path: root/presentations/comprehensive/monetative.tex

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\title{GNU Taler}
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\author[C. Grothoff]{J. Burdges, F. Dold, {\bf C. Grothoff}, M. Stanisci}
\date{\today}
\institute{The GNU Project}


\begin{document}

\justifying

\begin{frame}
  \begin{center}
    \LARGE {\bf GNU}

    \vfill
%    \includegraphics[width=0.66\textwidth]{logo-2017-fr.pdf}
    \includegraphics[width=0.66\textwidth]{logo-2020.jpg}
  \end{center}
\begin{textblock*}{6cm}(.5cm,7.7cm) % {block width} (coords)
    {\Large {\bf \href{https://taler.net/}{taler.net}} \\
    \href{https://twitter.com/taler}{taler@twitter} \\
    \href{https://taler-systems.com/}{taler-systems.com}}
\end{textblock*}

% Substitute based on who is giving the talk!
 \begin{textblock*}{6cm}(6.7cm,7.7cm) % {block width} (coords)
   {%\hfill {\Large {\bf Florian Dold \&} \\
    \hfill {\bf Christian Grothoff}} \\
    \hfill grothoff@taler.net
\end{textblock*}

\end{frame}



\section{What is GNU Taler?}
\begin{frame}{What is GNU Taler?}
  \begin{center}
Taler is an electronic instant payment system.
  \end{center}
  \begin{itemize}
  \item Uses electronic coins stored in {\bf wallets} on customer's device
  \item Like {\bf cash}
  \item Pay in {\bf existing currencies} (i.e. EUR, USD, BTC), \\
    or use it to create new {\bf regional currencies}
  \end{itemize}
  \vfill
  \pause
 \noindent
 However, Taler is
  \begin{itemize}
    \item \emph{not} a currency
    \item \emph{not} a long-term store of value
    \item \emph{not} a network or instance of a system
    \item \emph{not} decentralized
    \item \emph{not} based on proof-of-work or proof-of-stake
    \item \emph{not} a speculative asset / ``get-rich-quick scheme''
  \end{itemize}
\end{frame}


\begin{frame}{Design principles}
  \framesubtitle{https://taler.net/en/principles.html}
GNU Taler must ...
\begin{enumerate}
  \item {... be implemented as {\bf free software}.}
  \item {... protect the {\bf privacy of buyers}.}
  \item {... must enable the state to {\bf tax income} and crack down on
    illegal business activities.}
  \item {... prevent payment fraud.}
  \item {... only {\bf disclose the minimal amount of information
    necessary}.}
  \item {... be usable.}
  \item {... be efficient.}
  \item {... avoid single points of failure.}
  \item {... foster {\bf competition}.}
\end{enumerate}
\end{frame}


\begin{frame}
\frametitle{Taler Overview}
\begin{center}
\begin{tikzpicture}
 \tikzstyle{def} = [node distance= 5em and 6.5em, inner sep=1em, outer sep=.3em];
 \node (origin) at (0,0) {};
 \node (exchange) [def,above=of origin,draw]{Exchange};
 \node (customer) [def, draw, below left=of origin] {Customer};
 \node (merchant) [def, draw, below right=of origin] {Merchant};
 \node (auditor) [def, draw, above right=of origin]{Auditor};
% \node (regulator) [def, draw, above=of auditor]{CSSF};

 \tikzstyle{C} = [color=black, line width=1pt]

 \draw [<-, C] (customer) -- (exchange) node [midway, above, sloped] (TextNode) {withdraw coins};
 \draw [<-, C] (exchange) -- (merchant) node [midway, above, sloped] (TextNode) {deposit coins};
 \draw [<-, C] (merchant) -- (customer) node [midway, above, sloped] (TextNode) {spend coins};
 \draw [<-, C] (exchange) -- (auditor) node [midway, above, sloped] (TextNode) {verify};
% \draw [<-, C] (regulator) -- (auditor) node [midway, above, sloped] (TextNode) {report};

\end{tikzpicture}
\end{center}
\end{frame}

\begin{frame}
\frametitle{Architecture of Taler}
\begin{center}
  \includegraphics[width=1\textwidth]{operations.png}
\end{center}
\end{frame}


\begin{frame}{Usability of Taler}
  \vfill
  \begin{center}
    \url{https://demo.taler.net/}
  \end{center}
  \begin{enumerate}
  \item Install browser extension.
  \item Visit the {\tt bank.demo.taler.net} to withdraw coins.
  \item Visit the {\tt shop.demo.taler.net} to spend coins.
  \end{enumerate}
  \vfill
\end{frame}


\section{Impact}
\begin{frame}{Social Impact of Taler}
  \begin{center}
    \includegraphics[height=0.9\textheight]{../../social-impact.pdf}
  \end{center}
\end{frame}


\begin{frame}{Use Case: Journalism}
  Today:
  \begin{itemize}
    \item Corporate structure % ($\Rightarrow$ filter)
    \item Advertising primary revenue % ($\Rightarrow$ dependence)
    \item Tracking readers critical for business success
    \item Journalism and marketing hard to distinguish
  \end{itemize}\vfill\pause
  With GNU Taler:
  \begin{itemize}
    \item One-click micropayments per article
    \item Hosting requires no expertise % (no PCI DSS)
    \item Reader-funded reporting separated from marketing
    \item Readers can remain anonymous
  \end{itemize}
\end{frame}


\begin{frame}{Use Cases: Refugee Camps}
  Today:
  \begin{itemize}
  \item Non-bankable
  \item Direct distribution of goods to population
  \item Limited economic activity in camps
  \item High level of economic dependence
  \end{itemize}\vfill\pause
  With GNU Taler:
  \begin{itemize}
  \item Local currency issued as basic income backed by aid
  \item Taxation possible based on economic status
  \item Local governance enabled by local taxes
  \item Increased economic independence and political participation
  \end{itemize}
\end{frame}


\begin{frame}{Use Case: Anti-Spam}
  \framesubtitle{Background: \url{https://pep.security/}}
  Today, p$\equiv$p provides authenticated encryption for e-mail:
  \begin{itemize}
    \item Free software
    \item Easy to use opportunistic encryption
    \item Available for Outlook, Android, Enigmail
    \item Spies \& spam filters can no longer inspect content
  \end{itemize}\vfill\pause
  With GNU Taler:
  \begin{itemize}
    \item Peer-to-peer payments via e-mail
    \item If unsolicited sender, hide messages from user \&
          automatically request payment from sender
    \item Sender can attach payment to be moved to inbox
    \item Receiver may grant refund to sender
  \end{itemize}
\end{frame}


\begin{frame}{Taler: Unique Regulatory Features for Central Banks}
  \framesubtitle{\url{https://www.snb.ch/en/mmr/papers/id/working_paper_2021_03}}
  \begin{itemize}
    \item Central bank issues digital coins equivalent to issuing cash \\
          $\Rightarrow$ monetary policy remains under CB control
    \item Architecture with consumer accounts at commercial banks \\
          $\Rightarrow$ no competition for commercial banking (S\&L) \\
          $\Rightarrow$ CB does not have to manage KYC, customer support
    \item Withdrawal limits and denomination expiration \\
          $\Rightarrow$ protects against bank runs and hoarding
    \item Income transparency and possibility to set fees \\
          $\Rightarrow$ additional insights into economy and new policy options
    \item Revocation protocols and loss limitations \\
          $\Rightarrow$ exit strategy and handles catastrophic security incidents
    \item Privacy by cryptographic design not organizational compliance \\
          $\Rightarrow$ CB cannot be forced to facilitate mass-surveillance
  \end{itemize}
\end{frame}


