Consolodate oracle names

1 files changed, 7 insertions, 16 deletions

diff --git a/taler-fc19/paper.tex b/taler-fc19/paper.tex
index fa3baf8..db7fd45 100644
--- a/taler-fc19/paper.tex
+++ b/taler-fc19/paper.tex
@@ -473,6 +473,8 @@ adversary can send and receive messages.
 \end{itemize}

 

 We write \oraSet{All} for the set of all the oracles we just defined.

+We also let $\oraSet{NoShare} := \oraSet{All} - \{ \ora{Share} \}$

+stand for access to all oracles except the share oracle.

 

 The exchange does not need to be corrupted with an oracle. A corrupted exchange

 is modeled by giving the adversary the appropriate oracles and the exchange

@@ -523,8 +525,6 @@ anonymity game if they have a non-negligible advantage in correlating spending o
 with the withdrawal or refresh operations that created a coin used in the

 spending operation.

 

-Let $\oraSet{Anon} := \oraSet{All} - \{ \ora{Share} \}$ stand for access to all oracles

-except the share oracle.

 Let $b$ be the bit that will determine the mapping between customers and spend

 operations, which the adversary must guess.

 

@@ -544,7 +544,7 @@ in $\mathfrak{R}$.
 \begin{enumerate}

   \setlength\itemsep{0em}

   \item $(\V{sksE}, \V{pksE}, \V{skM}, \V{pkM}) \leftarrow {\prt{A}}()$

-  \item $(\V{pkCustomer}_0, \V{pkCustomer}_1, \V{transactionId}_0, \V{transactionId}_1, f) \leftarrow {\prt{A}}^{\oraSet{Anon}}()$

+  \item $(\V{pkCustomer}_0, \V{pkCustomer}_1, \V{transactionId}_0, \V{transactionId}_1, f) \leftarrow {\prt{A}}^{\oraSet{NoShare}}()$

   \item Select distinct fresh coins 

     \begin{align*}

       \V{coin}_0 &\in \V{wallet}[\V{pkCustomer}_0]\\

@@ -558,7 +558,7 @@ in $\mathfrak{R}$.
         &\algo{Deposit}(\prt{A}(), \prt{M}(\V{skM}, \V{pksE}, \V{dp}_i)) \\

         &\mathfrak{R}_i \leftarrow \algo{Refresh}(\prt{A}(), \prt{C}(\V{pkCustomer}_i, \V{pksE}, \V{coin}_{i-b}))

       \end{align*}

-  \item $b' \leftarrow {\cal A}^{\oraSet{Anon}}(\mathfrak{R}_0, \mathfrak{R}_1)$ \\

+  \item $b' \leftarrow {\cal A}^{\oraSet{NoShare}}(\mathfrak{R}_0, \mathfrak{R}_1)$ \\

   \item Return $0$ if $\ora{Spend}$ was used by the adversary on the coin handles

     for $\V{coin}_0$ or $\V{coin}_1$ or $\ora{CorruptCustomer}$ was used on $\V{pkCustomer}_0$ or $\V{pkCustomer}_1$.

   \item If $b = b'$ return $1$, otherwise return $0$.

@@ -582,9 +582,6 @@ completed withdrawals, payments or refreshes, as well as other (transient)
 misbehavior from the exchange or merchant do not result in the customer losing

 money or privacy.

 

-Let $\oraSet{Conserv} := \oraSet{All} - \{\ora{Share}\}$ stand for access to the

-all oracles except the sharing oracle.

-

 \begin{figure}

 \fbox{\begin{minipage}{\textwidth}

 \small

@@ -593,7 +590,7 @@ all oracles except the sharing oracle.
 \begin{enumerate}

   \setlength\itemsep{0em}

   \item $(\V{sksE}, \V{pksE}) \leftarrow \mathrm{ExchangeKeygen}(1^\lambda, 1^\kappa, M)$ 

-  \item $\V{pkCustomer} \leftarrow {\cal A}^{\oraSet{Conserv}}(\V{pksE})$

+  \item $\V{pkCustomer} \leftarrow {\cal A}^{\oraSet{NoShare}}(\V{pksE})$

   \item Return $0$ if $\V{pkCustomer}$ is not an uncorrupted, registered user.

   \item \label{game:conserv:run} Run $\algo{WithdrawPickup}$ for each withdraw identifier $\V{wid}$

     and $\algo{RefreshPickup}$ for each refresh identifier $\V{rid}$ that the user

@@ -631,9 +628,6 @@ coins with parties that they do not fully trust.
 Intuitively, adversarial customers win if they can obtain more valid coins than

 they legitimately withdraw.

 

-Let $\oraSet{Forge} := \oraSet{All}$ stand for access to the all 

-oracles.

-

 \begin{figure}

 \fbox{\begin{minipage}{\textwidth}

 \small

@@ -642,7 +636,7 @@ oracles.
 \begin{enumerate}

   \setlength\itemsep{0em}

   \item $(skE, pkE) \leftarrow \mathrm{ExchangeKeygen}()$ 

-  \item $(C_0, \dots, C_\ell) \leftarrow \mathcal{A}^{\oraSet{Forge}}(pkExchange)$

+  \item $(C_0, \dots, C_\ell) \leftarrow \mathcal{A}^{\oraSet{All}}(pkExchange)$

   \item Return $0$ if any $C_i$ is not of the form $(\V{skCoin}, \V{pkCoin}, \V{pkD}, \V{coinCert})$

     or any $\V{coinCert}$ is not a valid signature by $\V{pkD}$ on the respective $\V{pkCoin}$.

   \item Return $1$ if the sum of the unspent value of valid coins in $C_0

@@ -669,9 +663,6 @@ an explicit goal. The Link protocol introduces the threat of losing exclusive
 control of coins (despite having the option to refresh them) that were received

 without being visible as income to the exchange.

 

-Let $\oraSet{Income} := \oraSet{All}$ stand for access to the

-all oracles.

-

 \begin{figure}

 \fbox{\begin{minipage}{\textwidth}

 \small

@@ -680,7 +671,7 @@ all oracles.
 \begin{enumerate}

   \setlength\itemsep{0em}

   \item $(skE, pkE) \leftarrow \mathrm{ExchangeKeygen}()$ 

-  \item $(\V{coin}_1, \dots, \V{coin}_\ell) \leftarrow \mathcal{A}^{\oraSet{Income}}(pkExchange)$

+  \item $(\V{coin}_1, \dots, \V{coin}_\ell) \leftarrow \mathcal{A}^{\oraSet{All}}(pkExchange)$

     

     (The $\V{coin}_i$ must be coins, including secret key and signature by the

     denomination, for the adversary to win. However these coins need not be