edits to Taler paper, trying to clarify/improve writing/structure

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Christian Grothoff 2015-09-24 11:40:23 +02:00
parent 25c86ad506
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2 changed files with 263 additions and 189 deletions

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@ -4,6 +4,13 @@
year={2008} year={2008}
} }
@InProceedings{apod,
author = {Elli Androulaki and Steven Bellovin},
title = {APOD: Anonymous Physical Object Delivery},
booktitle = {Symposium on Privacy-Enhancing Technologies (PETS)},
year = {2009},
}
@Article{blum1981, @Article{blum1981,
author = {Manuel Blum}, author = {Manuel Blum},
title = {Coin Flipping by Telephone}, title = {Coin Flipping by Telephone},
@ -12,6 +19,23 @@
pages = {11-15}, pages = {11-15},
} }
@Misc{greece2015cash,
author = {Reuters},
title = {Greek council recommends 60 euro limit on ATM withdrawals from Tuesday},
howpublished = {\url{http://www.reuters.com/article/2015/06/28/eurozone-greece-limits-idUSA8N0Z302P20150628}},
month = {June},
year = {2015},
}
@Misc{france2015cash,
author = {Heinz-Peter Bader},
title = {France steps up monitoring of cash payments to fight low-cost terrorism},
howpublished = {\url{http://www.reuters.com/article/2015/03/18/us-france-security-financing-idUSKBN0ME14720150318}},
month = {Mar},
year = {2015},
}
@inproceedings{chaum1990untraceable, @inproceedings{chaum1990untraceable,
title={Untraceable electronic cash}, title={Untraceable electronic cash},
author={Chaum, David and Fiat, Amos and Naor, Moni}, author={Chaum, David and Fiat, Amos and Naor, Moni},

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@ -50,19 +50,18 @@
This paper introduces Taler, a Chaum-style digital currency using This paper introduces Taler, a Chaum-style digital currency using
blind signatures that enables anonymous payments while ensuring that blind signatures that enables anonymous payments while ensuring that
entities that receive payments are auditable and thus taxable. Taler entities that receive payments are auditable and thus taxable. Taler
differs from Chaum's original proposal in that customers can never defraud anyone, differs from Chaum's original proposal in that customers can never
merchants can only fail to deliver the merchandise to the customer, defraud anyone, merchants can only fail to deliver the merchandise to
and mints can be fully audited. Consequently, enforcement of honest the customer, and mints can be fully audited. Consequently,
behavior is better and more timely than with Chaum, and is at least as enforcement of honest behavior is better and more timely than with
strict as with legacy credit card payment systems that do not provide Chaum, and is at least as strict as with legacy credit card payment
for privacy. Furthermore, Taler allows fractional and incremental systems that do not provide for privacy. Furthermore, Taler allows
payments, and even in this case is still able to guarantee fractional payments, and even in this case is still able to guarantee
unlinkability of transactions via a new coin refreshing protocol. unlinkability of transactions via a new coin refreshing protocol. We
Finally, Taler also supports microdonations using probabilistic argue that Taler provides a secure digital currency for modern liberal
transactions. We argue that Taler provides a secure digital currency societies as it is a flexible, libre and efficient protocol and
for modern liberal societies as it is a flexible, libre and efficient adequately balances the state's need for monetary control with the
protocol and adequately balances the state's need for monetary control citizen's needs for private economic activity.
with the citizen's needs for private economic activity.
\end{abstract} \end{abstract}
\section{Introduction} \section{Introduction}
@ -79,115 +78,25 @@ states where economic activity is based largely on coins, paper money
or even barter. Here, the state is often unable to effectively or even barter. Here, the state is often unable to effectively
monitor or tax economic activity, and this limits the ability of the monitor or tax economic activity, and this limits the ability of the
state to shape the society. As bribery is virtually impossible to state to shape the society. As bribery is virtually impossible to
detect, it is widespread and not limited to social elites. detect, corruption is widespread and not limited to social elites.
ZeroCoin~\cite{miers2013zerocoin} is an example for translating such ZeroCoin~\cite{miers2013zerocoin} is an example for translating such
an economy into the digital realm. an economy into the digital realm.
Taler is supposed to offer a middleground between an authoritarian This paper describes Taler, a simple and practical payment system for
state in total control of the population and weak states with almost a modern social-liberal society, which is not be served well by
anarchistic economies. Specifically, we believe that a liberal current payment systems which enable either an authoritarian state in
democracy needs a payment system with the following properties: total control of the population, or create weak states with almost
anarchistic economies.
\begin{description}
\item[Customer Anonymity] It must be impossible for mints, merchants
and even a global active adversary, to trace the spending behavior
of a customer.