\section{Project status}
\begin{frame}{Competitor comparison}
  \begin{center} \small
    \begin{tabular}{l||c|c|c|c|c}
                & Cash & Bitcoin & Zerocoin & Creditcard & GNU Taler \\ \hline \hline
   Online      &$-$$-$$-$  &   ++    &    ++    &     +      &   +++  \\ \hline
    Offline     & +++  &   $-$$-$    &    $-$$-$    &     +      &   $-$$-$  \\ \hline
    Trans. cost & +    & $-$$-$$-$   & $-$$-$$-$  &     $-$      &   ++  \\ \hline
    Speed       & +    & $-$$-$$-$   & $-$$-$$-$  &     o      &   ++  \\ \hline
    Taxation    & $-$    &   $-$$-$    &  $-$$-$$-$   &    +++     &  +++  \\ \hline
    Payer-anon  &  ++  &   o     &    ++    &  $-$$-$$-$   &  +++  \\ \hline
    Payee-anon  & ++   &   o     &    ++    &  $-$$-$$-$    &  $-$$-$$-$ \\ \hline
    Security    &  $-$   &   o     &    o     &    $-$$-$      &  ++   \\ \hline
    Conversion  & +++  &  $-$$-$$-$   & $-$$-$$-$ &    +++     &  +++  \\ \hline
    Libre       &  $-$   &  +++    &    +++   & $-$ $-$ $-$      &  +++  \\
  \end{tabular}
  \end{center}
\end{frame}


\begin{frame}{Taler: Project Status}
\begin{itemize}
    \item Protocols and core exchange component are stable
    \item Current focus: Merchant integration, settlement integration, wallet backup, 100k TPS scalability
    \item Pilot project at Bern University of Applied Sciences cafeteria
    \item Internal alpha deployment with a commercial bank in progress
  \end{itemize}
  \vfill
\begin{center}
\includegraphics[width=0.7\textwidth]{taler-in-use.png}
\end{center}
\end{frame}


\begin{frame}{Ongoing development}
We have ideas for protocol extensions and ``programmable money'':
  \begin{itemize}
    \item Mediated wallet-to-wallet payments (instead of customer-to-merchant)
    \item Age-restricted private payments for children (youth protection)
    \item Privacy-preserving auctions (trading, currency exchange)
  \end{itemize}
We also are looking into:
  \begin{itemize}
    \item General digital wallet usability and availability
    \item Accessibility features for illiterate and innumerate users
  \end{itemize}
\end{frame}


\begin{frame}{How to support?}
  \begin{description}
    \item[Join:] {\small \url{https://lists.gnu.org/mailman/listinfo/taler}}, \\
                 \url{irc://irc.freenode.net/\#taler}
    \item[Develop:] \url{https://bugs.taler.net/}, \url{https://git.taler.net/}
    \item[Translate:] \url{https://weblate.taler.net/}, \url{translation-volunteer@taler.net}
    \item[Integrate:] \url{https://docs.taler.net/}
    \item[Donate:] \url{https://gnunet.org/ev}
    \item[Invest:] \url{https://taler-systems.com/}
  \end{description}
  We are looking for:
  \begin{itemize}
    \item European media organizations (50+ staff, 2+M annual turnover)
          for pilot Taler integration paid by \url{https://stadiem.eu/} project
          ({\bf urgent})!
    \item Commercial banks to offer Taler to their customers
    \item Central banks to operate Taler as a CBDC
  \end{itemize}
\end{frame}


\begin{frame}
\frametitle{Do you have any questions?}
\vfill
References:
{\tiny
  \begin{enumerate}
 \item{David Chaum, Christian Grothoff and Thomas Moser.
       {\em How to issue a central bank digital currency}.
       {\bf SNB Working Papers, 2021}.}
 \item{Christian Grothoff, Bart Polot and Carlo von Loesch.
       {\em The Internet is broken: Idealistic Ideas for building a GNU Network}.
       {\bf W3C/IAB Workshop on Strengthening the Internet Against Pervasive Monitoring (STRINT)}, 2014.}
 \item{Jeffrey Burdges, Florian Dold, Christian Grothoff and Marcello Stanisci.
       {\em Enabling Secure Web Payments with GNU Taler}.
       {\bf SPACE 2016}.}
 \item{Florian Dold, Sree Harsha Totakura, Benedikt M\"uller, Jeffrey Burdges and Christian Grothoff.
       {\em Taler: Taxable Anonymous Libre Electronic Reserves}.
       Available upon request. 2016.}
 \item{Eli Ben-Sasson, Alessandro Chiesa, Christina Garman, Matthew Green, Ian Miers, Eran Tromer and Madars Virza.
       {\em Zerocash: Decentralized Anonymous Payments from Bitcoin}.
       {\bf IEEE Symposium on Security \& Privacy, 2016}.}
 \item{David Chaum, Amos Fiat and Moni Naor.
       {\em Untraceable electronic cash}.
       {\bf Proceedings on Advances in Cryptology, 1990}.}
  \item{Phillip Rogaway.
       {\em The Moral Character of Cryptographic Work}.
       {\bf Asiacrypt}, 2015.} \label{bib:rogaway}
\end{enumerate}
}
\end{frame}


\begin{frame}{The Distraction: Bitcoin}

\begin{itemize}
\item Unregulated payment system and currency:
\item[] $\Rightarrow$ lack of regulation is a feature!
\item Implemented in free software
\item Decentralised peer-to-peer system   \pause
\item Decentralised banking requires solving Byzantine consensus
\item Creative solution: tie initial accumulation to solving consensus \pause
\item[] $\Rightarrow$ Proof-of-work advances ledger
\item[] $\Rightarrow$ Very expensive banking
\end{itemize}
\end{frame}


\begin{frame}
  \frametitle{\includegraphics[height=0.5cm]{pics/bitcoin.png}?}
  \framesubtitle{Background: \url{https://blockchain.com/charts/}}
  \centering
\noindent
\includegraphics[width=\textwidth]{pics/btc-transaction-cost.png}

Current average transaction value: $\approx$ 1000 USD
\end{frame}


\begin{frame}
  \frametitle{\includegraphics[height=0.5cm]{pics/zerocoin.png}?}

Cryptography is rather primitive:
\begin{center}
  {\bf All Bitcoin transactions are public and linkable!}
\end{center}

\begin{itemize}
\item[] $\Rightarrow$ no privacy guarantees
\item[] $\Rightarrow$ enhanced with ``laundering'' services
\end{itemize}
ZeroCoin, CryptoNote (Monero) and ZeroCash (ZCash) offer anonymity.
\end{frame}


\begin{frame}{Requirements: Online vs. Offline Digital Currencies}
\framesubtitle{\url{https://taler.net/papers/euro-bearer-online-2021.pdf}}
\begin{itemize}
    \item Offline capabilities are sometimes cited as a requirement for digital payment solutions
    \item All implementations must either use restrictive hardware elements and/or introduce
      counterparty risk.
    \item[$\Rightarrow$] Permanent offline features weaken a digital payment solution (privacy, security)
    \item[$\Rightarrow$] Introduces unwarranted competition for physical cash (endangers emergency-preparedness).
  \end{itemize}
  We recommend a tiered approach:
      \begin{enumerate}
        \item Online-first, bearer-based digital currency with Taler
        \item (Optional:) Limited offline mode for network outages
        \item Physical cash for emergencies (power outage, catastrophic cyber incidents)
      \end{enumerate}
\end{frame}


\section{How does it work?}
\begin{frame}{How does it work?}
We use a few ancient constructions:
  \begin{itemize}
  \item Cryptographic hash function (1989)
  \item Blind signature (1983)
  \item Schnorr signature (1989)
  \item Diffie-Hellman key exchange (1976)
  \item Cut-and-choose zero-knowledge proof (1985)
  \end{itemize}
But of course we use modern instantiations.
\end{frame}


\begin{frame}{Definition: Taxability}
  We say Taler is taxable because:
  \begin{itemize}
  \item Merchant's income is visible from deposits.
  \item Hash of contract is part of deposit data.
  \item State can trace income and enforce taxation.
  \end{itemize}\pause
  Limitations:
  \begin{itemize}
  \item withdraw loophole
  \item {\em sharing} coins among family and friends
  \end{itemize}
\end{frame}


\begin{frame}{Exchange setup: Create a denomination key (RSA)}
   \begin{minipage}{6cm}
    \begin{enumerate}
    \item Pick random primes $p,q$.
    \item Compute $n := pq$, $\phi(n) = (p-1)(q-1)$
    \item Pick small $e < \phi(n)$ such that
          $d := e^{-1} \mod \phi(n)$ exists.
    \item Publish public key $(e,n)$.
    \end{enumerate}
  \end{minipage}
  \begin{minipage}{6cm}
  \begin{tikzpicture}
 \tikzstyle{def} = [node distance=1em and 1em, inner sep=0em, outer sep=.3em];
    \node (origin) at (0,0) {\includegraphics[width=0.2\textwidth]{dice.pdf}};
    \node (primes) [draw=none, below = of origin] at (0,0) {$(p, q)$};
    \node (seal) [def, draw=none, below left=of primes]{\includegraphics[width=0.15\textwidth]{seal.pdf}};
    \node (hammer) [def, draw=none, below right=of primes]{\includegraphics[width=0.15\textwidth]{hammer.pdf}};

