1422 lines
71 KiB
TeX
1422 lines
71 KiB
TeX
% RMS wrote:
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%The text does not mention GNU anywhere. This paper is an opportunity
|
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%to make people aware of GNU, but the current text fails to use the
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%opportunity.
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%
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%It should say that Taler is a GNU package.
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%
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%I suggest using the term "GNU Taler" in the title, once in the
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%abstract, and the first time the name is mentioned in the body text.
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%In the body text, it can have a footnote with more information
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||
%including a reference to http://gnu.org/gnu/the-gnu-project.html.
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%
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%At the top of page 3, where it says "a free software implementation",
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||
%it should add "(free as in freedom)", with a reference to
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%http://gnu.org/philosophy/free-sw.html and
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%http://gnu.org/philosophy/free-software-even-more-important.html.
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%
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%Would you please include these things in every article or posting?
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%
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% CG adds:
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% We SHOULD do this for the FINAL paper, not for the anon submission.
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\documentclass{llncs}
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%\usepackage[margin=1in,a4paper]{geometry}
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\usepackage[T1]{fontenc}
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\usepackage{palatino}
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\usepackage{xspace}
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\usepackage{microtype}
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\usepackage{tikz,eurosym}
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\usepackage{amsmath,amssymb}
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\usepackage{enumitem}
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\usetikzlibrary{shapes,arrows}
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\usetikzlibrary{positioning}
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\usetikzlibrary{calc}
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% Relate to:
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% http://fc14.ifca.ai/papers/fc14_submission_124.pdf
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% Terminology:
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% - SEPA-transfer -- avoid 'SEPA transaction' as we use
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% 'transaction' already when we talk about taxable
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% transfers of Taler coins and database 'transactions'.
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% - wallet = coins at customer
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% - reserve = currency entrusted to exchange waiting for withdrawal
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% - deposit = SEPA to exchange
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% - withdrawal = exchange to customer
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% - spending = customer to merchant
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% - redeeming = merchant to exchange (and then exchange SEPA to merchant)
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% - refreshing = customer-exchange-customer
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% - dirty coin = coin with exposed public key
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% - fresh coin = coin that was refreshed or is new
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% - denomination key = exchange's online key used to (blindly) sign coin
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% - message signing key = exchange's online key to sign exchange messages
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% - exchange master key = exchange's key used to sign other exchange keys
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% - owner = entity that knows coin private key
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% - transaction = coin ownership transfer that should be taxed
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% - sharing = coin copying that should not be taxed
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\title{Taler: Taxable Anonymous Libre Electronic Reserves}
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\begin{document}
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\mainmatter
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%\author{Florian Dold \and Sree Harsha Totakura \and Benedikt M\"uller \and Christian Grothoff}
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%\institute{The GNUnet Project}
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\maketitle
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\begin{abstract}
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This paper introduces Taler, a Chaum-style digital currency that
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enables anonymous payments while ensuring that entities that receive
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payments are auditable and thus taxable. In Taler, customers can
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never defraud anyone, merchants can only fail to deliver the
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merchandise to the customer, and payment service providers can be
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fully audited. All parties receive cryptographic evidence for all
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transactions; still, each party only receives the minimum information
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required to execute transactions. Enforcement of honest behavior is
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timely, and is at least as strict as with legacy credit card payment
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systems that do not provide for privacy. Taler allows fractional
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payments while maintaining unlinkability of transactions. We argue
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that Taler provides a secure digital currency for modern liberal
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societies as it is a flexible, libre and efficient protocol and
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adequately balances the state's need for monetary control with the
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citizen's needs for private economic activity.
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\end{abstract}
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\section{Introduction}
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The design of payment systems shapes economies and societies.
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Strong, developed nation states are evolving towards transparent
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payment systems, such as the MasterCard and VisaCard credit card
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schemes and computerized bank transactions such as SWIFT.
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These systems enable mass surveillance by both governments and
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private companies, chilling customer activity~\cite{???}.
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Aspects of this government control benifit the economy, by enabling
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taxation. Also, bribery and corruption are limited to elites who
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can afford to escape the dragnet.
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At the other extreme, weaker developing nation states have economic
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activity based largely on coins, paper money or even barter.
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Here, the state is often unable to effectively monitor or tax economic
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activity, and this limits the ability of the state to shape the society.
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As bribery is virtually impossible to detect, corruption is widespread
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and not limited to social elites.
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%
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ZeroCoin~\cite{miers2013zerocoin} is an example for translating an
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anarchistic economy into the digital realm.
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% FIXME: Unclear referee comment :
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% I didn’t understand why ZeroCoin is particularly suited for
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% developing nations?
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% => clarified: suited to model anarchistic economy.
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This paper describes Taler, a simple and practical payment system for
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a modern social-liberal society, which is not being served well by
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current payment systems which enable either an authoritarian state in
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total control of the population, or create weak states with almost
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anarchistic economies.
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The Taler protocol is influenced by ideas from
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Chaum~\cite{chaum1983blind} and also follows Chaum's basic architecture of
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customer, merchant and exchange (Figure~\ref{fig:cmm}).
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The two designs share the key first step where the {\em customer}
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withdraws digital {\em coins} from the {\em exchange} with unlinkability
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provided via blind signatures. The coins can then be spent at a
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{\em merchant} who {\em deposits} them at the exchange.
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Taler uses online detection of double-spending, thus assuring the merchant
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instantly that a transaction is valid.
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\begin{figure}[h]
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\centering
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\begin{tikzpicture}
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\tikzstyle{def} = [node distance= 5em and 7em, inner sep=1em, outer sep=.3em];
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\node (origin) at (0,0) {};
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\node (exchange) [def,above=of origin,draw]{Exchange};
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\node (customer) [def, draw, below left=of origin] {Customer};
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\node (merchant) [def, draw, below right=of origin] {Merchant};
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\node (auditor) [def, draw, above right=of origin]{Auditor};
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\tikzstyle{C} = [color=black, line width=1pt]
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\draw [<-, C] (customer) -- (exchange) node [midway, above, sloped] (TextNode) {withdraw coins};
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\draw [<-, C] (exchange) -- (merchant) node [midway, above, sloped] (TextNode) {deposit coins};
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\draw [<-, C] (merchant) -- (customer) node [midway, above, sloped] (TextNode) {spend coins};
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\draw [<-, C] (exchange) -- (auditor) node [midway, above, sloped] (TextNode) {verify};
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\end{tikzpicture}
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\caption{Taler's system model for the payment system is based on Chaum~\cite{chaum1983blind}.}
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\label{fig:cmm}
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\end{figure}
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A key issue for an efficient Chaumian digital payment system is the
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need to provide change. For example, a customer may want to pay
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\EUR{49,99}, but has withdrawn a \EUR{100,00} coin. Withdrawng 10,000
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pieces with a denomination of \EUR{0,01} and transferring 4,999 would
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be too inefficient, even for modern systems. The customer should not
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withdraw exact change from her account, as doing so reduces anonymity
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due to the obvious corrolation. A practical payment system must thus
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support giving change in the form of spendable coins, say a \EUR{0,01}
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coin and a \EUR{50,00} coin.
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Taler solves the problem of giving change by introducing a new {\em
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refresh} protocol. Using this protocol, a customer can obtain
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change in the form of fresh coins that other parties cannot link to
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the original transaction, the original coin, or each other.
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Additionally, the refresh protocol ensures that the change is owned by
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the same entity which owned the original coin.
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\section{Related Work}
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\subsection{Blockchain-based currencies}
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In recent years, a class of decentralized electronic payment systems,
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based on collectively recorded and verified append-only public
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ledgers, have gained immense popularity. The most well-known protocol
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in this class is Bitcoin~\cite{nakamoto2008bitcoin}. An initial
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concern with Bitcoin was the lack of anonymity, as all Bitcoin
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transactions are recorded for eternity, which can enable
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identification of users. In theory, this concern has been addressed
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with the Zerocoin extension to the protocol~\cite{miers2013zerocoin}.
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These protocols dispense with the need for a central, trusted
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authority, while providing a useful measure of pseudonymity.
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Yet, there are several major irredeemable problems inherent in their designs:
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\begin{itemize}
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\item The computational puzzles solved by Bitcoin nodes with the purpose
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of securing the block chain consume a considerable amount of energy.
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So Bitcoin is an environmentally irresponsible design.
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\item Bitcoin transactions have pseduononymous recipients, making taxation
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hard to systematically enforce.
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The Zerocoin extension makes this worse.
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% FIXME: need refs for following claim:
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\item Bitcoin seemingly requires speculation to offset the mining cost,
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creating fluctuations in value, and making it hard to bind to national
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currencies. These fluctuations may be desirable in a high-risk investment
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instrument, but they make Bitcoin unsuitable as a medium of exchange.
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\item Anyone can start an alternative Bitcoin transaction chain,
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called an AltCoin, and, if successful, reap the benefits of the low
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cost to initially create coins cheaply as the proof-of-work
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difficulty adjusts to the computation power of all
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miners in the network. As participants are
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de facto investors, AltCoins become a form of ponzi scheme.
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% As a result, dozens of
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% AltCoins have been created, often without any significant changes to the
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% technology. A large number of AltCoins creates additional overheads for
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% currency exchange and exacerbates the problems with currency fluctuations.
