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be precise about domain of generated values

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Christian Grothoff 2017-05-18 13:22:35 +02:00
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doc/paper/taler.tex
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@ -70,6 +70,9 @@
%\setcopyright{cagovmixed} %\setcopyright{cagovmixed}
\newcommand\inecc{\in \mathbb{Z}_{|\mathbb{E}|}}
\newcommand\inept{\in {\mathbb{E}}}
\newcommand\inrsa{\in \mathbb{Z}_{|\mathrm{dom}(\FDH_K)|}}
% DOI % DOI
\acmDOI{10.475/123_4} \acmDOI{10.475/123_4}
@ -813,8 +816,8 @@ exchange and one of its public denomination public keys $K_p$ whose
value $K_v$ corresponds to an amount the customer wishes to withdraw. value $K_v$ corresponds to an amount the customer wishes to withdraw.
We let $K_s$ denote the exchange's private key corresponding to $K_p$. We let $K_s$ denote the exchange's private key corresponding to $K_p$.
We use $\FDH_K$ to denote a full-domain hash where the domain is the We use $\FDH_K$ to denote a full-domain hash where the domain is the
public key $K_p$. Now the customer carries out the following modulos of the public key $K_p$. Now the customer carries out the
interaction with the exchange: following interaction with the exchange:
% FIXME: These steps occur at very different points in time, so probably % FIXME: These steps occur at very different points in time, so probably
% they should be restructured into more of a protocol description. % they should be restructured into more of a protocol description.
@ -824,9 +827,9 @@ interaction with the exchange:
\begin{enumerate} \begin{enumerate}
\item The customer randomly generates: \item The customer randomly generates:
\begin{itemize} \begin{itemize}
\item reserve key $W := (w_s,W_p)$ with private key $w_s$ and public key $W_p := w_sG$, \item reserve key $W := (w_s,W_p)$ with private key $w_s \inecc$ and public key $W_p := w_sG \inept$,
\item coin key $C := (c_s,C_p)$ with private key $c_s$ and public key $C_p := c_s G$, \item coin key $C := (c_s,C_p)$ with private key $c_s$ and public key $C_p := c_s G \inept$,
\item blinding factor $b$ \item RSA blinding factor $b \inrsa$.
\end{itemize} \end{itemize}
The customer first persists\footnote{When we say ``persist'', we mean that the value The customer first persists\footnote{When we say ``persist'', we mean that the value
is stored in such a way that it can be recovered after a system crash, and is stored in such a way that it can be recovered after a system crash, and
@ -1005,9 +1008,9 @@ than the comparable use of zk-SNARKs in ZeroCash~\cite{zerocash}.
\begin{enumerate} \begin{enumerate}
\item %[POST {\tt /refresh/melt}] \item %[POST {\tt /refresh/melt}]
For each $i = 1,\ldots,\kappa$, the customer randomly generates For each $i = 1,\ldots,\kappa$, the customer randomly generates
a transfer private key $t^{(i)}_s$ and computes a transfer private key $t^{(i)}_s \inecc$ and computes
\begin{enumerate} \begin{enumerate}
\item the transfer public key $T^{(i)}_p := t^{(i)}_s G$ and \item the transfer public key $T^{(i)}_p := t^{(i)}_s G \inept$ and
\item the new coin secret seed $L^{(i)} := H(c'_s T_p^{(i)})$. \item the new coin secret seed $L^{(i)} := H(c'_s T_p^{(i)})$.
\end{enumerate} \end{enumerate}
We have computed $L^{(i)}$ as a Diffie-Hellman shared secret between We have computed $L^{(i)}$ as a Diffie-Hellman shared secret between