    \tikzstyle{C} = [color=black, line width=1pt]

    \draw [<-, C] (primes) -- (origin) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (seal) -- (primes) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (hammer) -- (primes) node [midway, above, sloped] (TextNode) {};
  \end{tikzpicture}
%  \includegraphics[width=0.4\textwidth]{seal.pdf}
  \end{minipage}
\end{frame}


\begin{frame}{Merchant: Create a signing key (EdDSA)}
  \begin{minipage}{6cm}
    \begin{itemize}
  \item pick random $m \mod o$ as private key
  \item $M = mG$ public key
  \end{itemize}
  \end{minipage}
  \begin{minipage}{6cm}
  \begin{tikzpicture}
   \tikzstyle{def} = [node distance= 1em and 1em, inner sep=0em, outer sep=.3em];
    \node (origin) at (0,0) {\includegraphics[width=0.2\textwidth]{dice.pdf}};
    \node (m) [draw=none, below = of origin] at (0,0) {$m$};
    \node (seal) [draw=none, below=of m]{M};
   \tikzstyle{C} = [color=black, line width=1pt]

    \draw [<-, C] (m) -- (origin) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (seal) -- (primes) node [midway, above, sloped] (TextNode) {};
  \end{tikzpicture}
  \end{minipage}
  \parbox[t]{3cm}{{\bf Capability:} $m \Rightarrow$ }
  \raisebox{\dimexpr-\height+\baselineskip}{\includegraphics[width=0.1\textwidth]{merchant-sign.pdf}}
\end{frame}


\begin{frame}{Customer: Create a planchet (EdDSA)}
  \begin{minipage}{8cm}
  \begin{itemize}
  \item Pick random $c \mod o$ private key
  \item $C = cG$ public key
  \end{itemize}
  \end{minipage}
  \begin{minipage}{4cm}
  \begin{tikzpicture}
   \tikzstyle{def} = [node distance= 1em and 1em, inner sep=0em, outer sep=.3em];
    \node (origin) at (0,0) {\includegraphics[width=0.2\textwidth]{dice.pdf}};
    \node (c) [draw=none, below = of origin] at (0,0) {$c$};
    \node (planchet) [draw=none, below=of c]{\includegraphics[width=0.4\textwidth]{planchet.pdf}};
    \tikzstyle{C} = [color=black, line width=1pt]

    \draw [<-, C] (c) -- (origin) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (planchet) -- (c) node [midway, above, sloped] (TextNode) {};
  \end{tikzpicture}
  \end{minipage}
  \parbox[t]{3cm}{{\bf Capability:} $c \Rightarrow$ }
  \raisebox{\dimexpr-\height+\baselineskip}{\includegraphics[width=0.1\textwidth]{planchet-sign.pdf}}
\end{frame}


\begin{frame}{Customer: Blind planchet (RSA)}
  \begin{minipage}{6cm}
    \begin{enumerate}
    \item Obtain public key $(e,n)$
    \item Compute $f := FDH(C)$, $f < n$.
    \item Pick blinding factor $b \in \mathbb Z_n$
    \item Transmit $f' := f b^e \mod n$
    \end{enumerate}
  \end{minipage}
  \begin{minipage}{6cm}
  \begin{tikzpicture}
   \tikzstyle{def} = [node distance= 2em and 0.5em, inner sep=0em, outer sep=.3em];
    \node (origin) at (0,0) {\includegraphics[width=0.2\textwidth]{dice.pdf}};
    \node (b) [def, draw=none, below = of origin] at (0,-0.2) {$b$};
    \node (blinded) [def, draw=none, below right=of b]{\includegraphics[width=0.2\textwidth]{blinded.pdf}};
    \node (planchet) [def, draw=none, above right=of blinded]{\includegraphics[width=0.15\textwidth]{planchet.pdf}};
    \node (exchange) [node distance=4em and 0.5em, draw, below =of blinded]{Exchange};
    \tikzstyle{C} = [color=black, line width=1pt]

    \draw [<-, C] (b) -- (origin) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (blinded) -- (planchet) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (blinded) -- (b) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (exchange) -- (blinded) node [midway, above, sloped] (TextNode) {{\small transmit}};
  \end{tikzpicture}
  \end{minipage}
\end{frame}


\begin{frame}{Exchange: Blind sign (RSA)}
   \begin{minipage}{6cm}
    \begin{enumerate}
    \item Receive $f'$.
    \item Compute $s' := f'^d \mod n$.
    \item Send signature $s'$.
    \end{enumerate}
   \end{minipage}
  \begin{minipage}{6cm}
  \begin{tikzpicture}
   \tikzstyle{def} = [node distance= 2em and 0.5em, inner sep=0em, outer sep=.3em];
    \node (hammer) [def, draw=none] at (0,0) {\includegraphics[width=0.15\textwidth]{hammer.pdf}};
    \node (signed) [def, draw=none, below left=of hammer]{\includegraphics[width=0.2\textwidth]{sign.pdf}};
    \node (blinded) [def, draw=none, above left=of signed]{\includegraphics[width=0.15\textwidth]{blinded.pdf}};
    \node (customer) [node distance=4em and 0.5em, draw, below =of signed]{Customer};
    \tikzstyle{C} = [color=black, line width=1pt]

    \draw [<-, C] (signed) -- (hammer) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (signed) -- (blinded) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (customer) -- (signed) node [midway, above, sloped] (TextNode) {{\small transmit}};
  \end{tikzpicture}
  \end{minipage}
\end{frame}


\begin{frame}{Customer: Unblind coin (RSA)}
  \begin{minipage}{6cm}
   \begin{enumerate}
    \item Receive $s'$.
    \item Compute $s := s' b^{-1} \mod n$ % \\
    % ($(f')^d = (f b^e)^d = f^d b$).
    \end{enumerate}
   \end{minipage}
  \begin{minipage}{6cm}
  \begin{tikzpicture}
   \tikzstyle{def} = [node distance= 2em and 0.5em, inner sep=0em, outer sep=.3em];
    \node (b) [def, draw=none] at (0,0) {$b$};
    \node (coin) [def, draw=none, below left=of b]{\includegraphics[width=0.2\textwidth]{coin.pdf}};
    \node (signed) [def, draw=none, above left=of coin]{\includegraphics[width=0.15\textwidth]{sign.pdf}};
    \tikzstyle{C} = [color=black, line width=1pt]