\item[Unlinkability] Merchants must not be able to tell if two
transactions were performed by the same customer. It must be
infeasible to link a set of transactions to the same (anonymous)
customer. %, even when taking aborted transactions into account.
\item[Taxability] In many current legal systems, it is the
responsibility of the merchant to deduct (sales) taxes from
purchases made by customers, or to pay (income) taxes for payments
received for work.
%Taxation is neccessary for the state to
%provide legitimate social functions, such as education. Thus, a payment
%system must facilitate sales, income and transaction taxes.
This specifically means that it must be able to audit merchants (or
generally anybody receiving money), and thus the receiver of
electronic cash must be easily identifiable.
%non-anonymous, as this would enable tax fraud.
\item[Verifiability] The payment system should try to minimize the
trust necessary between the participants. In particular, digital
signatures should be used extensively in order to be able to
resolve disputes between the involved parties. Nevertheless,
customers must never be able to defraud anyone, and merchants must
at best be able to defraud their customers by not delivering the
on the agreed contract. Neither merchants nor customers must ever
be able to commit fraud against the mint. Both customers and
merchants must receive cryptographic proofs of bad behavior in
case of protocol violations by the mint. Thus, only the mint will
have to be tightly audited and regulated. The design must make it
easy to audit the finances of the mint.
\item[Ease of Deployment] %The system should be easy to deploy for
% real-world applications. In order to lower the entry barrier and
% acceptance of the system, a gateway to the existing financial
% system should be provided, i.e. by integrating internet-banking
% protocols such as HBCI/FinTAN.
The digital currency should be
tied 1:1 to existing currencies (such as EUR or USD) to avoid
exposing users to unnecessary risks from currency fluctuations.
Moreover, the system must have a free software reference
implementation and an open protocol standard.
% The protocol should
% be able to run easily over HTTP(S).
\item[Low resource consumption] In order to minimize the operating
costs and environmental impact of the payment system, it must
avoid the reliance on expensive and ``wasteful'' computations
such as proof-of-work.
\item[Large Payments and Microdonations] The payment system needs to
handle large payments in a reliable manner. Furthermore, for
microdonations the system should allow sacrificing reliability to
achieve economic viability.
\end{description}
Taler builds on ideas from Chaum~\cite{chaum1983blind}, who proposed a
digital currency system that would provide (some) customer anonymity
while disclosing the identity of the merchants. Chaum's digital cash
system had some limitations and ultimately failed to be widely
adopted. In our assessment, key reasons include:
\begin{itemize}
\item The use of patents to protect the technology; a payment system
must be libre --- free software --- to have a chance for widespread
adoption.
\item The use of off-line payments and thus deferred detection of
double-spending, which could require the mint to attempt to recover
funds from customers via the legal system. This creates a
significant business risk for the mint, as the system is not
self-enforcing from the perspective of the mint. In 1983 off-line
payments might have been a necessary feature. However, today
requiring network connectivity is feasible and avoids the business
risks associated with deferred fraud detection.
\item % In addition to the risk of legal disputes with fradulent
% merchants and customers,
Chaum's published design does not clearly
limit the financial damage a mint might suffer from the
disclosure of its private online signing key.
% \item Chaum did not support fractional payments, and Brand's
% extensions for fractional payments broke unlinkability and thus
% limited anonymity. Chaum also did not support microdonations,
% leaving an opportunity for expanding payments into additional areas
% unexplored.
% \item Chaum's system was implemented at a time where the US market
% was still dominated by paper checks and the European market was
% fragmented into dozens of currencies. Today, SEPA provides a
% unified currency and currency transfer method for most of Europe,
% significantly lowering the barrier to entry into this domain for
% a larger market.
\end{itemize}
This paper describes Taler, a simple and practical payment with the
above goals in mind. The basic idea is to use Chaum's model of
customer, merchant and mint (Figure~\ref{fig:cmm}) where the customer
withdraws digital currency from the mint with unlinkability provided
via blind signatures. In contrast to Chaum, Taler uses online
detection of double-spending, thus ensuring the merchant instantly
that a transaction is valid. Instead of using cryptographic methods
to enable fractional payments, the customer can simply include
the fraction of a coin's value that is to be paid to the merchant in
his message to the merchant.
