Switch to X for exchanges
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@ -684,10 +684,10 @@ with signature $\widetilde{C} := S_K(\FDH_K(C_p))$
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\begin{enumerate}
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\begin{enumerate}
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\item\label{contract}
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\item\label{contract}
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Let $\vec{D} := D_1, \ldots, D_n$ be the list of exchanges accepted by
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Let $\vec{X} := \langle X_1, \ldots, X_n \rangle$ denote the list of
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the merchant where each $D_j$ is a exchange's public key.
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exchanges accepted by the merchant where each $X_j$ is a exchange's
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The merchant creates a digitally signed contract
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public key. The merchant creates a digitally signed contract
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$\mathcal{A} := S_M(m, f, a, H(p, r), \vec{D})$
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$\mathcal{A} := S_M(m, f, a, H(p, r), \vec{X})$
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where $m$ is an identifier for this transaction, $a$ is data relevant
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where $m$ is an identifier for this transaction, $a$ is data relevant
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to the contract indicating which services or goods the merchant will
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to the contract indicating which services or goods the merchant will
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deliver to the customer, $f$ is the price of the offer, and
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deliver to the customer, $f$ is the price of the offer, and
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@ -697,11 +697,11 @@ with signature $\widetilde{C} := S_K(\FDH_K(C_p))$
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\item\label{deposit}
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\item\label{deposit}
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The customer should already possess a coin issued by a exchange that is
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The customer should already possess a coin issued by a exchange that is
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accepted by the merchant, meaning $K$ should be publicly signed by
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accepted by the merchant, meaning $K$ should be publicly signed by
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some $D_j \in \{D_1, D_2, \ldots, D_n\}$, and has a value $\geq f$.
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some $X_j$ from $\vec{X}$, and has a value $\geq f$.
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\item The customer generates a \emph{deposit-permission} $\mathcal{D} :=
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\item The customer generates a \emph{deposit-permission} $\mathcal{D} :=
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S_c(\widetilde{C}, m, f, H(a), H(p,r), M_p)$
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S_c(\widetilde{C}, m, f, H(a), H(p,r), M_p)$
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and sends $\langle \mathcal{D}, D_j\rangle$ to the merchant,
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and sends $\langle \mathcal{D}, X_j\rangle$ to the merchant,
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where $D_j$ is the exchange which signed $K$.
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where $X_j$ is the exchange which signed $K$.
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\item The merchant gives $(\mathcal{D}, p, r)$ to the exchange, thereby
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\item The merchant gives $(\mathcal{D}, p, r)$ to the exchange, thereby
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revealing $p$ only to the exchange.
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revealing $p$ only to the exchange.
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\item The exchange validates $\mathcal{D}$ and checks for double spending.
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\item The exchange validates $\mathcal{D}$ and checks for double spending.
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@ -1227,8 +1227,8 @@ data being committed to disk are represented in between $\langle\rangle$.
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\item[$\widetilde{C}$]{Exchange signature $S_K(C_p)$ indicating validity of a fresh coin (with key $C$)}
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\item[$\widetilde{C}$]{Exchange signature $S_K(C_p)$ indicating validity of a fresh coin (with key $C$)}
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\item[$n$]{Number of exchanges accepted by a merchant}
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\item[$n$]{Number of exchanges accepted by a merchant}
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\item[$j$]{Index into a set of accepted exchanges, $i \in \{1,\ldots,n\}$}
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\item[$j$]{Index into a set of accepted exchanges, $i \in \{1,\ldots,n\}$}
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\item[$D_j$]{Public key of a exchange (not used to sign coins)}
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\item[$X_j$]{Public key of a exchange (not used to sign coins)}
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\item[$\vec{D}$]{Vector of $D_j$ signifying exchanges accepted by a merchant}
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\item[$\vec{X}$]{Vector of $X_j$ signifying exchanges accepted by a merchant}
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\item[$a$]{Complete text of a contract between customer and merchant}
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\item[$a$]{Complete text of a contract between customer and merchant}
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\item[$f$]{Amount a customer agrees to pay to a merchant for a contract}
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\item[$f$]{Amount a customer agrees to pay to a merchant for a contract}
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\item[$m$]{Unique transaction identifier chosen by the merchant}
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\item[$m$]{Unique transaction identifier chosen by the merchant}
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@ -1328,19 +1328,20 @@ lock permission expires to ensure that no other merchant redeems the
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coin first.
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coin first.
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\begin{enumerate}
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\begin{enumerate}
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\item\label{offer2} The merchant sends an \emph{offer:} $\langle S_M(m, f),
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\item\label{offer2} The merchant sends an \emph{offer:}
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\vec{D} \rangle$ containing the price of the offer $f$, a transaction
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$\langle S_M(m, f), \vec{X} \rangle$ containing the price of the offer $f$,
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ID $m$ and the list of exchanges $D_1, \ldots, D_n$ accepted by the merchant
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a transaction ID $m$ and the list of exchanges
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where each $D_j$ is a exchange's public key.
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$\vec{X} = \langle X_1, \ldots, X_n \rangle$ accepted by the merchant,
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where each $X_j$ is a exchange's public key.
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\item\label{lock2} The customer must possess or acquire a coin $\widetilde{C}$
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\item\label{lock2} The customer must possess or acquire a coin $\widetilde{C}$
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signed by a exchange that is
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signed by a exchange that is accepted by the merchant,
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accepted by the merchant, i.e. $K$ should be signed by some $D_j
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i.e.\ $K$ should be signed by some $X_j$ and has a value $\geq f$.
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\in \{D_1, D_2, \ldots, D_n\}$, and has a value $\geq f$.
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Customer then generates a \emph{lock-permission} $\mathcal{L} :=
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Customer then generates a \emph{lock-permission}
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S_c(\widetilde{C}, t, m, f, M_p)$ where $t$ specifies the time until which the
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$\mathcal{L} := S_c(\widetilde{C}, t, m, f, M_p)$ where
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lock is valid and sends $\langle \mathcal{L}, D_j\rangle$ to the merchant,
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$t$ specifies the time until which the lock is valid and sends
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where $D_j$ is the exchange which signed $K$.
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$\langle \mathcal{L}, X_j\rangle$ to the merchant,
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where $X_j$ is the exchange which signed $K$.
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\item The merchant asks the exchange to apply the lock by sending $\langle
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\item The merchant asks the exchange to apply the lock by sending $\langle
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\mathcal{L} \rangle$ to the exchange.
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\mathcal{L} \rangle$ to the exchange.
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\item The exchange validates $\widetilde{C}$ and detects double spending
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\item The exchange validates $\widetilde{C}$ and detects double spending
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