    \draw [<-, C] (coin) -- (b) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (coin) -- (signed) node [midway, above, sloped] (TextNode) {};
  \end{tikzpicture}
  \end{minipage}
\end{frame}


\begin{frame}{Customer: Build shopping cart}
  \begin{center}
  \begin{tikzpicture}
   \tikzstyle{def} = [node distance= 1em and 1em, inner sep=0em, outer sep=.3em];
    \node (origin) at (0,0) {\includegraphics[width=0.2\textwidth]{shop.pdf}};
    \node (cart) [draw=none, below=of m]{\includegraphics[width=0.2\textwidth]{cart.pdf}};
    \node (merchant) [node distance=4em and 0.5em, draw, below =of cart]{Merchant};
    \tikzstyle{C} = [color=black, line width=1pt];
    \draw [<-, C] (cart) -- (origin) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (merchant) -- (cart) node [midway, above, sloped] (TextNode) {{\small transmit}};
  \end{tikzpicture}
  \end{center}
\end{frame}


\begin{frame}{Merchant: Propose contract (EdDSA)}
   \begin{minipage}{6cm}
   \begin{enumerate}
    \item Complete proposal $D$.
    \item Send $D$, $EdDSA_m(D)$
    \end{enumerate}
   \end{minipage}
  \begin{minipage}{6cm}
  \begin{tikzpicture}
   \tikzstyle{def} = [node distance=2em and 0.5em, inner sep=0em, outer sep=.3em];
    \node (cart) [def, draw=none] at (0,0) {\includegraphics[width=0.15\textwidth]{cart.pdf}};
    \node (proposal) [def, draw=none, below right=of cart]{\includegraphics[width=0.5\textwidth]{merchant_propose.pdf}};
    \node (customer) [node distance=4em and 0.5em, draw, below =of proposal]{Customer};
    \tikzstyle{C} = [color=black, line width=1pt];
    \node (sign) [def, draw=none, above right=of proposal] {$m$};
    \tikzstyle{C} = [color=black, line width=1pt]

    \draw [<-, C] (proposal) -- (sign) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (proposal) -- (cart) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (customer) -- (proposal) node [midway, above, sloped] (TextNode) {{\small transmit}};
  \end{tikzpicture}
  \end{minipage}
\end{frame}


\begin{frame}{Customer: Spend coin (EdDSA)}
  \begin{minipage}{6cm}
   \begin{enumerate}
    \item Receive proposal $D$, $EdDSA_m(D)$.
    \item Send $s$, $C$, $EdDSA_c(D)$
    \end{enumerate}
   \end{minipage}
  \begin{minipage}{6cm}
  \begin{tikzpicture}
   \tikzstyle{def} = [node distance=2em and 0.4em, inner sep=0em, outer sep=.3em];
    \node (proposal) [def, draw=none] at (0,0) {\includegraphics[width=0.15\textwidth]{merchant_propose.pdf}};
    \node (contract) [def, draw=none, below right=of cart]{\includegraphics[width=0.3\textwidth]{contract.pdf}};
    \node (c) [def, draw=none, above=of contract] {$c$};
    \node (merchant) [node distance=4em and 0.5em, draw, below=of contract]{Merchant};
    \node (coin) [def, draw=none, right=of contract]{\includegraphics[width=0.2\textwidth]{coin.pdf}};
    \tikzstyle{C} = [color=black, line width=1pt]

    \draw [<-, C] (contract) -- (c) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (contract) -- (proposal) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (merchant) -- (contract) node [midway, above, sloped] (TextNode) {{\small transmit}};
    \draw [<-, C] (merchant) -- (coin) node [midway, below, sloped] (TextNode) {{\small transmit}};
  \end{tikzpicture}
  \end{minipage}
\end{frame}


\begin{frame}{Merchant and Exchange: Verify coin (RSA)}
   \begin{minipage}{6cm}
 \begin{equation*}
   s^e \stackrel{?}{\equiv} FDH(C) \mod n
   \end{equation*}
   \end{minipage}
  \begin{minipage}{6cm}
  \begin{minipage}{0.2\textwidth}
    \includegraphics[width=\textwidth]{coin.pdf}
  \end{minipage}
  $\stackrel{?}{\Leftrightarrow}$
  \begin{minipage}{0.2\textwidth}
    \includegraphics[width=\textwidth]{seal.pdf}
  \end{minipage}
  \end{minipage}
  \vfill
  The exchange does not only verify the signature, but also
  checks that the coin was not double-spent.
  \vfill
  \pause
  \begin{center}
  {\bf Taler is an online payment system.}
  \end{center}
  \vfill
\end{frame}


\begin{frame}{Giving change}
  It would be inefficient to pay EUR 100 with 1 cent coins!
  \begin{itemize}
  \item Denomination key represents value of a coin.
  \item Exchange may offer various denominations for coins.
  \item Wallet may not have exact change!
  \item Usability requires ability to pay given sufficient total funds.
  \end{itemize}\pause
  Key goals:
  \begin{itemize}
  \item maintain unlinkability
  \item maintain taxability of transactions
  \end{itemize}\pause
  Method:
  \begin{itemize}
    \item Contract can specify to only pay {\em partial value} of a coin.
    \item Exchange allows wallet to obtain {\em unlinkable change}
      for remaining coin value.
  \end{itemize}
\end{frame}


\begin{frame}{Diffie-Hellman (ECDH)}
  \begin{minipage}{8cm}
   \begin{enumerate}
    \item Create private keys $c,t \mod o$
    \item Define $C = cG$
    \item Define $T = tG$
    \item Compute DH \\ $cT = c(tG) = t(cG) = tC$
    \end{enumerate}
   \end{minipage}
  \begin{minipage}{6cm}
  \begin{tikzpicture}
   \tikzstyle{def} = [node distance= 2em and 0.5em, inner sep=0em, outer sep=.3em];
    \node (t) [def, draw=none] at (0,0) {$t$};
    \node (ct) [def, draw=none, below left=of b]{\includegraphics[width=0.2\textwidth]{dh.pdf}};
    \node (c) [def, draw=none, above left= of ct]  {$c$};
    \tikzstyle{C} = [color=black, line width=1pt]

    \draw [<-, C] (ct) -- (c) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (ct) -- (t) node [midway, above, sloped] (TextNode) {};
  \end{tikzpicture}
  \end{minipage}
\end{frame}


\begin{frame}{Strawman solution}
  \begin{minipage}{8cm}
    Given partially spent private coin key $c_{old}$:
   \begin{enumerate}
%    \item Let $C_{old} := c_{old}G$ (as before)
    \item Pick random $c_{new} \mod o$ private key
    \item $C_{new} = c_{new}G$ public key
    \item Pick random $b_{new}$
    \item Compute $f_{new} := FDH(C_{new})$, $m < n$.
    \item Transmit $f'_{new} := f_{new} b_{new}^e \mod n$
   \end{enumerate}
   ... and sign request for change with $c_{old}$.
   \end{minipage}
  \begin{minipage}{4cm}
  \begin{tikzpicture}
   \tikzstyle{def} = [node distance= 1.5em and 0.5em, inner sep=0em, outer sep=.3em];
    \node (blinded) [def, draw=none]{\includegraphics[width=0.15\textwidth]{blinded.pdf}};
    \node (planchet) [def, draw=none, above left= of blinded]  {\includegraphics[width=0.15\textwidth]{planchet.pdf}};
    \node (cnew) [def, draw=none, above= of planchet]  {$c_{new}$};
    \node (bnew) [def, draw=none, above right= of blinded]  {$b_{new}$};
    \node (dice1) [def, draw=none, above = of cnew]{\includegraphics[width=0.2\textwidth]{dice.pdf}};
    \node (dice2) [def, draw=none, above = of bnew]{\includegraphics[width=0.2\textwidth]{dice.pdf}};
    \node (exchange) [node distance=4em and 0.5em, draw, below =of blinded]{Exchange};

    \tikzstyle{C} = [color=black, line width=1pt]

    \draw [<-, C] (cnew) -- (dice1) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (planchet) -- (cnew) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (bnew) -- (dice2) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (blinded) -- (planchet) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (blinded) -- (bnew) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (exchange) -- (blinded) node [midway, above, sloped] (TextNode) {{\small transmit}};
  \end{tikzpicture}
  \end{minipage}
  \pause
  \vfill
  {\bf Problem: Owner of $c_{new}$ may differ from owner of $c_{old}$!}
\end{frame}


\begin{frame}{Customer: Transfer key setup (ECDH)}
  \begin{minipage}{8cm}
    Given partially spent private coin key $c_{old}$:
   \begin{enumerate}
    \item Let $C_{old} := c_{old}G$ (as before)
    \item Create random private transfer key $t \mod o$
    \item Compute $T := tG$
    \item Compute $X := c_{old}(tG) = t(c_{old}G) = tC_{old}$
    \item Derive $c_{new}$ and $b_{new}$ from $X$
    \item Compute $C_{new} := c_{new}G$
    \item Compute $f_{new} := FDH(C_{new})$
    \item Transmit $f_{new}' := f_{new} b_{new}^e$
    \end{enumerate}
   \end{minipage}
  \begin{minipage}{4cm}
  \begin{tikzpicture}
   \tikzstyle{def} = [node distance= 1.5em and 0.5em, inner sep=0em, outer sep=.3em];
    \node (t) [def, draw=none] at (0,0) {$t$};
    \node (dice) [def, draw=none, above = of t]{\includegraphics[width=0.2\textwidth]{dice.pdf}};
    \node (dh) [def, draw=none, below left=of b]{\includegraphics[width=0.2\textwidth]{ct.pdf}};
    \node (d) [def, draw=none, above left= of dh]  {$c_{old}$};
    \node (cp) [def, draw=none, below left= of dh]  {$c_{new}$};
    \node (bp) [def, draw=none, below right= of dh]  {$b_{new}$};
    \node (blinded) [def, draw=none, below right=of cp]{\includegraphics[width=0.15\textwidth]{blinded.pdf}};
    \node (exchange) [node distance=4em and 0.5em, draw, below =of blinded]{Exchange};