The Taler protocol is havily based on ideas from
Chaum~\cite{1983blind} and also follows Chaum's basic architecture of
customer, merchant and mint (Figure~\ref{fig:cmm}). The two designs
share the key first step where the {\em customer} withdraws digital
{\em coins} from the {\em mint} with unlinkability provided via blind
signatures. The coins can then be spend at a {\em merchant} who {\em
deposits} them at the mint. Taler uses online detection of
double-spending, thus assuring the merchant instantly that a
transaction is valid.
\begin{figure}[h] \begin{figure}[h]
\centering \centering
@ -211,23 +120,102 @@ his message to the merchant.
\label{fig:cmm} \label{fig:cmm}
\end{figure} \end{figure}
Taler was designed for use in a modern social-liberal society, which we
believe needs a payment system with the following properties:
\begin{description}
\item[Customer Anonymity] It must be impossible for mints, merchants
and even a global active adversary, to trace the spending behavior
of a customer.
\item[Unlinkability] Merchants must not be able to tell if two
transactions were performed by the same customer. It must be
infeasible to link a set of transactions to the same (anonymous)
customer. %, even when taking aborted transactions into account.
\item[Taxability] In many current legal systems, it is the
responsibility of the merchant to deduct (sales) taxes from
purchases made by customers, or to pay (income) taxes for payments
received for work.
%Taxation is neccessary for the state to
%provide legitimate social functions, such as education. Thus, a payment
%system must facilitate sales, income and transaction taxes.
This specifically means that the state must be able to audit merchants (or
generally anybody receiving money), and thus the receiver of
electronic cash must be easily identifiable.
%non-anonymous, as this would enable tax fraud.
\item[Verifiability] The payment system should try to minimize the
trust necessary between the participants. In particular, digital
signatures should be used extensively in order to be able to
resolve disputes between the involved parties. Nevertheless,
customers must never be able to defraud anyone, and merchants must
at best be able to defraud their customers by not delivering the
on the agreed contract. Neither merchants nor customers must ever
be able to commit fraud against the mint. Both customers and
merchants must receive cryptographic proofs of bad behavior in
case of protocol violations by the mint. Thus, only the mint will
have to be tightly audited and regulated. The design must make it
easy to audit the finances of the mint.
\item[Ease of Deployment] %The system should be easy to deploy for
% real-world applications. In order to lower the entry barrier and
% acceptance of the system, a gateway to the existing financial
% system should be provided, i.e. by integrating internet-banking
% protocols such as HBCI/FinTAN.
The digital currency should be
tied 1:1 to existing currencies (such as EUR or USD) to avoid
exposing citizens to unnecessary risks from currency fluctuations.
Moreover, the system must have a free software reference
implementation and an open protocol standard.
% The protocol should
% be able to run easily over HTTP(S).
\item[Low resource consumption] In order to minimize the operating
costs and environmental impact of the payment system, it must
avoid the reliance on expensive and ``wasteful'' computations
such as proof-of-work.
\item[Fractional payments] The payment system needs to handle both
small and large payments in an efficient and reliable manner.
Thus, coins cannot just be issued in the smallest unit of currency,
and a mechanism to give {\em change} must be provided to ensure
that customers with sufficient total funds can always spend them.
For example, a customer may want to pay \eur{49,99} using a
\eur{100,00} coin. The system must then support giving change in
the form of say two fresh \eur{0,01} and \eur{50,00} coins. Those
coins must be {\em unlinkable}: an adversary should not be able to
relate transactions with either of the new coins to the original
\eur{100,00} coin or transaction or the other change being generated.
\end{description}
Instead of using cryptographic methods like restrictive blind
signatures to achieve divisiblity, Taler's fractional payments use a
simpler, more powerful mechanism. In Taler, a coin is not simply a
unique random token, but a private key. Thus, the transfer of a coin
can be performed by signing a message using this private key. Thus,
the customer can simply specify the fraction of a coin's value that is
to be paid to the merchant in the cryptographically signed deposit
message given to the merchant. A key contribution of Taler is the
{\em refresh} protocol, which enables a customer to exchange the
residual value of a coin for fresh coins, thereby providing unlinkable
change. Using online checks, the mint can trivially ensure that all
transactions involving the same coin do not exceed the total value of
the coin.
