {\tt/deposit}]
+ The merchant gives $(\mathcal{D}, p, r)$ to the exchange, thereby
revealing $p$ only to the exchange.
-\item The exchange validates $\mathcal{D}$ and checks for double spending.
+\item[200 OK / 409 CONFLICT]
+ The exchange validates $\mathcal{D}$ and checks for double spending.
If the coin has been involved in previous transactions and the new
one would exceed its remaining value, it sends an error
- with the records from the previous transactions back to the merchant.
-%
+ with the records from the previous transactions back to the merchant. \\
+ %
If double spending is not found, the exchange commits $\langle \mathcal{D} \rangle$ to disk
and notifies the merchant that the deposit operation was successful.
-\item The merchant commits and forwards the notification from the exchange to the
+\item[200 OK / ???]
+ The merchant commits and forwards the notification from the exchange to the
customer, confirming the success or failure of the operation.
-\end{enumerate}
+\end{description}
We have simplified the exposition by assuming that one coin suffices,
but in practice a customer can use multiple coins from the same
@@ -771,9 +784,10 @@ generator of the elliptic curve.
% FIXME: I'm explicit about the rounds in postquantum.tex
-\begin{enumerate}
- \item For each $i = 1,\ldots,\kappa$, the customer randomly generates
- a transfer private key $t^{(i)}_s$ and computes
+\begin{description}
+ \item[POST {\tt /refresh/melt}]
+ For each $i = 1,\ldots,\kappa$, the customer randomly generates
+ a transfer private key $t^{(i)}_s$ and computes
\begin{itemize}
\item the transfer public key $T^{(i)}_p := t^{(i)}_s G$ and
\item the new coin secret seed $L_i := H(c'_s T_p^{(i)})$.
@@ -800,19 +814,21 @@ generator of the elliptic curve.
The customer computes $B^{(i)} := B_{b^{(i)}}(\FDH_K(C^{(i)}_p))$
for $i \in \{1,\ldots,\kappa\}$ and sends a commitment
$S_{C'}(\vec{B}, \vec{T_p})$ to the exchange.
- \item The exchange generates a random $\gamma$ with $1 \le \gamma \le \kappa$ and
+ \item[200 OK / 409 CONFLICT]
+ The exchange generates a random $\gamma$ with $1 \le \gamma \le \kappa$ and
marks $C'_p$ as spent by committing
$\langle C', \gamma, S_{C'}(\vec{B}, \vec{T_p}) \rangle$ to disk.
Auditing processes should assure that $\gamma$ is unpredictable until
- this time to prevent the exchange from assisting tax evasion.
- \item The exchange sends $S_{K'}(C'_p, \gamma)$ to the customer where
+ this time to prevent the exchange from assisting tax evasion. \\
+ %
+ The exchange sends $S_{K'}(C'_p, \gamma)$ to the customer where
$K'$ is the exchange's message signing key.
- \item The customer commits $\langle C', S_K(C'_p, \gamma) \rangle$ to disk.
-
- % \item
- Also, the customer assembles $\mathfrak{R} := \left(t_s^{(i)}\right)_{i \ne \gamma}$
- and sends $S_{C'}(\mathfrak{R})$ to the exchange.
- \item \label{step:refresh-ccheck}
+ \item[POST {\tt /refresh/reveal}]
+ The customer commits $\langle C', S_K(C'_p, \gamma) \rangle$ to disk.
+ Also, the customer assembles
+ $\mathfrak{R} := \left(t_s^{(i)}\right)_{i \ne \gamma}$
+ and sends $S_{C'}(\mathfrak{R})$ to the exchange.
+ \item[200 OK / 400 BAD REQUEST] % \label{step:refresh-ccheck}
The exchange checks whether $\mathfrak{R}$ is consistent with
the commitments; specifically, it computes for $i \not= \gamma$:
@@ -835,12 +851,12 @@ generator of the elliptic curve.
and checks if $\overline{B^{(i)}} = B^{(i)}$
and $\overline{T^{(i)}_p} = T^{(i)}_p$.
- \item \label{step:refresh-done}
+ % \item[200 OK / 409 CONFLICT] % \label{step:refresh-done}
If the commitments were consistent, the exchange sends the
blind signature $\widetilde{C} := S_{K}(B^{(\gamma)})$ to the customer.
Otherwise, the exchange responds with an error indicating
the location of the failure.
-\end{enumerate}
+\end{description}
%\subsection{N-to-M Refreshing}
%
generated by cgit v1.2.3 (git 2.39.1) at 2025-10-31 11:00:00 +0000