    \tikzstyle{C} = [color=black, line width=1pt]

    \draw [<-, C] (dh) -- (d) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (dh) -- (t) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (t) -- (dice) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (cp) -- (dh) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (bp) -- (dh) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (blinded) -- (cp) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (blinded) -- (bp) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (exchange) -- (blinded) node [midway, above, sloped] (TextNode) {{\small transmit}};
  \end{tikzpicture}
  \end{minipage}
\end{frame}


\begin{frame}{Cut-and-Choose}
  \begin{minipage}{4cm}
  \begin{tikzpicture}
   \tikzstyle{def} = [node distance= 1.5em and 0.5em, inner sep=0em, outer sep=.3em];
    \node (t) [def, draw=none] at (0,0) {$t_1$};
    \node (dice) [def, draw=none, above = of t]{\includegraphics[width=0.2\textwidth]{dice.pdf}};
    \node (dh) [def, draw=none, below left=of b]{\includegraphics[width=0.2\textwidth]{ct.pdf}};
    \node (d) [def, draw=none, above left= of dh]  {$c_{old}$};
    \node (cp) [def, draw=none, below left= of dh]  {$c_{new,1}$};
    \node (bp) [def, draw=none, below right= of dh]  {$b_{new,1}$};
    \node (blinded) [def, draw=none, below right=of cp]{\includegraphics[width=0.15\textwidth]{blinded.pdf}};
    \node (exchange) [node distance=4em and 0.5em, draw, below =of blinded]{Exchange};

    \tikzstyle{C} = [color=black, line width=1pt]

    \draw [<-, C] (t) -- (dice) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (dh) -- (d) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (dh) -- (t) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (cp) -- (dh) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (bp) -- (dh) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (blinded) -- (cp) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (blinded) -- (bp) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (exchange) -- (blinded) node [midway, above, sloped] (TextNode) {{\small transmit}};
  \end{tikzpicture}
  \end{minipage}
  \begin{minipage}{4cm}
  \begin{tikzpicture}
   \tikzstyle{def} = [node distance= 1.5em and 0.5em, inner sep=0em, outer sep=.3em];
    \node (t) [def, draw=none] at (0,0) {$t_2$};
    \node (dice) [def, draw=none, above = of t]{\includegraphics[width=0.2\textwidth]{dice.pdf}};
    \node (dh) [def, draw=none, below left=of b]{\includegraphics[width=0.2\textwidth]{ct.pdf}};
    \node (d) [def, draw=none, above left= of dh]  {$c_{old}$};
    \node (cp) [def, draw=none, below left= of dh]  {$c_{new,2}$};
    \node (bp) [def, draw=none, below right= of dh]  {$b_{new,2}$};
    \node (blinded) [def, draw=none, below right=of cp]{\includegraphics[width=0.15\textwidth]{blinded.pdf}};
    \node (exchange) [node distance=4em and 0.5em, draw, below =of blinded]{Exchange};

    \tikzstyle{C} = [color=black, line width=1pt]

    \draw [<-, C] (t) -- (dice) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (dh) -- (d) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (dh) -- (t) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (cp) -- (dh) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (bp) -- (dh) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (blinded) -- (cp) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (blinded) -- (bp) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (exchange) -- (blinded) node [midway, above, sloped] (TextNode) {{\small transmit}};
  \end{tikzpicture}
  \end{minipage}
  \begin{minipage}{4cm}
  \begin{tikzpicture}
   \tikzstyle{def} = [node distance= 1.5em and 0.5em, inner sep=0em, outer sep=.3em];
    \node (t) [def, draw=none] at (0,0) {$t_3$};
    \node (dice) [def, draw=none, above = of t]{\includegraphics[width=0.2\textwidth]{dice.pdf}};
    \node (dh) [def, draw=none, below left=of b]{\includegraphics[width=0.2\textwidth]{ct.pdf}};
    \node (d) [def, draw=none, above left= of dh]  {$c_{old}$};
    \node (cp) [def, draw=none, below left= of dh]  {$c_{new,3}$};
    \node (bp) [def, draw=none, below right= of dh]  {$b_{new,3}$};
    \node (blinded) [def, draw=none, below right=of cp]{\includegraphics[width=0.15\textwidth]{blinded.pdf}};
    \node (exchange) [node distance=4em and 0.5em, draw, below =of blinded]{Exchange};

    \tikzstyle{C} = [color=black, line width=1pt]

    \draw [<-, C] (t) -- (dice) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (dh) -- (d) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (dh) -- (t) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (cp) -- (dh) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (bp) -- (dh) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (blinded) -- (cp) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (blinded) -- (bp) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (exchange) -- (blinded) node [midway, above, sloped] (TextNode) {{\small transmit}};
  \end{tikzpicture}
  \end{minipage}
\end{frame}


\begin{frame}{Exchange: Choose!}
   \begin{center}
    \item Exchange sends back random $\gamma \in \{ 1, 2, 3 \}$ to the customer.
    \end{center}
\end{frame}


\begin{frame}{Customer: Reveal}
   \begin{enumerate}
   \item If $\gamma = 1$, send $t_2$, $t_3$ to exchange
   \item If $\gamma = 2$, send $t_1$, $t_3$ to exchange
   \item If $\gamma = 3$, send $t_1$, $t_2$ to exchange
  \end{enumerate}
\end{frame}


\begin{frame}{Exchange: Verify ($\gamma = 2$)}
  \begin{minipage}{4cm}
  \begin{tikzpicture}
   \tikzstyle{def} = [node distance= 1.5em and 0.5em, inner sep=0em, outer sep=.3em];
    \node (h) [def, draw=none] at (0,0) {$t_1$};
    \node (dh) [def, draw=none, below left=of b]{\includegraphics[width=0.2\textwidth]{ct.pdf}};
    \node (d) [def, draw=none, above left= of dh]  {$C_{old}$};
    \node (cp) [def, draw=none, below left= of dh]  {$c_{new,1}$};
    \node (bp) [def, draw=none, below right= of dh]  {$b_{new,1}$};
    \node (blinded) [def, draw=none, below right=of cp]{\includegraphics[width=0.15\textwidth]{blinded.pdf}};

    \tikzstyle{C} = [color=black, line width=1pt]

    \draw [<-, C] (dh) -- (d) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (dh) -- (h) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (cp) -- (dh) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (bp) -- (dh) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (blinded) -- (cp) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (blinded) -- (bp) node [midway, above, sloped] (TextNode) {};
  \end{tikzpicture}
  \end{minipage}
  \begin{minipage}{4cm}
 \
  \end{minipage}
  \begin{minipage}{4cm}
  \begin{tikzpicture}
   \tikzstyle{def} = [node distance= 1.5em and 0.5em, inner sep=0em, outer sep=.3em];
    \node (h) [def, draw=none] at (0,0) {$t_3$};
    \node (dh) [def, draw=none, below left=of b]{\includegraphics[width=0.2\textwidth]{ct.pdf}};
    \node (d) [def, draw=none, above left= of dh]  {$C_{old}$};
    \node (cp) [def, draw=none, below left= of dh]  {$c_{new,3}$};
    \node (bp) [def, draw=none, below right= of dh]  {$b_{new,3}$};
    \node (blinded) [def, draw=none, below right=of cp]{\includegraphics[width=0.15\textwidth]{blinded.pdf}};