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\end{itemize}
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GreenCoinX\footnote{\url{https://www.greencoinx.com/}} is a more
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recent AltCoin where the company promises to identify the owner of
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each coin via e-mail addresses and phone numbers. While it is unclear
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from their technical description how this identification would be
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enforced against a determined adversary, the resulting payment system
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would also merely impose a totalitarian financial panopticon on a
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BitCoin-style money supply and transaction model, thus largely
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combining what we would consider to be the drawbacks of existing
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credit card systems.
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\subsection{Chaum-style electronic cash}
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Chaum~\cite{chaum1983blind} proposed a digital payment system that
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would provide some customer anonymity while disclosing the identity of
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the merchants. DigiCash, a commercial implementation of Chaum's
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proposal, had some limitations and ultimately failed to be widely
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adopted. In our assessment, key reasons for DigiCash's failure
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include:
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\begin{itemize}
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\item The use of patents to protect the technology; a payment system
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should be free software (libre) to have a chance for widespread adoption.
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\item Support for payments to off-line merchants, and thus deferred
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detection of double-spending, requires the exchange to attempt to
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recover funds from delinquent customers via the legal system.
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Any system that fails to be self-enforcing creates a major
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business risk for the exchange and merchants.
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In 1983, there were merchants without network connectivity, making that
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feature relevant, but today network connectivity is feasible for most
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merchants, and saves both the exchange and merchants the business risks
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associated with deferred fraud detection.
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\item % In addition to the risk of legal disputes with fraudulent
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% merchants and customers,
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Chaum's published design does not clearly
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limit the financial damage a exchange might suffer from the
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disclosure of its private online signing key.
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\item Chaum did not support fractional payments or refunds without
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weakening customer anonymity.
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%, and Brand's
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% extensions for fractional payments broke unlinkability and thus
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% limited anonymity.
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% \item Chaum's system was implemented at a time where the US market
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% was still dominated by paper checks and the European market was
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% fragmented into dozens of currencies. Today, SEPA provides a
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% unified currency and currency transfer method for most of Europe,
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% significantly lowering the barrier to entry into this domain for
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% a larger market.
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\end{itemize}
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Chaum's original digital cash system~\cite{chaum1983blind} was
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extended by Brands~\cite{brands1993efficient} with the ability to {\em
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divide} coins and thus spend certain fractions of a coin using
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restrictive blind signatures. Restrictive blind signatures create
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privacy risks: if a transaction is interrupted, then any coins sent to
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the merchant become tainted, but may never arrive or be spent. It
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becomes tricky to extract the value of the tainted coins without
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linking to the aborted transaction and risking deanonymization.
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Ian Goldberg's HINDE system allowed the merchant to provide change,
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but the mechanism could be abused to hide income from
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taxation.\footnote{Description based on personal communication. HINDE
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was never published.} $k$-show
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signatures~\cite{brands1993efficient} were proposed to achieve
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divisibility for coins. However, with $k$-show signatures multiple
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transactions can be linked to each other. Performing fractional
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payments using $k$-show signatures is also rather expensive.
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%
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%Some argue that the focus on technically perfect but overwhelmingly
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%complex protocols, as well as the the lack of usable, practical
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%solutions lead to an abandonment of these ideas by
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%practitioners~\cite{selby2004analyzing}.
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%
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% FIXME: ask OpenCoin dev's about this! Then make statement firmer!
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To our knowledge, the only publicly available effort to implement
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Chaum's idea is Opencoin~\cite{dent2008extensions}. However, Opencoin
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is neither actively developed nor used, and it is not clear
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to what degree the implementation is even complete. Only a partial
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description of the Opencoin protocol is available to date.
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\subsection{Peppercoin}
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Peppercoin~\cite{rivest2004peppercoin} is a microdonation protocol.
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The main idea of the protocol is to reduce transaction costs by
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minimizing the number of transactions that are processed directly by
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the exchange. Instead of always paying, the customer ``gambles'' with the
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merchant for each microdonation. Only if the merchant wins, the
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microdonation is upgraded to a macropayment to be deposited at the
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exchange. Peppercoin does not provide customer-anonymity. The proposed
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statistical method by which exchanges detect fraudulent cooperation between
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customers and merchants at the expense of the exchange not only creates
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legal risks for the exchange, but would also require that the exchange learns
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about microdonations where the merchant did not get upgraded to a
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macropayment. It is therefore unclear how Peppercoin would actually
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reduce the computational burden on the exchange.
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\section{Design}
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The Taler system comprises three principal types of actors
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(Figure~\ref{fig:cmm}): The \emph{customer} is interested in receiving
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goods or services from the \emph{merchant} in exchange for payment.
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When making a transaction, both the customer and the merchant use the
|
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same \emph{exchange}, which serves as a payment service provider for
|
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the financial transaction between the two. The exchange is
|
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responsible for allowing the customer to convert financial reserves to
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the anonymous digital coins, and for enabling the merchant to convert
|
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spent digital coins back to funds in a financial reserve. In
|
||
addition, we describe an \emph{auditor} who assures customers and
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merchants that the exchange operates correctly.
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\subsection{Security model}
|
||
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Taler's security model assumes that cryptographic primitives are
|
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secure and that each participant is under full control of his system.
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The contact information of the exchange is known to both customer and
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merchant from the start. We further assume that the customer can
|
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authenticate the merchant, e.g. using X.509
|
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certificates~\cite{rfc5280}. Finally, we assume that customer has an
|
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anonymous bi-directional channel, such as Tor, to communicate with
|
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both the exchange and the merchant.
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The exchange is trusted to hold funds of its customers and to forward
|
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them when receiving the respective deposit instructions from the
|
||
merchants. Customer and merchant can have assurances about the
|
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exchange's liquidity and operation though published audits by
|
||
financial regulators or other trusted third parties. If sufficently
|
||
regular, audits of the exchange's accounts should reveal any possible
|
||
fraud. Online signing keys expire regularly, allowing the exchange to
|
||
destroy the corresponding accumulated cryptographic proofs.
|
||
|
||
The merchant is trusted to deliver the service or goods to the
|
||
customer upon receiving payment. The customer can seek legal relief
|
||
to achieve this, as he receives cryptographic proofs of the contract
|
||
and has proof that he paid his obligations.
|
||
|
||
Neither the merchant nor the customer have any ability to {\em effectively}
|
||
defraud the exchange or the state collecting taxes. Here, ``effectively''
|
||
means that the expected return for fraud is negative.
|
||
%
|
||
Note that customers do not need to be trusted in any way, and that in
|
||
particular it is never necessary for anyone to try to recover funds
|
||
from customers using legal coersion.
|
||
|
||
\subsection{Taxability and Entities}
|
||
|
||
Taler ensures that the state can tax {\em transactions}. We must,
|
||
howerver, clarify what constitutes a transaction that can be taxed.
|
||
For ethical and practical reasons, we assume that coins can freely be
|
||
copied between machines, and that coin deletion cannot be verified.
|
||
Avoiding these assumptions would require extreme measures, like custom
|
||
hardware supplied by the exchange. Also, it would be inappropriate to
|
||
tax the moving of funds between two computers owned by the same
|
||
entity. Finally, we assume that at the time digital coins are
|
||
withdrawn, the wallet receiving the coins is owned by the individual
|
||
who is performing the authentication to authorize the withdrawal.
|
||
Preventing the owner of the reserve from deliberately authorizing
|
||
someone else to withdraw electronic coins would require extreme
|
||
measures, including preventing them from communicating with anyone but
|
||
the exchange terminal during withdrawal. As such measures would be
|
||
totally impractical for a minor loophole, we are not concerned with
|
||
enabling the state to strongly identify the recipient of coins
|
||
from a withdrawal operation.
|
||
|
||
We view ownership of a coin's private key as a ``capability'' to spend
|
||
the funds. A taxable transaction occurs when a merchant entity gains
|
||
control over the funds while at the same time a customer entity looses
|
||
control over the funds in a manner verifiable to the merchant. In
|
||
other words, we restrict the definition of taxable transactions to
|
||
those transfers of funds where the recipient merchant is distrustful
|
||
of the spending customer, and requires verification that the customer
|
||
lost the capability to spend the funds.
|
||
|
||
Conversely, if a coin's 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 spend 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.
|
||
It follows that sharing coins by copying a private key implies mutual
|
||
trust between the two parties, in which case we treat them as the same
|
||
entity for taxability.
|
||
|
||
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 does, however, ensure
|
||
taxability when a merchant entity acquires exclusive control over the
|
||
value represented by a digital coins. For such transactions, the state
|
||
can obtain information from the exchange, or a bank, that identifies
|
||
the entity that received the digital coins as well as the exact value
|
||
of those coins. Taler also allows the exchange, and hence the state,
|
||
to learn the value of digital coins withdrawn by a customer---but not
|
||
how, where, or when they were spent.
|
||
|
||
\subsection{Anonymity}
|
||
|
||
We assume that an anonymous communication channel
|
||
such as Tor~\cite{tor-design} is
|
||
used for all communication between the customer and the merchant,
|
||
as well as for refreshing tainted coins with the exchange and for
|
||
retrieving the exchange's denomination key.
|
||
Ideally, the customer's anonymity is limited only by this channel;
|
||
however, the payment system does additionally reveal that the customer
|
||
is one of the patrons of the exchange.
|
||
There are naturally risks that the customer-merchant business operation
|
||
may leak identifying information about the customer.
|
||
We consider information leakage specific to the business logic to be
|
||
outside of the scope of the design of Taler.
|
||
|
||
Aside from refreshing and obtaining denomination key, the customer
|
||
should ideally use an anonymous communication channel with the exchange
|
||
to obscure their IP address for location privacy, but naturally
|
||
the exchange would typically learn the customer's identity from the wire
|
||
transfer that funds the customer's withdrawal of anonymous digital coins.
