add sentence on double-spending detection during refresh
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@ -1013,7 +1013,10 @@ than the comparable use of zk-SNARKs in ZeroCash~\cite{zerocash}.
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for $i \in \{1,\ldots,\kappa\}$ and sends a signed commitment
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for $i \in \{1,\ldots,\kappa\}$ and sends a signed commitment
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$S_{C'}(\vec{B}, \vec{T_p})$ to the exchange.
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$S_{C'}(\vec{B}, \vec{T_p})$ to the exchange.
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\item % [200 OK / 409 CONFLICT]
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\item % [200 OK / 409 CONFLICT]
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The exchange generates a random $\gamma$ with $1 \le \gamma \le \kappa$ and
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The exchange checks that $C'_p$ is a valid coin of sufficient balance
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to cover the value of the fresh coins to be generated and prevent
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double-spending. Then,
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the exchange generates a random $\gamma$ with $1 \le \gamma \le \kappa$ and
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marks $C'_p$ as spent by persisting
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marks $C'_p$ as spent by persisting
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$\langle C', \gamma, S_{C'}(\vec{B}, \vec{T_p}) \rangle$.
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$\langle C', \gamma, S_{C'}(\vec{B}, \vec{T_p}) \rangle$.
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Auditing processes should assure that $\gamma$ is unpredictable until
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Auditing processes should assure that $\gamma$ is unpredictable until
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