    \tikzstyle{C} = [color=black, line width=1pt]

    \draw [<-, C] (dh) -- (d) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (dh) -- (h) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (cp) -- (dh) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (bp) -- (dh) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (blinded) -- (cp) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (blinded) -- (bp) node [midway, above, sloped] (TextNode) {};
  \end{tikzpicture}
  \end{minipage}
\end{frame}


\begin{frame}{Exchange: Blind sign change (RSA)}
   \begin{minipage}{6cm}
    \begin{enumerate}
    \item Take $f_{new,\gamma}'$.
    \item Compute $s' := f_{new,\gamma}'^d \mod n$.
    \item Send signature $s'$.
    \end{enumerate}
   \end{minipage}
  \begin{minipage}{6cm}
  \begin{tikzpicture}
   \tikzstyle{def} = [node distance= 2em and 0.5em, inner sep=0em, outer sep=.3em];
    \node (hammer) [def, draw=none] at (0,0) {\includegraphics[width=0.15\textwidth]{hammer.pdf}};
    \node (signed) [def, draw=none, below left=of hammer]{\includegraphics[width=0.2\textwidth]{sign.pdf}};
    \node (blinded) [def, draw=none, above left=of signed]{\includegraphics[width=0.15\textwidth]{blinded.pdf}};
    \node (customer) [node distance=4em and 0.5em, draw, below =of signed]{Customer};
    \tikzstyle{C} = [color=black, line width=1pt]

    \draw [<-, C] (signed) -- (hammer) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (signed) -- (blinded) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (customer) -- (signed) node [midway, above, sloped] (TextNode) {{\small transmit}};
  \end{tikzpicture}
  \end{minipage}
\end{frame}


\begin{frame}{Customer: Unblind change (RSA)}
  \begin{minipage}{6cm}
   \begin{enumerate}
    \item Receive $s'$.
    \item Compute $s := s' b_{new,\gamma}^{-1} \mod n$.
    \end{enumerate}
   \end{minipage}
  \begin{minipage}{6cm}
  \begin{tikzpicture}
   \tikzstyle{def} = [node distance= 2em and 0.5em, inner sep=0em, outer sep=.3em];
    \node (b) [def, draw=none] at (0,0) {$b_{new,\gamma}$};
    \node (coin) [def, draw=none, below left=of b]{\includegraphics[width=0.2\textwidth]{coin.pdf}};
    \node (signed) [def, draw=none, above left=of coin]{\includegraphics[width=0.15\textwidth]{sign.pdf}};
    \tikzstyle{C} = [color=black, line width=1pt]

    \draw [<-, C] (coin) -- (b) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (coin) -- (signed) node [midway, above, sloped] (TextNode) {};
  \end{tikzpicture}
  \end{minipage}
\end{frame}


\begin{frame}{Exchange: Allow linking change}
  \begin{minipage}{7cm}
    \begin{center}
    Given $C_{old}$

    \vspace{1cm}

    return $T_\gamma$, $s := s' b_{new,\gamma}^{-1} \mod n$.
  \end{center}
   \end{minipage}
  \begin{minipage}{5cm}
   \begin{tikzpicture}
    \tikzstyle{def} = [node distance= 3em and 0.5em, inner sep=0.5em, outer sep=.3em];
    \node (co) [def, draw=none] at (0,0) {$C_{old}$};
    \node (T) [def, draw=none, below left=of co]{$T_\gamma$};
    \node (sign) [def, draw=none, below right=of co]{\includegraphics[width=0.15\textwidth]{sign.pdf}};
    \node (customer) [def, draw, below right=of T] {Customer};

    \tikzstyle{C} = [color=black, line width=1pt]

    \draw [<-, C] (T) -- (co) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (sign) -- (co) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (customer) -- (T) node [midway, above, sloped] (TextNode) {link};
    \draw [<-, C] (customer) -- (sign) node [midway, above, sloped] (TextNode) {link};
  \end{tikzpicture}
  \end{minipage}
\end{frame}


\begin{frame}{Customer: Link (threat!)}
  \begin{minipage}{6.3cm}
   \begin{enumerate}
    \item Have $c_{old}$.
    \item Obtain $T_\gamma$, $s$ from exchange
    \item Compute $X_\gamma = c_{old}T_\gamma$
    \item Derive $c_{new,\gamma}$ and $b_{new,\gamma}$ from $X_\gamma$
    \item Unblind $s := s' b_{new,\gamma}^{-1} \mod n$
  \end{enumerate}

   \end{minipage}
  \begin{minipage}{5.7cm}
  \begin{tikzpicture}
  \tikzstyle{def} = [node distance= 1.5em and 0.5em, inner sep=0em, outer sep=.3em];
    \node (T) [def, draw=none] at (0,0) {$T_\gamma$};
    \node (exchange) [def, inner sep=0.5em, draw, above left=of T] {Exchange};
    \node (signed) [def, draw=none, below left=of T]{\includegraphics[width=0.15\textwidth]{sign.pdf}};
    \node (dh) [def, draw=none, below right=of T]{\includegraphics[width=0.2\textwidth]{ct.pdf}};
    \node (bp) [def, draw=none, below left= of dh]  {$b_{new,\gamma}$};
    \node (co) [def, draw=none, above right= of dh]  {$c_{old}$};
    \node (cp) [def, draw=none, below= of dh]  {$c_{new,\gamma}$};
    \node (coin) [def, draw=none, below left = of bp]{\includegraphics[width=0.2\textwidth]{coin.pdf}};
    \node (psign) [def, node distance=2.5em and 0em, draw=none, below = of cp]{\includegraphics[width=0.2\textwidth]{planchet-sign.pdf}};

    \tikzstyle{C} = [color=black, line width=1pt]

    \draw [<-, C] (dh) -- (co) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (dh) -- (T) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (cp) -- (dh) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (bp) -- (dh) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (coin) -- (signed) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (coin) -- (bp) node [midway, above, sloped] (TextNode) {};
    \draw [<-, C] (T) -- (exchange) node [midway, above, sloped] (TextNode) {link};
    \draw [<-, C] (signed) -- (exchange) node [midway, below, sloped] (TextNode) {link};
    \draw [<-, C, double] (psign) -- (cp) node [midway, below, sloped] (TextNode) {};
  \end{tikzpicture}
  \end{minipage}
\end{frame}


\begin{frame}{Refresh protocol summary}
  \begin{itemize}
  \item Customer asks exchange to convert old coin to new coin
  \item Protocol ensures new coins can be recovered from old coin
  \item[$\Rightarrow$] New coins are owned by the same entity!
  \end{itemize}
  Thus, the refresh protocol allows:
  \begin{itemize}
  \item To give unlinkable change.
  \item To give refunds to an anonymous customer.
  \item To expire old keys and migrate coins to new ones.
  \item To handle protocol aborts.
  \end{itemize}
  \noindent
  \begin{center}
    \bf
   Transactions via refresh are equivalent to {\em sharing} a wallet.
\end{center}
\end{frame}








\end{document}




\begin{frame}{Taler {\tt /withdraw/sign}}
% Customer withdrawing coins with blind signatures
% \bigskip
  \begin{figure}[th]
    \begin{minipage}[b]{0.45\linewidth}
      \begin{center}
        \begin{tikzpicture}[scale = 0.4,
            transform shape,
            msglabel/.style    = { text = Black, yshift = .3cm,
                                   sloped, midway },
            okmsg/.style       = { ->, color = MidnightBlue, thick,
                                   >=stealth },
            rstmsg/.style      = { ->, color = BrickRed, thick,
                                   >=stealth }
          ]
          \node[draw = MidnightBlue,
            fill = CornflowerBlue,
            minimum width = .3cm,
            minimum height = 10cm
          ] (h1) at (-4, 0) {};
          \node[draw = MidnightBlue,
            fill = CornflowerBlue,
            minimum width = .3cm,
            minimum height = 10cm
          ] (h2) at (4, 0) {};
          \node[above = 0cm of h1] {Wallet};
          \node[above = 0cm of h2] {Exchange};

