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avoid triplicating 'randomly computes'

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Christian Grothoff 2015-10-05 00:35:02 +02:00
parent 41126e6d24
commit 3b3af8a077
1 changed files with 7 additions and 7 deletions
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doc/paper/taler.tex
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@ -808,15 +808,15 @@ protocol, $\kappa \ge 3$ is a security parameter and $G$ is the
generator of the elliptic curve. generator of the elliptic curve.
\begin{enumerate} \begin{enumerate}
\item For each $i = 1,\ldots,\kappa$, the customer \item For each $i = 1,\ldots,\kappa$, the customer randomly generates
\begin{itemize} \begin{itemize}
\item randomly generates transfer key $T^{(i)} := \left(t^{(i)}_s,T^{(i)}_p\right)$ where $T^{(i)}_p := t^{(i)}_s G$, \item transfer key $T^{(i)} := \left(t^{(i)}_s,T^{(i)}_p\right)$ where $T^{(i)}_p := t^{(i)}_s G$,
\item randomly generates coin key pair \\ $C^{(i)} := \left(c_s^{(i)}, C_p^{(i)}\right)$ where $C^{(i)}_p := c^{(i)}_s G$, \item coin key pair \\ $C^{(i)} := \left(c_s^{(i)}, C_p^{(i)}\right)$ where $C^{(i)}_p := c^{(i)}_s G$,
\item randomly generates blinding factors $b^{(i)}$, \item blinding factors $b^{(i)}$.
\item computes $E^{(i)} := E_{K_i}\left(c_s^{(i)}, b^{(i)}\right)$ where $K_i := H(c'_s T_p^{(i)})$. (The encryption key $K_i$ is \end{itemize}
The customer then computes $E^{(i)} := E_{K_i}\left(c_s^{(i)}, b^{(i)}\right)$ where $K_i := H(c'_s T_p^{(i)})$. (The encryption key $K_i$ is
computed by multiplying the private key $c'_s$ of the original coin with the point on the curve computed by multiplying the private key $c'_s$ of the original coin with the point on the curve
that represents the public key $T^{(i)}_p$ of the transfer key $T^{(i)}$. This is basically DH between coin and transfer key.), that represents the public key $T^{(i)}_p$ of the transfer key $T^{(i)}$. This is basically DH between coin and transfer key.),
\end{itemize}
and commits $\langle C', \vec{T}, \vec{C}, \vec{b} \rangle$ to disk. and commits $\langle C', \vec{T}, \vec{C}, \vec{b} \rangle$ to disk.
\item The customer computes $B^{(i)} := B_{b^{(i)}}(C^{(i)}_p)$ for $i \in \{1,\ldots,\kappa\}$ and sends a commitment \item The customer computes $B^{(i)} := B_{b^{(i)}}(C^{(i)}_p)$ for $i \in \{1,\ldots,\kappa\}$ and sends a commitment
$S_{C'}(\vec{E}, \vec{B}, \vec{T_p}))$ to the mint. $S_{C'}(\vec{E}, \vec{B}, \vec{T_p}))$ to the mint.