|
||
We believe this may even be desirable as there are laws, or bank policies,
|
||
that limit the amount of cash that an individual customer can withdraw
|
||
in a given time period~\cite{france2015cash,greece2015cash}.
|
||
Taler is thus only anonymous with respect to {\em payments}.
|
||
In particular, the exchange
|
||
is unable to link the known identity of the customer that withdrew
|
||
anonymous digital coins to the {\em purchase} performed later at the
|
||
merchant.
|
||
|
||
While the customer thus has anonymity for purchases, the exchange will
|
||
always learn the merchant's identity in order to credit the merchant's
|
||
account. This is also necessary for taxation, as Taler deliberately
|
||
exposes these events as anchors for tax audits on income.
|
||
|
||
% Technically, the merchant could still
|
||
%use an anonymous communication channel to communicate with the exchange.
|
||
%However, in order to receive the traditional currency the exchange will
|
||
%require (SEPA) account details for the deposit.
|
||
|
||
%As both the initial transaction between the customer and the exchange as
|
||
%well as the transactions between the merchant and the exchange do not have
|
||
%to be done anonymously, there might be a formal business contract
|
||
%between the customer and the exchange and the merchant and the exchange. Such
|
||
%a contract may provide customers and merchants some assurance that
|
||
%they will actually receive the traditional currency from the exchange
|
||
%given cryptographic proof about the validity of the transaction(s).
|
||
%However, given the business overheads for establishing such contracts
|
||
%and the natural goal for the exchange to establish a reputation and to
|
||
%minimize cost, it is more likely that the exchange will advertise its
|
||
%external auditors and proven reserves and thereby try to convince
|
||
%customers and merchants to trust it without a formal contract.
|
||
|
||
|
||
\subsection{Coins}
|
||
|
||
A \emph{coin} in Taler is a public-private key pair where the private
|
||
key is only known to the owner of the coin. A coin derives its
|
||
financial value from an RSA signature over a the full domain hash
|
||
(FDH) of the coin's public key. An FDH is used so that ``one-more
|
||
forgery'' is provably hard assuming the RSA known-target inversion
|
||
problem is hard~cite[Theorem 12]{RSA-HDF-KTIvCTI}. The exchange has
|
||
multiple RSA {\em denomination key} pairs available for blind-signing
|
||
coins of different value.
|
||
|
||
Denomination keys have an expiration date, before which any coins
|
||
signed with it must be spent or refreshed. This allows the exchange
|
||
to eventually discard records of old transactions, thus limiting the
|
||
records that the exchange must retain and search to detect
|
||
double-spending attempts. Furthermore, the exchange uses each
|
||
denomination key only for a limited number of coins. In this way, if
|
||
a private denomination key were to be compromised, the exchange would
|
||
detect this once more coins were redeemed than the total that was
|
||
signed into existence using that denomination key. In this case, the
|
||
exchange can allow authentic customers to exchange their unspent
|
||
coins that were signed with the compromised private key, while
|
||
refusing further anonymous transactions involving those coins. As a
|
||
result, the financial damage of losing a private signing key can be
|
||
limited to at most twice the amount originally signed with that key.
|
||
|
||
We also ensure that the exchange cannot deanonymize users by signing
|
||
each coin with a fresh denomination key. For this, exchanges are
|
||
required to publicly announce their denomination keys in advance.
|
||
These announcements are expected to be signed with an off-line
|
||
long-term private {\em master signing key} of the exchange and the
|
||
auditor. Additionally, customers should obtain these announcements
|
||
using an anonymous communication channel.
|
||
|
||
Before a customer can withdraw a coin from the exchange, he has to pay
|
||
the exchange the value of the coin, as well as processing fees. This
|
||
is done using other means of payment, such as wire transfers or by
|
||
having a financial {\em reserve} at the exchange. Taler assumes that
|
||
the customer has a {\em withdrawal authorization key} to identify
|
||
himself as authorized to withdraw funds from the reserve. By signing
|
||
the withdrawal request using this withdrawal authorization key, the
|
||
customer can prove to the exchange that he is authorized to withdraw
|
||
anonymous digital coins from his reserve. The exchange records the
|
||
withdrawal message as proof that the reserve was debited correctly.
|
||
|
||
%To put it differently, unlike
|
||
%modern cryptocurrencies like BitCoin, Taler's design simply
|
||
%acknowledges that primitive accumulation~\cite{engels1844} predates
|
||
%the system and that a secure method to authenticate owners exists.
|
||
|
||
After a coin is issued, the customer is the only entity that knows the
|
||
private key of the coin, making him the \emph{owner} of the coin. Due
|
||
to the use of blind signatures, the exchange does not even learn the
|
||
public key during the withdrawal process. If the private key is
|
||
shared with others, they become co-owners of the coin. Knowledge of
|
||
the private key of the coin enables the owner to spent the coin.
|
||
|
||
|
||
\subsection{Coin spending}
|
||
|
||
A customer spends a coin at a merchant by cryptographically signing a
|
||
{\em deposit authorization} with the coin's private key. A deposit
|
||
authorization specifies the fraction of the coin's value to be paid to
|
||
the merchant, the salted hash of a merchant's financial reserve
|
||
routing information and a {\em business transaction-specific hash}.
|
||
Taler exchanges ensure that all transactions involving the same coin
|
||
do not exceed the total value of the coin simply by requiring that
|
||
merchants clear transactions immediately with the exchange.
|
||
|
||
If the customer is cheating and the coin was already spent, the
|
||
exchange provides the previous deposit authorization as cryptographic
|
||
proof of the fraud to the merchant. If the deposit authorization is
|
||
correct, the exchange transfers the funds to the merchant by crediting
|
||
the merchant's financial reserve, e.g. using a wire transfer.
|
||
|
||
|
||
\subsection{Refreshing Coins}
|
||
|
||
If only a fraction of a coin's value has been spent, or if a
|
||
transaction fails for other reasons, it is possible that a customer
|
||
has revealed the public key of a coin to a merchant, but not
|
||
ultimately spent the full value of the coin. If the customer then
|
||
continues to directly use the coin in other transactions, merchants
|
||
and the exchange could link the various transactions as they all share
|
||
the same public key for the coin. We call a coin {\em dirty} if its
|
||
public key is known to anyone but the owner.
|
||
|
||
To avoid linkability of transactions, Taler allows the owner of a
|
||
dirty coin to exchange it for a {\em fresh} coin using the {\em coin
|
||
refreshing protocol}. Even if a coin is not dirty, the owner of a
|
||
coin may want to exchange it if the respective denomination key is
|
||
about to expire. The {\em coin refreshing protocol}, allows the owner
|
||
of a coin to {\em melt} it for fresh coins of the same total value with a
|
||
new public-private key pairs. Refreshing does not use the ordinary
|
||
spending operation as the owner of a coin should not have to pay
|
||
(income) taxes for refreshing. However, to ensure that refreshing is
|
||
not used for money laundering or tax evasion, the refreshing protocol
|
||
assures that the owner stays the same.
|
||
|
||
The refresh protocol has two key properties: First, the exchange is
|
||
unable to link the fresh coin's public key to the public key of the
|
||
dirty coin. Second, it is assured that the owner of the dirty coin
|
||
can determine the private key of the fresh coin, thereby preventing
|
||
the refresh protocol from being used to transfer ownership.
|
||
|
||
|
||
\section{Taler's Cryptographic Protocols}
|
||
|
||
% In this section, we describe the protocols for Taler in detail.
|
||
|
||
For the sake of brevity we omit explicitly saying each time that a
|
||
recipient of a signed message always first checks that the signature
|
||
is valid. Furthermore, the receiver of a signed message is either
|
||
told the respective public key, or knows it from the context. Also,
|
||
all signatures contain additional identification as to the purpose of
|
||
the signature, making it impossible to use a signature in a different
|
||
context.
|
||
|
||
An exchange has a long-term offline key which is used to certify
|
||
denomination keys and {\em online message signing keys} of the
|
||
exchange. {\em Online message signing keys} are used for signing
|
||
protocol messages; denomination keys are used for blind-signing coins.
|
||
The exchange's long-term offline key is assumed to be known to both
|
||
customers and merchants and is certified by the auditors.
|
||
|
||
As we are dealing with financial transactions, we explicitly describe
|
||
whenever entities need to safely commit data to persistent storage.
|
||
As long as those commitments persist, the protocol can be safely
|
||
resumed at any step. Commitments to disk are cumulative, that is an
|
||
additional commitment does not erase the previously committed
|
||
information. Keys and thus coins always have a well-known expiration
|
||
date; information committed to disk can be discarded after the
|
||
expiration date of the respective public key.
|
||
Customers may discard information once the respective coins have been
|
||
fully spent, so long as refunds are not required.
|
||
Merchants may discard information once payments from the exchange have
|
||
been received, assuming the records are also no longer needed for tax
|
||
purposes. The exchange's bank transfers dealing in traditional currency
|
||
are expected to be recorded for tax authorities to ensure taxability.
|
||
|
||
\subsection{Withdrawal}
|
||
|
||
Let $G$ be the generator of an elliptic curve. To withdraw anonymous
|
||
digital coins, the customer first identifies a exchange with a
|
||
denomination public-private key pair $K := (K_s, K_p)$ corresponding
|
||
to a denomination the customer would like to withdraw, and then
|
||
performs the following interaction with the exchange:
|
||
|
||
% FIXME: We say withdrawal key in this document, but say reserve key in
|
||
% others, so probably withdrawal key should be renamed to reserve key.