          \path[->, color = MidnightBlue, very thick, >=stealth]
            (-5, 4.5) edge
            node[rotate=90, text = Black, yshift = .3cm] {Time}
            (-5, -4.5);
          \path[okmsg, dashed]
             ($(h1.east)+(0, 4.0)+(0, -1.0)$) edge
             node[msglabel] {SEPA(RK,A)}
             ($(h2.west)+(0, 3.5)+(0, -1.0)$);
          \path[okmsg]
            ($(h1.east)+(0, -1.0)$) edge
            node[msglabel] {POST {\tt /withdraw/sign} $S_{RK}(DK, B_b(C))$}
            ($(h2.west)+(0, -1.5)$);
          \path[okmsg]
            ($(h2.west)+(0, -2.0)$) edge
            node[msglabel] {200 OK: $S_{DK}(B_b(C))$)}
            ($(h1.east)+(0, -2.5)$);
          \path[rstmsg]
            ($(h2.west)+(0, -3.5)$) edge
            node[msglabel] {402 PAYMENT REQUIRED: $S_{RK}(DK, B_b(C))$)}
            ($(h1.east)+(0, -4)$);
          \node at (5.3, 0) {};
        \end{tikzpicture}
      \end{center}
      Result: $\langle c, S_{DK}(C) \rangle$.
    \end{minipage}
    \hspace{0.5cm}
    \begin{minipage}[b]{0.45\linewidth}
      \tiny
      \begin{description}
      \item[$A$] Some amount, $A \ge A_{DK}$
      \item[$RK$] Reserve key
      \item[$DK$] Denomination key
      \item[$b$] Blinding factor
      \item[$B_b()$] RSA-FDH blinding % DK supressed
      \item[$C$] Coin public key $C := cG$
      \item[$S_{RK}()$] EdDSA signature
      \item[$S_{DK}()$] RSA-FDH signature
      \end{description}
    \end{minipage}
  \end{figure}
\end{frame}


\begin{frame}[t]{Taler {\tt /deposit}}
Merchant and exchange see only the public coin $\langle C, S_{DK}(C) \rangle$.
\bigskip
  \begin{figure}[th]
    \begin{minipage}[b]{0.45\linewidth}
      \begin{center}
        \begin{tikzpicture}[scale = 0.4,
            transform shape,
            msglabel/.style    = { text = Black, yshift = .3cm,
                                   sloped, midway },
            okmsg/.style       = { ->, color = MidnightBlue, thick,
                                   >=stealth },
            rstmsg/.style      = { ->, color = BrickRed, thick,
                                   >=stealth }
          ]
          \node[draw = MidnightBlue,
            fill = CornflowerBlue,
            minimum width = .3cm,
            minimum height = 10cm
          ] (h1) at (-4, 0) {};
          \node[draw = MidnightBlue,
            fill = CornflowerBlue,
            minimum width = .3cm,
            minimum height = 10cm
          ] (h2) at (4, 0) {};
          \node[above = 0cm of h1] {Merchant};
          \node[above = 0cm of h2] {Exchange};

          \path[->, color = MidnightBlue, very thick, >=stealth]
            (-5, 4.5) edge
            node[rotate=90, text = Black, yshift = .3cm] {Time}
            (-5, -4.5);
          \path[->, color = MidnightBlue, thick, >=stealth]
            ($(h1.east)+(0,3)$) edge
            node[text = Black, yshift = .3cm, sloped] {POST {\tt /deposit} $S_{DK}(C), S_{c}(D)$}
            ($(h2.west)+(0,2)$);
          \path[->, color = MidnightBlue, thick, >=stealth]
            ($(h2.west)+(0,0.5)$) edge
            node[text = Black, yshift = .3cm, sloped] {200 OK: $S_{SK}(S_{c}(D))$}
            ($(h1.east)+(0,-0.5)$);
          \path[rstmsg]
            ($(h2.west)+(0, -2.5)$) edge
            node[msglabel] {409 CONFLICT: $S_{c}(D')$}
            ($(h1.east)+(0, -3.5)$);
          \node at (5.3, 0) {};
        \end{tikzpicture}
      \end{center}
    \end{minipage}
    \hspace{0.5cm}
    \begin{minipage}[b]{0.45\linewidth}
      \tiny
      \begin{description}
      \item[$DK$] Denomination key
      \item[$S_{DK}()$] RSA-FDH signature using $DK$
      \item[$c$] Private coin key, $C := cG$.
      \item[$S_{C}()$] EdDSA signature using $c$
      \item[$D$] Deposit details
      \item[$SK$] Exchange's signing key
      \item[$S_{SK}()$] EdDSA signature using $SK$
      \item[$D'$] Conficting deposit details $D' \not= D$
      \end{description}
    \end{minipage}
  \end{figure}
\end{frame}


\begin{frame}{Taler {\tt /refresh/melt}}
  \begin{figure}[th]
    \begin{minipage}[b]{0.45\linewidth}
      \begin{center}
	\begin{tikzpicture}[scale = 0.4,
            transform shape,
            msglabel/.style    = { text = Black, yshift = .3cm,
                                   sloped, midway },
            okmsg/.style       = { ->, color = MidnightBlue, thick,
                                   >=stealth },
            rstmsg/.style      = { ->, color = BrickRed, thick,
                                   >=stealth }
	  ]
	  \node[draw = MidnightBlue,
	    fill = CornflowerBlue,
	    minimum width = .3cm,
	    minimum height = 10cm
	  ] (h1) at (-4, 0) {};
	  \node[draw = MidnightBlue,
	    fill = CornflowerBlue,
	    minimum width = .3cm,
	    minimum height = 10cm
	  ] (h2) at (4, 0) {};
	  \node[above = 0cm of h1] {Customer};
	  \node[above = 0cm of h2] {Exchange};

	  \path[->, color = MidnightBlue, very thick, >=stealth]
	    (-5, 4.5) edge
	    node[rotate=90, text = Black, yshift = .3cm] {Time}
	    (-5, -4.5);
	  \path[->, color = MidnightBlue, thick, >=stealth]
	    ($(h1.east)+(0,3)$) edge
	    node[text = Black, yshift = .3cm, sloped] {POST {\tt /refresh/melt} $S_{DK}(C), S_c({\cal DK}, {\cal T},{\cal B})$}
	    ($(h2.west)+(0,2)$);
	  \path[->, color = MidnightBlue, thick, >=stealth]
	    ($(h2.west)+(0,0.5)$) edge
	    node[text = Black, yshift = .3cm, sloped] {200 OK: $S_{SK}(H({\cal T}, {\cal B}),\gamma)$}
	    ($(h1.east)+(0,-0.5)$);
	  \path[rstmsg]
	    ($(h2.west)+(0, -2.5)$) edge
	    node[msglabel] {409 CONFLICT: $S_{C}(X), \ldots$}
	    ($(h1.east)+(0, -3.5)$);
	  \node at (5.3, 0) {};
	\end{tikzpicture}
      \end{center}
    \end{minipage}
    \hspace{0.5cm}
    \begin{minipage}[b]{0.45\linewidth}
      \tiny
      \begin{description}
      \item[$\kappa$] System-wide security parameter, usually 3.
      \\ \smallskip
      \item[$\cal DK$] $:= [DK^{(i)}]_i$ \\ List of denomination keys \\
      $D + \sum_i A_{DK^{(i)}} < A_{DK}$
      \item[$t_j$] Random scalar for $j<\kappa$
      \item[${\cal T}$] $:= [T_j]_\kappa$ where $T_j = t_j G$
      \item[$k_j$] $:= c T_j = t_j C$ is an ECDHE
      \item[$b_j^{(i)}$] $:= KDF_b(k_j,i)$ % blinding factor
      \item[$c_j^{(i)}$] $:= KDF_c(k_j,i)$ % coin secret keys
      \item[$C_j^{(i)}$] $: = c_j^{(i)} G$ % new coin publics % keys
      \item[${\cal B}$] $:= [H( \beta_j )]_\kappa$ where \\
         $\beta_j := \left[ B_{b_j^{(i)}}(C_j^{(i)}) \right]_i$
      \\ \smallskip
      \item[$\gamma$] Random value in $[0,\kappa)$
%      \\ \smallskip
%      \item[$X$] Deposit or refresh
      \end{description}
    \end{minipage}
  \end{figure}
\end{frame}