Online fraud detection can create problems if the network fails during Online fraud detection can create problems if the network fails during
the initial steps of a transaction. For example, a law enforcement the initial steps of a transaction. For example, a law enforcement
agency might try to entrap a customer by offering illicit goods and agency might try to entrap a customer by offering illicit goods and
then aborting the transaction after learning the public key of the then cancelling the transaction after learning the public key of the
coin. If the customer were to then later spend that coin on a coin. This is equivalent to a benign merchant giving a dissatisfied
purchase with shipping, the law enforcement agency could link the two (anonymous) customer a {\em refund} by sending a message affirming
transactions and might be able to use the shipping to deanonymize the the cancellation.
customer. Similarly, fractional payments also lead to the
possibility of customers wanting to legitimately use the same coin If the customer later spends the refunded coin on a purchase with
twice. Taler addresses this problem by allowing customers to {\em shipping, the state can link the two transactions and might be able to
refresh} coins. Refreshing means that a customer is able to use the shipping address to deanonymize the customer. As with support
exchange one coin for a fresh coin, with the old and the new coin for fractional payments, Taler addresses this problem by allowing
being unlinkable (except for the customer himself). Taler ensures customers to refresh coins, thereby destroying the link between the
that the {\em entity} of the user owning the new coin is the same as the refunded (or aborted) transaction and the coin.
entity of the user owning the old coin, thus making sure that the
refreshing protocol cannot be abused for money laundering or other Taler ensures that the {\em entity} of the user owning the new coin is
illicit transactions. the same as the entity of the user owning the old coin, thus making
sure that the refreshing protocol cannot be abused for money
laundering or other illicit transactions.
\section{Related Work} \section{Related Work}
@ -268,24 +256,75 @@ irredeemable problems inherent in these systems:
currency exchange and exascerbates the problems with currency fluctuations. currency exchange and exascerbates the problems with currency fluctuations.
\end{itemize} \end{itemize}
GreenCoinX\footnote{\url{https://www.greencoinx.com/}} is a more
recent AltCoin where the company promises to identify the owner of
each coin via e-mail addresses and phone numbers. While it is unclear
from their technical description how this identification would be
enforced against a determined adversary, the resulting payment system
would also merely impose a totalitarian financial panopticon on a
BitCoin-style money supply and transaction model, thus largely
combining what we would consider to be the drawbacks of these existing
systems.
\subsection{Chaum-style electronic cash} \subsection{Chaum-style electronic cash}
Taler builds on ideas from Chaum~\cite{chaum1983blind}, who proposed a
digital payment system that would provide (some) customer anonymity
while disclosing the identity of the merchants. Chaum's digital cash
(DigiCash) system had some limitations and ultimately failed to be widely
adopted. In our assessment, key reasons for DigiCash's failure that
Taler avoids include:
\begin{itemize}
\item The use of patents to protect the technology; a payment system
must be libre --- free software --- to have a chance for widespread
adoption.
\item The use of off-line payments and thus deferred detection of
double-spending, which could require the mint to attempt to recover
funds from customers via the legal system. This creates a
significant business risk for the mint, as the system is not
self-enforcing from the perspective of the mint. In 1983 off-line
payments might have been a necessary feature. However, today
requiring network connectivity is feasible and avoids the business
risks associated with deferred fraud detection.
\item % In addition to the risk of legal disputes with fradulent
% merchants and customers,
Chaum's published design does not clearly
limit the financial damage a mint might suffer from the
disclosure of its private online signing key.
\item Chaum did not support fractional payments or refunds without
breaking customer anonymity.
%, and Brand's
% extensions for fractional payments broke unlinkability and thus
% limited anonymity.
% \item Chaum's system was implemented at a time where the US market
% was still dominated by paper checks and the European market was
% fragmented into dozens of currencies. Today, SEPA provides a
% unified currency and currency transfer method for most of Europe,
% significantly lowering the barrier to entry into this domain for
% a larger market.
\end{itemize}
Chaum's original digital cash system~\cite{chaum1983blind} was Chaum's original digital cash system~\cite{chaum1983blind} was
extended by Brands~\cite{brands1993efficient} with the ability to extended by Brands~\cite{brands1993efficient} with the ability to {\em
perform fractional payments; however, the transactions performed with divide} coins and thus spend (certain) fractions of a coin using
the same coin then become linkable. restrictive blind signatures. Compared to Taler, performing
fractional payments is cryptographically way more expensive and
moreover the transactions performed with ``divisions'' from the same
coin do become linkable.