|
||
|
||
% FIXME: These steps occur at very different points in time, so probably
|
||
% they should be restructured into more of a protocol discription.
|
||
% It does create some confusion, like is a withdrawal key semi-ephemeral
|
||
% like a linking key?
|
||
|
||
\begin{enumerate}
|
||
\item The customer randomly generates:
|
||
\begin{itemize}
|
||
\item withdrawal key $W := (w_s,W_p)$ with private key $w_s$ and public key $W_p$,
|
||
\item coin key $C := (c_s,C_p)$ with private key $c_s$ and public key $C_p := c_s G$,
|
||
\item blinding factor $b$, and commits $\langle W, C, b \rangle$ to disk.
|
||
\end{itemize}
|
||
\item The customer transfers an amount of money corresponding to at least $K_p$ to the exchange, with $W_p$ in the subject line of the transaction.
|
||
\item The exchange receives the transaction and credits the $W_p$ reserve with the respective amount in its database.
|
||
\item The customer sends $S_W(B_b(C_p))$ to the exchange to request withdrawal of $C$; here, $B_b$ denotes Chaum-style blinding with blinding factor $b$.
|
||
\item The exchange checks if the same withdrawal request was issued before; in this case, it sends $S_{K}(B_b(C_p))$ to the customer.\footnote{$S_K$
|
||
denotes a Chaum-style blind signature with private key $K_s$.}
|
||
If this is a fresh withdrawal request, the exchange performs the following transaction:
|
||
\begin{enumerate}
|
||
\item checks if the reserve $W_p$ has sufficient funds for a coin of value corresponding to $K$
|
||
\item stores the withdrawal request and response $\langle S_W(B_b(C_p)), S_K(B_b(C_p)) \rangle$ in its database for future reference,
|
||
\item deducts the amount corresponding to $K$ from the reserve,
|
||
\end{enumerate}
|
||
and then sends $S_{K}(B_b(C_p))$ to the customer.
|
||
If the guards for the transaction fail, the exchange sends a descriptive error back to the customer,
|
||
with proof that it operated correctly.
|
||
Assuming the signature was valid, this would involve showing the transaction history for the reserve.
|
||
\item The customer computes and verifies the unblinded signature $S_K(C_p) = U_b(S_K(B_b(C_p)))$.
|
||
The customer saves the coin $\langle S_K(C_p), c_s \rangle$ to local wallet on disk.
|
||
\end{enumerate}
|
||
|
||
|
||
\subsection{Exact and partial spending}
|
||
|
||
A customer can spend coins at a merchant, under the condition that the
|
||
merchant trusts the specific exchange that issued the coin. Merchants are
|
||
identified by their key $M := (m_s, M_p)$ where the public key $M_p$
|
||
must be known to the customer a priori.
|
||
|
||
We now describe the protocol between the customer, merchant, and exchange
|
||
for a transaction in which the customer spends a coin $C := (c_s, C_p)$
|
||
with signature $\widetilde{C} := S_K(C_p)$
|
||
where $K$ is the exchange's demonination key.
|
||
|
||
% FIXME: Again, these steps occur at different points in time, maybe
|
||
% that's okay, but refresh is slightly different.
|
||
|
||
\begin{enumerate}
|
||
\item\label{contract}
|
||
Let $\vec{D} := D_1, \ldots, D_n$ be the list of exchanges accepted by
|
||
the merchant where each $D_j$ is a exchange's public key.
|
||
The merchant creates a digitally signed contract
|
||
$\mathcal{A} := S_M(m, f, a, H(p, r), \vec{D})$
|
||
where $m$ is an identifier for this transaction, $a$ is data relevant
|
||
to the contract indicating which services or goods the merchant will
|
||
deliver to the customer, $f$ is the price of the offer, and
|
||
$p$ is the merchant's payment information (e.g. his IBAN number), and
|
||
$r$ is a random nonce. The merchant commits $\langle \mathcal{A} \rangle$
|
||
to disk and sends $\mathcal{A}$ to the customer.
|
||
\item\label{deposit}
|
||
The customer should already possess a coin issued by a exchange that is
|
||
accepted by the merchant, meaning $K$ should be publicly signed by
|
||
some $D_j \in \{D_1, D_2, \ldots, D_n\}$, and has a value $\geq f$.
|
||
\item The customer generates a \emph{deposit-permission} $\mathcal{D} :=
|
||
S_c(\widetilde{C}, m, f, H(a), H(p,r), M_p)$
|
||
and sends $\langle \mathcal{D}, D_j\rangle$ to the merchant,
|
||
where $D_j$ is the exchange which signed $K$.
|
||
\item The merchant gives $(\mathcal{D}, p, r)$ to the exchange, revealing $p$
|
||
only to the exchange.
|
||
\item The exchange validates $\mathcal{D}$ and checks for double spending.
|
||
If the coin has been involved in previous transactions and the new
|
||
one would exceed its remaining value, it sends an error
|
||
with the records from the previous transactions back to the merchant.
|
||
%
|
||
If double spending is not found, the exchange commits $\langle \mathcal{D} \rangle$ to disk
|
||
and notifies the merchant that the deposit operation was successful.
|
||
\item The merchant commits and forwards the notification from the exchange to the
|
||
customer, confirming the success or failure of the operation.
|
||
\end{enumerate}
|
||
|
||
We have simplified the exposition by assuming that one coin suffices,
|
||
but in practice a customer can use multiple coins from the same
|
||
exchange where the total value adds up to $f$ by running the above
|
||
steps for each of the coins.
|
||
|
||
If a transaction is aborted after Step~\ref{deposit},
|
||
subsequent transactions with the same coin could be linked to the coin,
|
||
but not directly to the coin's owner. The same applies to partially
|
||
spent coins where $f$ is smaller than the actual value of the coin.
|
||
To unlink subsequent transactions from a coin, the customer has to
|
||
execute the coin refreshing protocol with the exchange.
|
||
|
||
%\begin{figure}[h]
|
||
%\centering
|
||
%\begin{tikzpicture}
|
||
%
|
||
%\tikzstyle{def} = [node distance= 1em, inner sep=.5em, outer sep=.3em];
|
||
%\node (origin) at (0,0) {};
|
||
%\node (offer) [def,below=of origin]{make offer (merchant $\rightarrow$ customer)};
|
||
%\node (A) [def,below=of offer]{permit lock (customer $\rightarrow$ merchant)};
|
||
%\node (B) [def,below=of A]{apply lock (merchant $\rightarrow$ exchange)};
|
||
%\node (C) [def,below=of B]{confirm (or refuse) lock (exchange $\rightarrow$ merchant)};
|
||
%\node (D) [def,below=of C]{sign contract (merchant $\rightarrow$ customer)};
|
||
%\node (E) [def,below=of D]{permit deposit (customer $\rightarrow$ merchant)};
|
||
%\node (F) [def,below=of E]{make deposit (merchant $\rightarrow$ exchange)};
|
||
%\node (G) [def,below=of F]{transfer confirmation (exchange $\rightarrow$ merchant)};
|
||
%
|
||
%\tikzstyle{C} = [color=black, line width=1pt]
|
||
%\draw [->,C](offer) -- (A);
|
||
%\draw [->,C](A) -- (B);
|
||
%\draw [->,C](B) -- (C);
|
||
%\draw [->,C](C) -- (D);
|
||
%\draw [->,C](D) -- (E);
|
||
%\draw [->,C](E) -- (F);
|
||
%\draw [->,C](F) -- (G);
|
||
%
|
||
%\draw [->,C, bend right, shorten <=2mm] (E.east)
|
||
% to[out=-135,in=-45,distance=3.8cm] node[left] {aggregate} (D.east);
|
||
%\end{tikzpicture}
|
||
%\caption{Interactions between a customer, merchant and exchange in the coin spending
|
||
% protocol}
|
||
%\label{fig:spending_protocol_interactions}
|
||
%\end{figure}
|
||
|
||
|
||
\subsection{Refreshing} \label{sec:refreshing}
|
||
|
||
We now describe the refresh protocol whereby a dirty coin $C'$ of
|
||
denomination $K$ is melted to obtain a fresh coin $\widetilde{C}$
|
||
with the same denomination. In practice, Taler uses a natural
|
||
extension where multiple fresh coins are generated a the same time to
|
||
enable giving precise change matching any amount.
|
||
In the protocol, $\kappa \ge 3$ is a security parameter and $G$ is the
|
||
generator of the elliptic curve.
|
||
|
||
% FIXME: I'm explicit about the rounds in postquantum.tex
|
||
|
||
\begin{enumerate}
|
||
\item For each $i = 1,\ldots,\kappa$, the customer randomly generates
|
||
\begin{itemize}
|
||
\item transfer key $T^{(i)} := \left(t^{(i)}_s,T^{(i)}_p\right)$
|
||
where $T^{(i)}_p := t^{(i)}_s G$,
|
||
\item coin key pair $C^{(i)} := \left(c_s^{(i)}, C_p^{(i)}\right)$
|
||
where $C^{(i)}_p := c^{(i)}_s G$, and
|
||
\item blinding factors $b^{(i)}$.
|
||
\end{itemize}
|
||
The customer then computes
|
||
$E^{(i)} := E_{K_i}\left(c_s^{(i)}, b^{(i)}\right)$
|
||
where $K_i := H(c'_s T_p^{(i)})$, and
|
||
commits $\langle C', \vec{T}, \vec{C}, \vec{b} \rangle$ to disk.
