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Diffstat (limited to 'doc/paper/taler.tex')
| -rw-r--r-- | doc/paper/taler.tex | 69 |
1 files changed, 34 insertions, 35 deletions
diff --git a/doc/paper/taler.tex b/doc/paper/taler.tex index 0da9c14b..d85f5594 100644 --- a/doc/paper/taler.tex +++ b/doc/paper/taler.tex @@ -716,25 +716,24 @@ Now the customer carries out the following interaction with the exchange: % It does create some confusion, like is a reserve key semi-ephemeral % like a linking key? -\begin{description} - \item[Setup] The customer randomly generates: +\begin{enumerate} + \item The customer randomly generates: \begin{itemize} \item reserve 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[Wire transfer send] - The customer transfers an amount of money corresponding to + The customer then 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[Wire transfer recieve] + \item The exchange receives the transaction and credits the reserve $W_p$ with the respective amount in its database. - \item[POST {\tt /withdraw/sign}] + \item The customer computes $B := B_b(\FDH_K(C_p))$ and sends $S_W(B)$ to the exchange to request withdrawal of $C$; here, $B_b$ denotes Chaum-style blinding with blinding factor $b$. - \item[200 OK / 403 FORBIDDEN] + \item 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. \\ @@ -752,11 +751,11 @@ Now the customer carries out the following interaction with the exchange: error back to the customer, with proof that it operated correctly. Assuming the signature was valid, this would involve showing the transaction history for the reserve. - \item[Done] The customer computes the unblinded signature $U_b(S_K(B))$ and + \item The customer computes the unblinded signature $U_b(S_K(B))$ and verifies that $S_K(\FDH_K(C_p)) = U_b(S_K(B))$. Finally the customer saves the coin $\langle S_K(\FDH_K(C_p)), c_s \rangle$ to their local wallet on disk. -\end{description} +\end{enumerate} \subsection{Exact and partial spending} @@ -777,53 +776,53 @@ 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{description} -\item[Merchant Setup] % \label{contract} +\begin{enumerate} +\item \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. -\item[Proposal] +\item The merchant creates a signed contract $\mathcal{A} := S_M(m, f, a, H(p, r), \vec{X})$ where $m$ is an identifier for this transaction, $f$ is the price of the offer, and $a$ is data relevant to the contract indicating which services or goods the merchant will - deliver to the customer, including the {\tt /merchant-specific} URI for the payment. + deliver to the customer, including the merchant specific URI for the payment. $p$ 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[Customer Setup] +\item The customer should already possess a coin $\widetilde{C}$ issued by a exchange that is accepted by the merchant, meaning $K$ of $\widetilde{C}$ should be publicly signed by some $X_j$ from $\vec{X}$, and has a value $\geq f$. -\item[POST {\tt /merchant-specific}] +% \item Let $X_j$ be the exchange which signed $\widetilde{C}$ with $K$. 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. -\item[POST {\tt/deposit}] + $$\mathcal{D} := S_c(\widetilde{C}, m, f, H(a), H(p,r), M_p)$$ + and sends $\langle \mathcal{D}, X_j\rangle$ to the merchant. \label{step:first-post} +\item The merchant gives $(\mathcal{D}, p, r)$ to the exchange, thereby revealing $p$ only to the exchange. -\item[200 OK / 403 FORBIDDEN] +\item 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 a ``403 FORBIDDEN'' error + one would exceed its remaining value, it sends an error 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 signs a ``200 OK'' message affirming the deposit operation was successful. -\item[200 OK / 424 FAILED DEPENDENCY] + and signs a message affirming the deposit operation was successful. +\item The merchant commits and forwards the notification from the exchange to the - customer, confirming the success (``200 OK'') or failure (``424 FAILED DEPENDENCY'') + customer, confirming the success or failure of the operation. -\end{description} +\end{enumerate} We have simplified the exposition by assuming that one coin suffices, but in practice a customer can use multiple coins from the same exchange where the total value adds up to $f$ by running the above steps for each of the coins. -If a transaction is aborted after the first POST, subsequent +If a transaction is aborted after step~\ref{step:first-post}, subsequent transactions with the same coin could be linked to this operation. The same applies to partially spent coins where $f$ is smaller than the actual value of the coin. To unlink subsequent transactions from @@ -884,23 +883,23 @@ than the comparable use of zk-SNARKs in ZeroCash~\cite{zerocash}. % FIXME: I'm explicit about the rounds in postquantum.tex -\begin{description} - \item[POST {\tt /refresh/melt}] +\begin{enumerate} +\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} + \begin{enumerate} \item the transfer public key $T^{(i)}_p := t^{(i)}_s G$ and \item the new coin secret seed $L^{(i)} := H(c'_s T_p^{(i)})$. - \end{itemize} + \end{enumerate} We have computed $L_i$ as a Diffie-Hellman shared secret between the transfer key pair $T^{(i)} := \left(t^{(i)}_s,T^{(i)}_p\right)$ and old coin key pair $C' := \left(c_s', C_p'\right)$; as a result, $L^{(i)} = H(t^{(i)}_s C'_p)$ also holds. Now the customer applies key derivation functions $\KDF_{\textrm{blinding}}$ and $\KDF_{\textrm{Ed25519}}$ to $L^{(i)}$ to generate - \begin{itemize} + \begin{enumerate} \item a blinding factor $b^{(i)} = \FDH_K(\KDF_{\textrm{blinding}}(L^{(i)}))$. \item $c_s^{(i)} = \KDF_{\textrm{Ed25519}}(L^{(i)})$ - \end{itemize} + \end{enumerate} Now the customer can compute her new coin key pair $C^{(i)} := \left(c_s^{(i)}, C_p^{(i)}\right)$ where $C^{(i)}_p := c^{(i)}_s G$. @@ -914,7 +913,7 @@ than the comparable use of zk-SNARKs in ZeroCash~\cite{zerocash}. 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[200 OK / 409 CONFLICT] + \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. @@ -923,12 +922,12 @@ than the comparable use of zk-SNARKs in ZeroCash~\cite{zerocash}. % The exchange sends $S_{K'}(C'_p, \gamma)$ to the customer where $K'$ is the exchange's message signing key, thereby commmitting the exchange to $\gamma$. - \item[POST {\tt /refresh/reveal}] + \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} + \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 $i \not= \gamma$: @@ -956,7 +955,7 @@ than the comparable use of zk-SNARKs in ZeroCash~\cite{zerocash}. 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{description} +\end{enumerate} % FIXME: Maybe explain why we don't need n-m refreshing? % FIXME: What are the privacy implication of not having n-m refresh? |