% %
%Some argue that the focus on technically perfect but overwhelmingly %Some argue that the focus on technically perfect but overwhelmingly
%complex protocols, as well as the the lack of usable, practical %complex protocols, as well as the the lack of usable, practical
%solutions lead to an abandonment of these ideas by %solutions lead to an abandonment of these ideas by
%practitioners~\cite{selby2004analyzing}. %practitioners~\cite{selby2004analyzing}.
% %
To our knowledge, the only publicly available effort to implement To our knowledge, the only publicly available effort to implement
Chaum's idea is Chaum's idea is Opencoin~\cite{dent2008extensions}. However, Opencoin
Opencoin~\cite{dent2008extensions}. However, seems to be neither actively developed nor used, and it is not clear
Opencoin seems to be neither actively developed nor used, and it is to what degree the implementation is even complete. Only a partial
not clear to what degree the implementation is even complete. Only a description of the Opencoin protocol is available to date.
partial description of the Opencoin protocol is available to date.
\subsection{Peppercoin} \subsection{Peppercoin}
@ -313,14 +352,14 @@ constructions to provide unlinkability, online fraud detection and
taxability. taxability.
As with Chaum, the Taler system comprises three principal types of As with Chaum, the Taler system comprises three principal types of
actors: The \emph{customer} is interested in receiving goods or actors (Figure~\ref{fig:cmm}): The \emph{customer} is interested in
services from the \emph{merchant} in exchange for payment. When receiving goods or services from the \emph{merchant} in exchange for
making a transaction, both the customer and the merchant must agree on payment. When making a transaction, both the customer and the
the same \emph{mint}, which serves as an intermediary for the merchant must agree on the same \emph{mint}, which serves as an
financial transaction between the two. The mint is responsible for intermediary for the financial transaction between the two. The mint
allowing the customer to obtain the anonymous digital currency and for is responsible for allowing the customer to obtain the anonymous
enabling the merchant to convert the anonymous digital currency back digital currency and for enabling the merchant to convert the
to some traditional currency. anonymous digital currency back to some traditional currency.
\subsection{Security model} \subsection{Security model}
@ -362,63 +401,72 @@ After all, without instrusive measures to take away control of the
computing platform from its users, copying an electronic wallet from computing platform from its users, copying an electronic wallet from
one computer to another can hardly be prevented by a payment system. one computer to another can hardly be prevented by a payment system.
Furthermore, it would also hardly be appropriate to tax the moving of Furthermore, it would also hardly be appropriate to tax the moving of
funds between two computers owned by the same individual. We thus funds between two computers owned by the same entity. We thus
need to clarify which kinds of transfers we expect to tax. need to clarify which kinds of transfers we expect to tax.
Taler is supposed to ensure that the state can tax {\em transactions}. Taler is supposed to ensure that the state can tax {\em transactions}.
We define a transaction as the transfer of funds between {\em mutually
distrustful} entities. Two entities are assumed to be mutually
distrustful if they are unwilling to share control over assets. If a
private key is shared between two entities, then both entities have
equal access to the credentials represented by the private key. In a
payment system this means that either entity could spent the
associated funds. Assuming the payment system has effective
double-spending detection, this means that either entity has to
constantly fear that the funds might no longer be available to it.
Thus, ``transferring'' funds by sharing a private key implies that
receiving party must trust the sender. In Taler, making funds
available by sharing a private key and thus sharing control is {\bf
not} considered a {\em transaction} and thus {\bf not} recorded for
taxation.
A {\em transaction} is a transfer where it is assured that one entity A {\em transaction} is a transfer where it is assured that one entity
gains control over funds while at the same time another entity looses gains control over funds while at the same time another entity looses
control over those funds. Taler ensures taxability only when some control over those funds. We further restrict transactions to apply
entity acquires exclusive control over digital coins. For only to the transfer of funds between {\em mutually distrustful}
transactions, the state can obtain information from the mint (or the entities. Two entities are assumed to be mutually distrustful if they
bank) that identifies the entity that received the digital coins as are unwilling to share control over coins. If a private key is shared
well as the exact value of those coins. Taler also allows the mint between two entities, then both entities have equal access to the
(and thus the state) to learn the value of digital coins withdrawn by credentials represented by the private key. In a payment system this
a customer --- but not how, where or when they were spent. Finally, means that either entity could spent the associated funds. Assuming
to enable audits, the current balance and profits of the mint are also the payment system has effective double-spending detection, this means
easily determined. that either entity has to constantly fear that the funds might no
longer be available to it. Thus, sharing coins by copying a private
key implies mutual trust between the two parties, in which case Taler
will treat them as the same entity. In Taler, making funds available
by copying a private key and thus sharing control is {\bf not}
considered a {\em transaction} and thus {\bf not} recorded for
taxation.