|
||
|
||
Our computation of $K_i$ is effectively a Diffie-Hellman operation
|
||
between the private key $c'_s$ of the original coin with
|
||
the public transfer key $T_p^{(i)}$.
|
||
\item The customer computes $B^{(i)} := B_{b^{(i)}}(C^{(i)}_p)$ for $i \in \{1,\ldots,\kappa\}$ and sends a commitment
|
||
$S_{C'}(\vec{E}, \vec{B}, \vec{T_p})$ to the exchange.
|
||
\item The exchange generates a random $\gamma$ with $1 \le \gamma \le \kappa$ and
|
||
marks $C'_p$ as spent by committing
|
||
$\langle C', \gamma, S_{C'}(\vec{E}, \vec{B}, \vec{T_p}) \rangle$ to disk.
|
||
Auditing processes should assure that $\gamma$ is unpredictable until
|
||
this time to prevent the exchange from assisting tax evasion.
|
||
\item The exchange sends $S_{K'}(C'_p, \gamma)$ to the customer where
|
||
$K'$ is the exchange's message signing key.
|
||
\item The customer commits $\langle C', S_K(C'_p, \gamma) \rangle$ to disk.
|
||
\item The customer computes $\mathfrak{R} := \left(t_s^{(i)}\right)_{i \ne \gamma}$
|
||
and sends $S_{C'}(\mathfrak{R})$ to the exchange.
|
||
\item \label{step:refresh-ccheck} The exchange checks whether $\mathfrak{R}$ is consistent with the commitments;
|
||
specifically, it computes for $i \not= \gamma$:
|
||
|
||
\vspace{-2ex}
|
||
\begin{minipage}{5cm}
|
||
\begin{align*}
|
||
\overline{K}_i :&= H(t_s^{(i)} C_p'), \\
|
||
(\overline{c}_s^{(i)}, \overline{b_i}) :&= D_{\overline{K}_i}(E^{(i)}), \\
|
||
\overline{C^{(i)}_p} :&= \overline{c}_s^{(i)} G,
|
||
\end{align*}
|
||
\end{minipage}
|
||
\begin{minipage}{5cm}
|
||
\begin{align*}
|
||
\overline{T_p^{(i)}} :&= t_s^{(i)} G, \\ \\
|
||
\overline{B^{(i)}} :&= B_{\overline{b_i}}(\overline{C_p^{(i)}}),
|
||
\end{align*}
|
||
\end{minipage}
|
||
|
||
and checks if $\overline{B^{(i)}} = B^{(i)}$
|
||
and $\overline{T^{(i)}_p} = T^{(i)}_p$.
|
||
|
||
|
||
\item \label{step:refresh-done} If the commitments were consistent,
|
||
the exchange sends the blind signature $\widetilde{C} :=
|
||
S_{K}(B^{(\gamma)})$ to the customer. Otherwise, the exchange responds
|
||
with an error indicating the location of the failure.
|
||
\end{enumerate}
|
||
|
||
%\subsection{N-to-M Refreshing}
|
||
%
|
||
%TODO: Explain, especially subtleties regarding session key / the spoofing attack that requires signature.
|
||
|
||
\subsection{Linking}
|
||
|
||
% FIXME: What is \mathtt{link} ?
|
||
|
||
For a coin that was successfully refreshed, the exchange responds to a
|
||
request $S_{C'}(\mathtt{link})$ with $(T^{(\gamma)}_p$, $E^{(\gamma)},
|
||
\widetilde{C})$.
|
||
%
|
||
This allows the owner of the melted coin to also obtain the private
|
||
key of the new coin, even if the refreshing protocol was illicitly
|
||
executed with the help of another party who generated $\vec{c_s}$ and only
|
||
provided $\vec{C_p}$ and other required information to the old owner.
|
||
As a result, linking ensures that access to the new coins issued in
|
||
the refresh protocol is always {\em shared} with the owner of the
|
||
melted coins. This makes it impossible to abuse the refresh protocol
|
||
for {\em transactions}.
|
||
|
||
The linking request is not expected to be used at all during ordinary
|
||
operation of Taler. If the refresh protocol is used by Alice to
|
||
obtain change as designed, she already knows all of the information
|
||
and thus has little reason to request it via the linking protocol.
|
||
The fundamental reason why the exchange must provide the link protocol is
|
||
simply to provide a threat: if Bob were to use the refresh protocol
|
||
for a transaction of funds from Alice to him, Alice may use a link
|
||
request to gain shared access to Bob's coins. Thus, this threat
|
||
prevents Alice and Bob from abusing the refresh protocol to evade
|
||
taxation on transactions. If Bob trusts Alice to not execute the link
|
||
protocol, then they can already conspire to evade taxation by simply
|
||
exchanging the original private coin keys. This is permitted in our
|
||
taxation model as with such trust they are assumed to be the same
|
||
entity.
|
||
|
||
The auditor can anonymously check if the exchange correctly implements the
|
||
link request, thus preventing the exchange operator from legally disabling
|
||
this protocol component. Without the link operation, Taler would
|
||
devolve into a payment system where both sides can be anonymous, and
|
||
thus no longer provide taxability.
|
||
|
||
|
||
\subsection{Error handling}
|
||
|
||
During operation, there are three main types of errors that are
|
||
expected. First, in the case of faulty clients, the responding server
|
||
will generate an error message with detailed cryptographic proofs
|
||
demonstrating that the client was faulty, for example by providing
|
||
proof of double-spending or providing the previous commit and the
|
||
location of the missmatch in the case of the reveal step in the
|
||
refresh protocol. It is also possible that the server may claim that
|
||
the client has been violating the protocol. In these cases, the
|
||
clients should verify any proofs provided and if they are acceptable,
|
||
notify the user that they are somehow faulty. Similar, if the
|
||
server indicates that the client is violating the protocol, the
|
||
client should record the interaction and enable the user to file a
|
||
bug report.
|
||
|
||
The second case is a faulty exchange service provider. Here, faults
|
||
will be detected when the exchange provides a faulty proof or no
|
||
proof. In this case, the client is expected to notify the auditor,
|
||
providing a transcript of the interaction. The auditor can then
|
||
anonymously replay the transaction, and either provide the now correct
|
||
response to the client or take appropriate legal action against the
|
||
faulty exchange.
|
||
|
||
The third case are transient failures, such as network failures or
|
||
temporary hardware failures at the exchange service provider. Here, the
|
||
client may receive an explicit protocol indication, such as an HTTP
|
||
response code 500 ``internal server error'' or simply no response.
|
||
The appropriate behavior for the client is to automatically retry
|
||
after 1s, and twice more at randomized times within 1 minute.
|
||
If those three attempts fail, the user should be informed about the
|
||
delay. The client should then retry another three times within the
|
||
next 24h, and after that time the auditor be informed about the outage.
|
||
|
||
Using this process, short term failures should be effectively obscured
|
||
from the user, while malicious behavior is reported to the auditor who
|
||
can then presumably rectify the situation, using methods such as
|
||
shutting down the operator and helping customers to regain refunds for
|
||
coins in their wallets. To ensure that such refunds are possible, the
|
||
operator is expected to always provide adequate securities for the
|
||
amount of coins in circulation as part of the certification process.
|
||
|
||
|
||
%As with support for fractional payments, Taler addresses these
|
||
%problems by allowing customers to refresh tainted coins, thereby
|
||
%destroying the link between the refunded or aborted transaction and
|
||
%the new coin.
|
||
|
||
|
||
\subsection{Refunds}
|
||
|
||
The refresh protocol offers an easy way to enable refunds to
|
||
customers, even if they are anonymous. Refunds can be supported
|
||
by including a public signing key of the merchant in the transaction
|
||
details, and having the customer keep the private key of the spent
|
||
coins on file.
|
||
|
||
Given this, the merchant can simply sign a {\em refund confirmation}
|
||
and share it with the exchange and the customer. Assuming the
|
||
exchange has a way to recover the funds from the merchant, or has not
|
||
yet performed the wire transfer, the exchange can simply add the value
|
||
of the refunded transaction back to the original coin, re-enabling
|
||
those funds to be spent again by the original customer. This customer
|
||
can then use the refresh protocol to anonymously melt the refunded
|
||
coin and create a fresh coin that is unlinkable to the refunded
|
||
transaction.
|
||
|
||
|
||
\section{Discussion}
|
||
|
||
Taler was designed for use in a modern social-liberal society and
|
||
provides a payment system with the following key properties:
|
||
|
||
\begin{description}
|
||
\item[Customer Anonymity]
|
||
It is impossible for exchanges, merchants and even a global active
|
||
adversary, to trace the spending behavior of a customer.
|
||
As a strong form of customer anonymity, it is also infeasible to
|
||
link a set of transactions to the same (anonymous) customer.
|
||
%, even when taking aborted transactions into account.
|
||
|
||
There is, however, a risk of metadata leakage if a customer
|
||
acquires coins matching exactly the price quoted by a merchant, or
|
||
if a customer uses coins issued by multiple exchanges for the same
|
||
transaction. Hence, our implementation does not allow this.
|
||
|
||
\item[Taxability]
|
||
In many current legal systems, it is the responsibility of the merchant
|
||
to deduct sales taxes from purchases made by customers, or for workers
|
||
to pay income taxes for payments received for work.
|
||
Taler ensures that merchants are easily identifiable and that
|
||
an audit trail is generated, so that the state can ensure that its
|
||
taxation regime is obeyed.
