From 3fbf12b6f74f9bea23ccbdc7a091094eb058d258 Mon Sep 17 00:00:00 2001
From: Christian Grothoff
Date: Thu, 18 May 2017 13:22:35 +0200
Subject: be precise about domain of generated values
---
doc/paper/taler.tex | 17 ++++++++++-------
1 file changed, 10 insertions(+), 7 deletions(-)
diff --git a/doc/paper/taler.tex b/doc/paper/taler.tex
index 30f9934c..91087fca 100644
--- a/doc/paper/taler.tex
+++ b/doc/paper/taler.tex
@@ -70,6 +70,9 @@
%\setcopyright{cagovmixed}
+\newcommand\inecc{\in \mathbb{Z}_{|\mathbb{E}|}}
+\newcommand\inept{\in {\mathbb{E}}}
+\newcommand\inrsa{\in \mathbb{Z}_{|\mathrm{dom}(\FDH_K)|}}
% DOI
\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.
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
-public key $K_p$. Now the customer carries out the following
-interaction with the exchange:
+modulos of the public key $K_p$. Now the customer carries out the
+following interaction with the exchange:
% FIXME: These steps occur at very different points in time, so probably
% they should be restructured into more of a protocol description.
@@ -824,9 +827,9 @@ interaction with the exchange:
\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 $W_p := w_sG$,
- \item coin key $C := (c_s,C_p)$ with private key $c_s$ and public key $C_p := c_s G$,
- \item blinding factor $b$
+ \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 $C_p := c_s G \inept$,
+ \item RSA blinding factor $b \inrsa$.
\end{itemize}
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
@@ -1005,9 +1008,9 @@ than the comparable use of zk-SNARKs in ZeroCash~\cite{zerocash}.
\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
+ a transfer private key $t^{(i)}_s \inecc$ and computes
\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 $L^{(i)} := H(c'_s T_p^{(i)})$.
\end{enumerate}
We have computed $L^{(i)}$ as a Diffie-Hellman shared secret between
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