Taler ensures taxability only when some entity acquires exclusive
control over the value of digital coins, which requires an interaction
with the mint. For such transactions, the state can obtain
information from the mint (or the bank) that identifies the entity
that received the digital coins as well as the exact value of those
coins. Taler also allows the mint (and thus the state) to learn the
value of digital coins withdrawn by a customer --- but not how, where
or when they were spent.
\subsection{Anonymity} \subsection{Anonymity}
An anonymous communication channel (e.g. via Tor~\cite{tor-design}) is An anonymous communication channel (e.g. via Tor~\cite{tor-design}) is
used for all communication between the customer and the merchant. used for all communication between the customer and the merchant.
Thus, the customer can remain anonymous; however, the system does reveal Thus, the customer can remain anonymous limited only by the anonymous
that the customer is one of the patrons of the mint. Naturally, the communication channel; however, the payment system does additionally
customer-merchant operation might leak other information about the reveal that the customer is one of the patrons of the mint.
customer, such as a shipping address. Such purchase-specific Naturally, the customer-merchant business operation might leak other
information leakage is outside of the scope of this work. information about the customer, such as a shipping address.
Information leakage from shipping is in theory avoidable~\cite{apod}.
Nevertheless, for Taler as a payment system, information leakage
specific to the business logic is outside of the scope of the design.
The customer may use an anonymous communication channel for the The customer may use an anonymous communication channel for the
communication with the mint to avoid leaking IP address information; communication with the mint to avoid leaking IP address information;
however, the mint will anyway be able to determine the customer's however, the mint will anyway be able to determine the customer's
identity from the wire transfer or some other authentication process identity from the wire transfer or some other authentication process
that the customer initiates to withdraw anonymous digital cash. The that the customer initiates to withdraw anonymous digital cash. In
scheme is anonymous because the mint will be unable to link the known fact, this is desirable as there might be rules and regulations
identity of the customer that withdrew anonymous digital currency to designed to limit the amount of anonymous digital cash that an
the {\em purchase} performed later at the merchant. individual customer can withdraw in a given time period, similar to
% All the mint will be how states today sometimes impose limits on cash
%able to confirm is that the customer is {\em one} of its patrons who withdrawals~\cite{france2015cash,greece2015cash}. Taler is only
%previously obtained the anonymous digital currency --- and of course anonymous with respect to {\em payments}, as the mint will be unable
%that the coin was not spent before. to link the known identity of the customer that withdrew anonymous
digital currency to the {\em purchase} performed later at the
merchant. In this respect, Taler provides exactly the same scheme for
unconditional anonymous payments as was proposed by
Chaum~\cite{chaum1983blind,chaum1990untraceable} over 30 years ago.
While the customer thus has anonymity for his purchase, the mint will While the customer thus has anonymity for his purchase, the mint will
always learn the merchant's identity (which is necessary for always learn the merchant's identity in order to credit the merchant's
taxation), and thus the merchant has no reason to anonymize his account. This is also necessary for taxation, as Taler is supposed
to make information about funds received by any entity transparent
to the state. The merchant has thus no reason to anonymize his
communication with the mint. communication with the mint.
% Technically, the merchant could still % Technically, the merchant could still
%use an anonymous communication channel to communicate with the mint. %use an anonymous communication channel to communicate with the mint.
@ -934,7 +982,9 @@ We have presented an efficient electronic payment system that
simultaneously addresses the conflicting objectives created by the simultaneously addresses the conflicting objectives created by the
citizen's need for privacy and the state's need for taxation. The citizen's need for privacy and the state's need for taxation. The
coin refreshing protocol makes the design flexible and enables a coin refreshing protocol makes the design flexible and enables a
variety of payment methods. The libre implementation and open variety of payment methods. The current balance and profits of the
mint are also easily determined, thus audits can be used to ensure
that the mint operates correctly. The libre implementation and open
protocol may finally enable modern society to upgrade to proper protocol may finally enable modern society to upgrade to proper
electronic wallets with efficient, secure and privacy-preserving electronic wallets with efficient, secure and privacy-preserving
transactions. transactions.