\begin{frame}{Taler {\tt /refresh/reveal}}
  \begin{figure}[th]
    \begin{minipage}[b]{0.45\linewidth}
      \begin{center}
	\begin{tikzpicture}[scale = 0.4,
            transform shape,
            msglabel/.style    = { text = Black, yshift = .3cm,
                                   sloped, midway },
            okmsg/.style       = { ->, color = MidnightBlue, thick,
                                   >=stealth },
            rstmsg/.style      = { ->, color = BrickRed, thick,
                                   >=stealth }
	  ]
	  \node[draw = MidnightBlue,
	    fill = CornflowerBlue,
	    minimum width = .3cm,
	    minimum height = 10cm
	  ] (h1) at (-4, 0) {};
	  \node[draw = MidnightBlue,
	    fill = CornflowerBlue,
	    minimum width = .3cm,
	    minimum height = 10cm
	  ] (h2) at (4, 0) {};
	  \node[above = 0cm of h1] {Customer};
	  \node[above = 0cm of h2] {Exchange};

	  \path[->, color = MidnightBlue, very thick, >=stealth]
	    (-5, 4.5) edge
	    node[rotate=90, text = Black, yshift = .3cm] {Time}
	    (-5, -4.5);
	  \path[->, color = MidnightBlue, thick, >=stealth]
	    ($(h1.east)+(0,3)$) edge
	    node[text = Black, yshift = .3cm, sloped] {POST {\tt /refresh/reveal} $H({\cal T}, {\cal B}), {\tilde{\cal T}}, \beta_\gamma$}
	    ($(h2.west)+(0,2)$);
	  \path[->, color = MidnightBlue, thick, >=stealth]
	    ($(h2.west)+(0,0.5)$) edge
	    node[text = Black, yshift = .3cm, sloped] {200 OK: $\cal S$}
	    ($(h1.east)+(0,-0.5)$);
	  \path[rstmsg]
	    ($(h2.west)+(0, -2.5)$) edge
	    node[msglabel] {400 BAD REQUEST: $Z$}
	    ($(h1.east)+(0, -3.5)$);
	  \node at (5.3, 0) {};
	\end{tikzpicture}
      \end{center}
    \end{minipage}
    \hspace{0.5cm}
    \begin{minipage}[b]{0.45\linewidth}
      \tiny
      \begin{description}
      \item[$\cal DK$] $:= [DK^{(i)}]_i$
      \item[$t_j$] .. \\ \smallskip

      \item[$\tilde{\cal T}$] $:= [t_j | j \in \kappa, j \neq \gamma]$ \\ \smallskip

      \item[$k_\gamma$] $:= c T_\gamma = t_\gamma C$
      \item[$b_\gamma^{(i)}$] $:= KDF_b(k_\gamma,i)$
      \item[$c_\gamma^{(i)}$] $:= KDF_c(k_\gamma,i)$
      \item[$C_\gamma^{(i)}$] $: = c_\gamma^{(i)} G$

      \item[$B_\gamma^{(i)}$] $:= B_{b_\gamma^{(i)}}(C_\gamma^{(i)})$
      \item[$\beta_\gamma$] $:= \big[ B_\gamma^{(i)} \big]_i$
      \item[$\cal S$] $:= \left[ S_{DK^{(i)}}( B_\gamma^{(i)} ) \right]_i$ \\ \smallskip

      \item[$Z$] Cut-and-choose missmatch information
      \end{description}
    \end{minipage}
  \end{figure}
\end{frame}


\begin{frame}{Taler {\tt /refresh/link}}
  \begin{figure}[th]
    \begin{minipage}[b]{0.45\linewidth}
      \begin{center}
	\begin{tikzpicture}[scale = 0.4,
            transform shape,
            msglabel/.style    = { text = Black, yshift = .3cm,
                                   sloped, midway },
            okmsg/.style       = { ->, color = MidnightBlue, thick,
                                   >=stealth },
            rstmsg/.style      = { ->, color = BrickRed, thick,
                                   >=stealth }
	  ]
	  \node[draw = MidnightBlue,
	    fill = CornflowerBlue,
	    minimum width = .3cm,
	    minimum height = 10cm
	  ] (h1) at (-4, 0) {};
	  \node[draw = MidnightBlue,
	    fill = CornflowerBlue,
	    minimum width = .3cm,
	    minimum height = 10cm
	  ] (h2) at (4, 0) {};
	  \node[above = 0cm of h1] {Customer};
	  \node[above = 0cm of h2] {Exchagne};

	  \path[->, color = MidnightBlue, very thick, >=stealth]
	    (-5, 4.5) edge
	    node[rotate=90, text = Black, yshift = .3cm] {Time}
	    (-5, -4.5);
	  \path[->, color = MidnightBlue, thick, >=stealth]
	    ($(h1.east)+(0,3)$) edge
	    node[text = Black, yshift = .3cm, sloped] {POST {\tt /refresh/link} $C$}
	    ($(h2.west)+(0,2)$);
	  \path[->, color = MidnightBlue, thick, >=stealth]
	    ($(h2.west)+(0,0.5)$) edge
	    node[text = Black, yshift = .3cm, sloped] {200 OK: $T_\gamma$}
	    ($(h1.east)+(0,-0.5)$);
	  \path[rstmsg]
	    ($(h2.west)+(0, -2.5)$) edge
	    node[msglabel] {404 NOT FOUND}
	    ($(h1.east)+(0, -3.5)$);
	  \node at (5.3, 0) {};
	\end{tikzpicture}
      \end{center}
    \end{minipage}
    \hspace{0.5cm}
    \begin{minipage}[b]{0.45\linewidth}
      \tiny
      \begin{description}
      \item[$C$] Old coind public key \\ \smallskip
      \item[$T_\gamma$] Linkage data $\cal L$ at $\gamma$
      \end{description}
    \end{minipage}
  \end{figure}
\end{frame}


\begin{frame}{Operational security}
  \begin{center}
    \resizebox{\textwidth}{!}{
\begin{tikzpicture}[
  font=\sffamily,
  every matrix/.style={ampersand replacement=\&,column sep=2cm,row sep=2cm},
  source/.style={draw,thick,rounded corners,fill=green!20,inner sep=.3cm},
  process/.style={draw,thick,circle,fill=blue!20},
  sink/.style={source,fill=green!20},
  datastore/.style={draw,very thick,shape=datastore,inner sep=.3cm},
  dots/.style={gray,scale=2},
  to/.style={->,>=stealth',shorten >=1pt,semithick,font=\sffamily\footnotesize},
  every node/.style={align=center}]

  % Position the nodes using a matrix layout
  \matrix{
    \node[source] (wallet) {Wallet};
      \& \node[process] (browser) {Browser};
      \& \node[process] (shop) {Web shop};
      \& \node[sink] (backend) {Taler backend}; \\
  };

  % Draw the arrows between the nodes and label them.
  \draw[to] (browser) to[bend right=50] node[midway,above] {(4) signed contract}
      node[midway,below] {(signal)} (wallet);
  \draw[to] (wallet) to[bend right=50] node[midway,above] {(signal)}
      node[midway,below] {(5) signed coins} (browser);
  \draw[<->] (browser) -- node[midway,above] {(3,6) custom}
      node[midway,below] {(HTTPS)} (shop);
  \draw[to] (shop) to[bend right=50] node[midway,above] {(HTTPS)}
      node[midway,below] {(1) proposed contract / (7) signed coins} (backend);
  \draw[to] (backend) to[bend right=50] node[midway,above] {(2) signed contract / (8) confirmation}
      node[midway,below] {(HTTPS)} (shop);
\end{tikzpicture}
}
\end{center}
\end{frame}