|
||
\item[Verifiability]
|
||
Taler minimizes the trust necessary between
|
||
participants. In particular, digital signatures are retained
|
||
whenever they would play a role in resolving disputes.
|
||
Additionally, customers cannot defraud anyone, and
|
||
merchants can only defraud their customers by not
|
||
delivering on the agreed contract. Neither merchants nor customers
|
||
are able to commit fraud against the exchange.
|
||
Only the exchange needs be tightly audited and regulated.
|
||
\item[No speculation] % It's actually "Specualtion not required"
|
||
The digital coins are denominated in existing currencies,
|
||
such as EUR or USD. This avoids exposing citizens to unnecessary risks
|
||
from currency fluctuations.
|
||
\item[Low resource consumption]
|
||
The design minimizes the operating costs and environmental impact of
|
||
the payment system. It uses few public key operations per
|
||
transaction and entirely avoids proof-of-work computations.
|
||
The payment system handles both small and large payments in
|
||
an efficient and reliable manner.
|
||
\end{description}
|
||
|
||
|
||
\subsection{Well-known attacks}
|
||
|
||
Taler's security is largely equivalent to that of Chaum's original
|
||
design without online checks or the cut-and-choose revelation of
|
||
double-spending customers for offline spending.
|
||
We specifically note that the digital equivalent of the ``Columbian
|
||
Black Market Exchange''~\cite{fatf1997} is a theoretical problem for
|
||
both Chaum and Taler, as individuals with a strong mutual trust
|
||
foundation can simply copy electronic coins and thereby establish a
|
||
limited form of black transfers. However, unlike the situation with
|
||
physical checks with blank recipients in the Columbian black market,
|
||
the transitivity is limited as each participant can deposit the electronic
|
||
coins and thereby cheat any other participant, while in the Columbian
|
||
black market each participant only needs to trust the issuer of the
|
||
check and not also all previous owners of the physical check.
|
||
|
||
As with any unconditionally anonymous payment system, the ``Perfect
|
||
Crime'' attack~\cite{solms1992perfect} where blackmail is used to
|
||
force the exchange to issue anonymous coins also continues to apply in
|
||
principle. However, as mentioned Taler does facilitate limits on
|
||
withdrawals, which we believe is a better trade-off than the
|
||
problematic escrow systems where the necessary intransparency
|
||
actually facilitates voluntary cooperation between the exchange and
|
||
criminals~\cite{sander1999escrow} and where the state could
|
||
deanonymize citizens.
|
||
|
||
\subsection{Offline Payments}
|
||
|
||
Chaum's original proposals for anonymous digital cash avoided the need
|
||
for online interactions with the exchange to detect double spending by
|
||
providing a means to deanonymize customers involved in
|
||
double-spending. This is problematic as the exchange or the merchant
|
||
still need out-of-band means to recover funds from the customer, which
|
||
may be infeasible in practice. Furthermore, a customer may
|
||
accidentally deanonymize himself, for example by double-spending a
|
||
coin after restoring from backup.
|
||
|
||
%\subsection{Merchant Tax Audits}
|
||
%
|
||
%For a tax audit on the merchant, the exchange includes the business
|
||
%transaction-specific hash in the transfer of the traditional
|
||
%currency. A tax auditor can then request the merchant to reveal
|
||
%(meaningful) details about the business transaction ($\mathcal{D}$,
|
||
%$a$, $p$, $r$), including proof that applicable taxes were paid.
|
||
%
|
||
%If a merchant is not able to provide theses values, he can be
|
||
%subjected to financial penalties by the state in relation to the
|
||
%amount transferred by the traditional currency transfer.
|
||
|
||
\subsection{Cryptographic proof vs. evidence}
|
||
|
||
In this paper we have use the term ``proof'' in many places as the
|
||
protocol provides cryptographic proofs of which parties behave
|
||
correctly or incorrectly. However, as~\cite{fc2014murdoch} point out,
|
||
in practice financial systems need to provide evidence that holds up
|
||
in courts. Taler's implementation is designed to export evidence and
|
||
upholds the core principles described in~\cite{fc2014murdoch}. In
|
||
particular, in providing the cryptographic proofs as evidence none of
|
||
the participants have to disclose their core secrets.
|
||
|
||
|
||
%\subsection{System Performance}
|
||
%
|
||
%We performed some initial performance measurements for the various
|
||
%operations on our exchange implementation. The main conclusion was that
|
||
%the computational and bandwidth cost for transactions described in
|
||
%this paper is smaller than $10^{-3}$ cent/transaction, and thus
|
||
%dwarfed by the other business costs for the exchange. However, this
|
||
%figure excludes the cost of currency transfers using traditional
|
||
%banking, which a exchange operator would ultimately have to interact with.
|
||
%Here, exchange operators should be able to reduce their expenses by
|
||
%aggregating multiple transfers to the same merchant.
|
||
|
||
|
||
%\section{Conclusion}
|
||
|
||
%We have presented an efficient electronic payment system that
|
||
%simultaneously addresses the conflicting objectives created by the
|
||
%citizen's need for privacy and the state's need for taxation. The
|
||
%coin refreshing protocol makes the design flexible and enables a
|
||
%variety of payment methods. The current balance and profits of the
|
||
%exchange are also easily determined, thus audits can be used to ensure
|
||
%that the exchange operates correctly. The libre implementation and open
|
||
%protocol may finally enable modern society to upgrade to proper
|
||
%electronic wallets with efficient, secure and privacy-preserving
|
||
%transactions.
|
||
|
||
% commented out for anonymized submission
|
||
%\subsection*{Acknowledgements}
|
||
|
||
%This work was supported by a grant from the Renewable Freedom Foundation.
|
||
% FIXME: ARED?
|
||
%We thank Tanja Lange, Dan Bernstein, Luis Ressel and Fabian Kirsch for feedback on an earlier
|
||
%version of this paper, Nicolas Fournier for implementing and running
|
||
%some performance benchmarks, and Richard Stallman, Hellekin Wolf,
|
||
%Jacob Appelbaum for productive discussions and support.
|
||
|
||
|
||
\bibliographystyle{alpha}
|
||
\bibliography{taler,rfc}
|
||
|
||
\newpage
|
||
\appendix
|
||
|
||
\section{Notation summary}
|
||
|
||
The paper uses the subscript $p$ to indicate public keys and $s$ to
|
||
indicate secret (private) keys. For keys, we also use small letters
|
||
for scalars and capital letters for points on an elliptic curve. The
|
||
capital letter without the subscript $p$ stands for the key pair. The
|
||
superscript $(i)$ is used to indicate one of the elements of a vector
|
||
during the cut-and-choose protocol. Bold-face is used to indicate a
|
||
vector over these elements. A line above indicates a value computed
|
||
by the verifier during the cut-and-choose operation. We use $f()$ to
|
||
indicate the application of a function $f$ to one or more arguments. Records of
|
||
data being committed to disk are represented in between $\langle\rangle$.
