similify

1 files changed, 11 insertions, 10 deletions

diff --git a/taler-fc19/paper.tex b/taler-fc19/paper.tex
index 052ebd8..43b72ac 100644
--- a/taler-fc19/paper.tex
+++ b/taler-fc19/paper.tex
@@ -753,11 +753,10 @@ is the signer and $\mathcal{R}$ is the signature requester:
     to blind a message $m$ that is to be signed later.  The result is a blinded message $\overline{m}$ and

     a residual $r$ that allows to unblind a blinded signature on $m$ made by $\V{sk}$.

   \item $\algo{Sign}_{BS}(\mathcal{S}(\V{sk}), \mathcal{R}(\overline{m})) \mapsto

-    \overline{\sigma}$ is a protocol to sign a blinded message $\overline{m}$.

+    \overline{\sigma}$ is an algorithm to sign a blinded message $\overline{m}$.

     The result $\overline{\sigma}$ is a blinded signature that must be unblinded

     using the $r$ returned from the corresponding blinding operation before

-    verification.  We restrict $\algo{Sign}_{BS}$ to be a two-move protocol, where the

-    requester sends the first message, and the signer responds.

+    verification.

   \item $\algo{UnblindSig}_{BS}(r, m, \overline{\sigma}) \mapsto \sigma$

     is an algorithm to unblind a blinded signature.

   \item $\algo{Verify}_{BS}(\V{pk}, m, \sigma) \mapsto b$ is a algorithm to check the validity of a blind

@@ -977,16 +976,18 @@ Using these primitives, we now instantiate the syntax:
     \end{align*}

 

     Now the exchange checks if $h_C = h_C'$, and aborts the protocol if the check fails.

-

-    Otherwise, the exchange sends a message back to $\prt{C}$ that the commitment verification succeeded.

+    Otherwise, the exchange sends a message back to $\prt{C}$ that the commitment verification succeeded and includes

+    the signature

+    \begin{equation*}

+      \overline{\sigma}_\gamma := \algo{Sign}_{BS}(\mathcal{E}(\V{skD}_u), \mathcal{C}(\overline{m}_\gamma)).

+    \end{equation*}

 

     As a last step, the customer obtains the signature $\sigma_\gamma$ on the new coin's public key $\V{pkCoin}_u$ with

-    \begin{align*}

-      \overline{\sigma}_\gamma &\leftarrow \algo{Sign}(\mathcal{E}(\V{skD}_u), \mathcal{C}(\overline{m}_\gamma))\\

-      \sigma_\gamma &\leftarrow \algo{UnblindSig}(r_\gamma, \V{pkCoin}_\gamma, \overline{\sigma}_\gamma).

-    \end{align*}

+    \begin{equation*}

+      \sigma_\gamma := \algo{UnblindSig}(r_\gamma, \V{pkCoin}_\gamma, \overline{\sigma}_\gamma).

+    \end{equation*}

 

-    Thus the new, unlinkable coin is $\V{coin}_u = (\V{skCoin}_\gamma, \V{pkCoin}_\gamma, \V{pkD}_u, \sigma_\gamma)$.

+    Thus the new, unlinkable coin is $\V{coin}_u := (\V{skCoin}_\gamma, \V{pkCoin}_\gamma, \V{pkD}_u, \sigma_\gamma)$.

 

   \item $\algo{Link}(\prt{E}(\V{sksE}), \prt{C}(\V{skCustomer}, \V{pksE}, \V{coin}_0))$:

     The customer sends the public key $\V{pkCoin}_0$ of $\V{coin}_0$ to the exchange.