|
||
|
||
\begin{description}
|
||
\item[$K_s$]{Denomination private (RSA) key of the exchange used for coin signing}
|
||
\item[$K_p$]{Denomination public (RSA) key corresponding to $K_s$}
|
||
\item[$K$]{Public-priate (RSA) denomination key pair $K := (K_s, K_p)$}
|
||
\item[$b$]{RSA blinding factor for RSA-style blind signatures}
|
||
\item[$B_b()$]{RSA blinding over the argument using blinding factor $b$}
|
||
\item[$U_b()$]{RSA unblinding of the argument using blinding factor $b$}
|
||
\item[$S_K()$]{Chaum-style RSA signature, $S_K(C) = U_b(S_K(B_b(C)))$}
|
||
\item[$w_s$]{Private key from customer for authentication}
|
||
\item[$W_p$]{Public key corresponding to $w_s$}
|
||
\item[$W$]{Public-private customer authentication key pair $W := (w_s, W_p)$}
|
||
\item[$S_W()$]{Signature over the argument(s) involving key $W$}
|
||
\item[$m_s$]{Private key from merchant for authentication}
|
||
\item[$M_p$]{Public key corresponding to $m_s$}
|
||
\item[$M$]{Public-private merchant authentication key pair $M := (m_s, M_p)$}
|
||
\item[$S_M()$]{Signature over the argument(s) involving key $M$}
|
||
\item[$G$]{Generator of the elliptic curve}
|
||
\item[$c_s$]{Secret key corresponding to a coin, scalar on a curve}
|
||
\item[$C_p$]{Public key corresponding to $c_s$, point on a curve}
|
||
\item[$C$]{Public-private coin key pair $C := (c_s, C_p)$}
|
||
\item[$S_{C}()$]{Signature over the argument(s) involving key $C$ (using EdDSA)}
|
||
\item[$c_s'$]{Private key of a ``dirty'' coin (otherwise like $c_s$)}
|
||
\item[$C_p'$]{Public key of a ``dirty'' coin (otherwise like $C_p$)}
|
||
\item[$C'$]{Dirty coin (otherwise like $C$)}
|
||
\item[$\widetilde{C}$]{Exchange signature $S_K(C_p)$ indicating validity of a fresh coin (with key $C$)}
|
||
\item[$n$]{Number of exchanges accepted by a merchant}
|
||
\item[$j$]{Index into a set of accepted exchanges, $i \in \{1,\ldots,n\}$}
|
||
\item[$D_j$]{Public key of a exchange (not used to sign coins)}
|
||
\item[$\vec{D}$]{Vector of $D_j$ signifying exchanges accepted by a merchant}
|
||
\item[$a$]{Complete text of a contract between customer and merchant}
|
||
\item[$f$]{Amount a customer agrees to pay to a merchant for a contract}
|
||
\item[$m$]{Unique transaction identifier chosen by the merchant}
|
||
\item[$H()$]{Hash function}
|
||
\item[$p$]{Payment details of a merchant (i.e. wire transfer details for a bank transfer)}
|
||
\item[$r$]{Random nonce}
|
||
\item[${\cal A}$]{Complete contract signed by the merchant}
|
||
\item[${\cal D}$]{Deposit permission, signing over a certain amount of coin to the merchant as payment and to signify acceptance of a particular contract}
|
||
\item[$\kappa$]{Security parameter $\ge 3$}
|
||
\item[$i$]{Index over cut-and-choose set, $i \in \{1,\ldots,\kappa\}$}
|
||
\item[$\gamma$]{Selected index in cut-and-choose protocol, $\gamma \in \{1,\ldots,\kappa\}$}
|
||
\item[$t^{(i)}_s$]{private transfer key, a scalar}
|
||
\item[$T^{(i)}_p$]{public transfer key, point on a curve (same curve must be used for $C_p$)}
|
||
\item[$T^{(i)}$]{public-private transfer key pair $T^{(i)} := (t^{(i)}_s,T^{(i)}_s)$}
|
||
\item[$\vec{T}$]{Vector of $T^{(i)}$}
|
||
\item[$c_s^{(i)}$]{Secret key corresponding to a fresh coin, scalar on a curve}
|
||
\item[$C_p^{(i)}$]{Public key corresponding to $c_s^{(i)}$, point on a curve}
|
||
\item[$C^{(i)}$]{Public-private coin key pair $C^{(i)} := (c_s^{(i)}, C_p^{(i)})$}
|
||
\item[$\vec{C}$]{Vector of $C^{(i)}$ (public and private keys)}
|
||
\item[$b^{(i)}$]{Blinding factor for RSA-style blind signatures}
|
||
\item[$\vec{b}$]{Vector of $b^{(i)}$}
|
||
\item[$B^{(i)}$]{Blinding of $C_p^{(i)}$}
|
||
\item[$\vec{B}$]{Vector of $B^{(i)}$}
|
||
\item[$K_i$]{Symmetric encryption key derived from ECDH operation via hashing}
|
||
\item[$E_{K_i}()$]{Symmetric encryption using key $K_i$}
|
||
\item[$E^{(i)}$]{$i$-th encryption of the private information $(c_s^{(i)}, b_i)$}
|
||
\item[$\vec{E}$]{Vector of $E^{(i)}$}
|
||
\item[$\cal{R}$]{Tuple of revealed vectors in cut-and-choose protocol,
|
||
where the vectors exclude the selected index $\gamma$}
|
||
\item[$\overline{K_i}$]{Encryption keys derived by the verifier from DH}
|
||
\item[$\overline{B^{(i)}}$]{Blinded values derived by the verifier}
|
||
\item[$\overline{T_p^{(i)}}$]{Public transfer keys derived by the verifier from revealed private keys}
|
||
\item[$\overline{c_s^{(i)}}$]{Private keys obtained from decryption by the verifier}
|
||
\item[$\overline{b_s^{(i)}}$]{Blinding factors obtained from decryption by the verifier}
|
||
\item[$\overline{C^{(i)}_p}$]{Public coin keys computed from $\overline{c_s^{(i)}}$ by the verifier}
|
||
\end{description}
|
||
|
||
|
||
|
||
\end{document}
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
\section{Optional features}
|
||
|
||
In this appendix we detail various optional features that can
|
||
be added to the basic protocol to reduce transaction costs for
|
||
certain interactions.
|
||
|
||
However, we note that Taler's transaction costs are expected to be so
|
||
low that these features are likely not particularly useful in
|
||
practice: When we performed some initial performance measurements for
|
||
the various operations on our exchange implementation, the main conclusion
|
||
was that the computational and bandwidth cost for transactions
|
||
described in this paper is smaller than $10^{-3}$ cent/transaction,
|
||
and thus dwarfed by the other business costs for the exchange. We note
|
||
that the $10^{-3}$ cent/transaction estimate excludes the cost of wire
|
||
transfers using traditional banking, which a exchange operator would
|
||
ultimately have to interact with. Here, exchange operators should be able
|
||
to reduce their expenses by aggregating multiple transfers to the same
|
||
merchant.
|
||
|
||
As a result of the low cost of the interaction with the exchange in Taler
|
||
today, we expect that transactions with amounts below Taler's internal
|
||
transaction costs to be economically meaningless. Nevertheless, we
|
||
document various ways how such transactions could be achieved within
|
||
Taler.
|
||
|
||
|
||
|
||
\subsection{Incremental spending}
|
||
|
||
For services that include pay-as-you-go billing, customers can over
|
||
time sign deposit permissions for an increasing fraction of the value
|
||
of a coin to be paid to a particular merchant. As checking with the
|
||
exchange for each increment might be expensive, the coin's owner can
|
||
instead sign a {\em lock permission}, which allows the merchant to get
|
||
an exclusive right to redeem deposit permissions for the coin for a
|
||
limited duration. The merchant uses the lock permission to determine
|
||
if the coin has already been spent and to ensure that it cannot be
|
||
spent by another merchant for the {\em duration} of the lock as
|
||
specified in the lock permission. If the coin has insufficient funds
|
||
because too much has been spent or is
|
||
already locked, the exchange provides the owner's deposit or locking
|
||
request and signature to prove the attempted fraud by the customer.
|
||
Otherwise, the exchange locks the coin for the expected duration of the
|
||
transaction (and remembers the lock permission). The merchant and the
|
||
customer can then finalize the business transaction, possibly
|
||
exchanging a series of incremental payment permissions for services.
|
||
Finally, the merchant then redeems the coin at the exchange before the
|
||
lock permission expires to ensure that no other merchant redeems the
|
||
coin first.
|
||
|
||
\begin{enumerate}
|
||
\item\label{offer2} The merchant sends an \emph{offer:} $\langle S_M(m, f),
|
||
\vec{D} \rangle$ containing the price of the offer $f$, a transaction
|
||
ID $m$ and the list of exchanges $D_1, \ldots, D_n$ accepted by the merchant
|
||
where each $D_j$ is a exchange's public key.
|
||
\item\label{lock2} The customer must possess or acquire a coin $\widetilde{C}$
|
||
signed by a exchange that is
|
||
accepted by the merchant, i.e. $K$ should be signed by some $D_j
|
||
\in \{D_1, D_2, \ldots, D_n\}$, and has a value $\geq f$.
|
||
|
||
Customer then generates a \emph{lock-permission} $\mathcal{L} :=
|
||
S_c(\widetilde{C}, t, m, f, M_p)$ where $t$ specifies the time until which the
|
||
lock is valid and sends $\langle \mathcal{L}, D_j\rangle$ to the merchant,
|
||
where $D_j$ is the exchange which signed $K$.
|
||
\item The merchant asks the exchange to apply the lock by sending $\langle
|
||
\mathcal{L} \rangle$ to the exchange.
|
||
\item The exchange validates $\widetilde{C}$ and detects double spending
|
||
in the form of existing \emph{deposit-permission} or
|
||
lock-permission records for $\widetilde{C}$. If such records exist
|
||
and indicate that insufficient funds are left, the exchange sends those
|
||
records to the merchant, who can then use the records to prove the double
|
||
spending to the customer.
|
||
|
||
If double spending is not found,
|
||
the exchange commits $\langle \mathcal{L} \rangle$ to disk
|
||
and notifies the merchant that locking was successful.
|
||
\item\label{contract2} The merchant creates a digitally signed contract
|
||
$\mathcal{A} := S_M(m, f, a, H(p, r))$ where $a$ is data relevant to the contract
|
||
indicating which services or goods the merchant will deliver to the customer, and $p$ is the
|
||
merchant's payment information (e.g. his IBAN number) and $r$ is an random nonce.
|
||
The merchant commits $\langle \mathcal{A} \rangle$ to disk and sends it to the customer.
|
||
\item The customer creates a
|
||
\emph{deposit-permission} $\mathcal{D} := S_c(\widetilde{C}, \widetilde{L}, f, m, M_p, H(a), H(p, r))$, commits
|
||
$\langle \mathcal{A}, \mathcal{D} \rangle$ to disk and sends $\mathcal{D}$ to the merchant.
|
||
\item\label{invoice_paid2} The merchant commits the received $\langle \mathcal{D} \rangle$ to disk.
|
||
\item The merchant gives $(\mathcal{D}, p, r)$ to the exchange, revealing his
|
||
payment information.
|
||
\item The exchange verifies $(\mathcal{D}, p, r)$ for its validity and
|
||
checks against double spending, while of
|
||
course permitting the merchant to withdraw funds from the amount that
|
||
had been locked for this merchant.
|
||
\item If $\widetilde{C}$ is valid and no equivalent \emph{deposit-permission} for $\widetilde{C}$ and $\widetilde{L}$ exists on disk, the
|
||
exchange performs the following transaction:
|
||
\begin{enumerate}
|
||
\item $\langle \mathcal{D}, p, r \rangle$ is committed to disk.
|
||
\item\label{transfer2} transfers an amount of $f$ to the merchant's bank account
|
||
given in $p$. The subject line of the transaction to $p$ must contain
|
||
$H(\mathcal{D})$.
|
||
\end{enumerate}
|
||
Finally, the exchange sends a confirmation to the merchant.
|
||
\item If the deposit record $\langle \mathcal{D}, p, r \rangle$ already exists,
|
||
the exchange sends the confirmation to the merchant,
|
||
but does not transfer money to $p$ again.
|
||
\end{enumerate}
|
||
|
||
To facilitate incremental spending of a coin $C$ in a single transaction, the
|
||
merchant makes an offer in Step~\ref{offer2} with a maximum amount $f_{max}$ he
|
||
is willing to charge in this transaction from the coin $C$. After obtaining the
|
||
lock on $C$ for $f_{max}$, the merchant makes a contract in Step~\ref{contract2}
|
||
with an amount $f \leq f_{max}$. The protocol follows with the following steps
|
||
repeated after Step~\ref{invoice_paid2} whenever the merchant wants to charge an
|
||
incremental amount up to $f_{max}$:
|
||
|
||
\begin{enumerate}
|
||
\setcounter{enumi}{4}
|
||
\item The merchant generates a new contract $ \mathcal{A}' := S_M(m, f', a', H(p,
|
||
r)) $ after obtaining the deposit-permission for a previous contract. Here
|
||
$f'$ is the accumulated sum the merchant is charging the customer, of which
|
||
the merchant has received a deposit-permission for $f$ from the previous
|
||
contract \textit{i.e.}~$f <f' \leq f_{max}$. Similarly $a'$ is the new
|
||
contract data appended to older contract data $a$.
|
||
The merchant commits $\langle \mathcal{A}' \rangle$ to disk and sends it to the customer.
|
||
\item Customer commits $\langle \mathcal{A}' \rangle$ to disk, creates
|
||
$\mathcal{D}' := S_c(\widetilde{C}, \mathcal{L}, f', m, M_p, H(a'), H(p, r))$, commits
|
||
$\langle \mathcal{D'} \rangle$ and sends it to the merchant.
|
||
\item The merchant commits the received $\langle \mathcal{D'} \rangle$ and
|
||
deletes the older $\mathcal{D}$.
|
||
\end{enumerate}
|
||
|
||
%Figure~\ref{fig:spending_protocol_interactions} summarizes the interactions of the
|
||
%coin spending protocol.
|
||
|
||
For transactions with multiple coins, the steps of the protocol are
|
||
executed in parallel for each coin. During the time a coin is locked,
|
||
the locked fraction may not be spent at a different merchant or via a
|
||
deposit permission that does not contain $\mathcal{L}$. The exchange will
|
||
release the locks when they expire or are used in a deposit operation.
|
||
Thus the coins can be used with other merchants once their locks
|
||
expire, even if the original merchant never executed any deposit for
|
||
the coin. However, doing so may link the new transaction to older
|
||
transaction.
|
||
|
||
Similarly, if a transaction is aborted after Step 2, subsequent
|
||
transactions with the same coin can be linked to the coin, but not
|
||
directly to the coin's owner. The same applies to partially spent
|
||
coins. Thus, to unlink subsequent transactions from a coin, the
|
||
customer has to execute the coin refreshing protocol with the exchange.
|
||
|
||
%\begin{figure}[h]
|
||
%\centering
|
||
%\begin{tikzpicture}
|
||
%
|
||
%\tikzstyle{def} = [node distance= 1em, inner sep=.5em, outer sep=.3em];
|
||
%\node (origin) at (0,0) {};
|
||
%\node (offer) [def,below=of origin]{make offer (merchant $\rightarrow$ customer)};
|
||
%\node (A) [def,below=of offer]{permit lock (customer $\rightarrow$ merchant)};
|
||
%\node (B) [def,below=of A]{apply lock (merchant $\rightarrow$ exchange)};
|
||
%\node (C) [def,below=of B]{confirm (or refuse) lock (exchange $\rightarrow$ merchant)};
|
||
%\node (D) [def,below=of C]{sign contract (merchant $\rightarrow$ customer)};
|
||
%\node (E) [def,below=of D]{permit deposit (customer $\rightarrow$ merchant)};
|
||
%\node (F) [def,below=of E]{make deposit (merchant $\rightarrow$ exchange)};
|
||
%\node (G) [def,below=of F]{transfer confirmation (exchange $\rightarrow$ merchant)};
|
||
%
|
||
%\tikzstyle{C} = [color=black, line width=1pt]
|
||
%\draw [->,C](offer) -- (A);
|
||
%\draw [->,C](A) -- (B);
|
||
%\draw [->,C](B) -- (C);
|
||
%\draw [->,C](C) -- (D);
|
||
%\draw [->,C](D) -- (E);
|
||
%\draw [->,C](E) -- (F);
|
||
%\draw [->,C](F) -- (G);
|
||
%
|
||
%\draw [->,C, bend right, shorten <=2mm] (E.east)
|
||
% to[out=-135,in=-45,distance=3.8cm] node[left] {aggregate} (D.east);
|
||
%\end{tikzpicture}
|
||
%\caption{Interactions between a customer, merchant and exchange in the coin spending
|
||
% protocol}
|
||
%\label{fig:spending_protocol_interactions}
|
||
%\end{figure}
|
||
|
||
|
||
\subsection{Probabilistic donations}
|
||
|
||
Similar to Peppercoin, Taler supports probabilistic {\em micro}donations of coins to
|
||
support cost-effective transactions for small amounts. We consider
|
||
amounts to be ``micro'' if the value of the transaction is close or
|
||
even below the business cost of an individual transaction to the exchange.
|
||
|
||
To support microdonations, an ordinary transaction is performed based
|
||
on the result of a biased coin flip with a probability related to the
|
||
desired transaction amount in relation to the value of the coin. More
|
||
specifically, a microdonation of value $\epsilon$ is upgraded to a
|
||
macropayment of value $m$ with a probability of $\frac{\epsilon}{m}$.
|
||
Here, $m$ is chosen such that the business transaction cost at the
|
||
exchange is small in relation to $m$. The exchange is only involved in the
|
||
tiny fraction of transactions that are upgraded. On average both
|
||
customers and merchants end up paying (or receiving) the expected
|
||
amount $\epsilon$ per microdonation.
|
||
|
||
Unlike Peppercoin, in Taler either the merchant wins and the customer
|
||
looses the coin, or the merchant looses and the customer keeps the
|
||
coin. Thus, there is no opportunity for the merchant and the customer
|
||
to conspire against the exchange. To determine if the coin is to be
|
||
transferred, merchant and customer execute a secure coin flipping
|
||
protocol~\cite{blum1981}. The commit values are included in the
|
||
business contract and are revealed after the contract has been signed
|
||
using the private key of the coin. If the coin flip is decided in
|
||
favor of the merchant, the merchant can redeem the coin at the exchange.
|
||
|
||
One issue in this protocol is that the customer may use a worthless
|
||
coin by offering a coin that has already been spent. This kind of
|
||
fraud would only be detected if the customer actually lost the coin
|
||
flip, and at this point the merchant might not be able to recover from
|
||
the loss. A fraudulent anonymous customer may run the protocol using
|
||
already spent coins until the coin flip is in his favor.
|
||
|
||
As with incremental spending, lock permissions could be used to ensure
|
||
that the customer cannot defraud the merchant by offering a coin that
|
||
has already been spent. However, as this means involving the exchange
|
||
even if the merchant looses the coin flip, such a scheme is unsuitable
|
||
for microdonations as the transaction costs from involving the exchange
|
||
might be disproportionate to the value of the transaction, and thus
|
||
with locking the probabilistic scheme has no advantage over simply
|
||
using fractional payments.
|
||
|
||
Hence, Taler uses probabilistic transactions {\em without} online
|
||
double-spending detection. This enables the customer to defraud the
|
||
merchant by paying with a coin that was already spent. However, as,
|
||
by definition, such microdonations are for tiny amounts, the incentive
|
||
for customers to pursue this kind of fraud is limited. Still, to
|
||
clarify that the customer must be honest, we prefer the term
|
||
micro{\em donations} over micro{\em payments} for this scheme.
|
||
|
||
|
||
The following steps are executed for microdonations with upgrade probability $p$:
|
||
\begin{enumerate}
|
||
\item The merchant sends an offer to the customer.
|
||
\item The customer sends a commitment $H(r_c)$ to a random
|
||
value $r_c \in [0,2^R)$, where $R$ is a system parameter.
|
||
\item The merchant sends random $r_m \in [0,2^R)$ to the customer.
|
||
\item The customer computes $p' := (|r_c - r_m|) / (2^R)$.
|
||
If $p' < p$, the customer sends a coin with deposit-permission to the merchant.
|
||
Otherwise, the customer sends $r_c$ to the merchant.
|
||
\item The merchant deposits the coin, or checks if $r_c$ is consistent
|
||
with $H(r_c)$.
|
||
\end{enumerate}
|
||
|
||
Evidently the customer can ``cheat'' by aborting the transaction in
|
||
Step 3 of the microdonation protocol if the outcome is unfavorable ---
|
||
and repeat until he wins. This is why Taler is suitable for
|
||
microdonations --- where the customer voluntarily contributes ---
|
||
and not for micropayments.
|
||
|
||
Naturally, if the donations requested are small, the incentive to
|
||
cheat for minimal gain should be quite low. Payment software could
|
||
embrace this fact by providing an appeal to conscience in form of an
|
||
option labeled ``I am unethical and want to cheat'', which executes
|
||
the dishonest version of the payment protocol.
|
||
|
||
If an organization detects that it cannot support itself with
|
||
microdonations, it can always choose to switch to the macropayment
|
||
system with slightly higher transaction costs to remain in business.
|
||
|
||
\newpage
|