% RMS wrote: %The text does not mention GNU anywhere. This paper is an opportunity %to make people aware of GNU, but the current text fails to use the %opportunity. % %It should say that Taler is a GNU package. % %I suggest using the term "GNU Taler" in the title, once in the %abstract, and the first time the name is mentioned in the body text. %In the body text, it can have a footnote with more information %including a reference to http://gnu.org/gnu/the-gnu-project.html. % %At the top of page 3, where it says "a free software implementation", %it should add "(free as in freedom)", with a reference to %http://gnu.org/philosophy/free-sw.html and %http://gnu.org/philosophy/free-software-even-more-important.html. % %Would you please include these things in every article or posting? % % CG adds: % We SHOULD do this for the FINAL paper, not for the anon submission. \documentclass{llncs} %\usepackage[margin=1in,a4paper]{geometry} \usepackage[T1]{fontenc} \usepackage{palatino} \usepackage{xspace} \usepackage{microtype} \usepackage{amsmath,amssymb,eurosym} \usepackage[dvipsnames]{xcolor} \usepackage{tikz} \usetikzlibrary{shapes,arrows} \usetikzlibrary{positioning} \usetikzlibrary{calc} % \usepackage{enumitem} \usepackage{caption} %\usepackage{subcaption} \usepackage{subfig} % \usepackage{sidecap} % \usepackage{wrapfig} % Relate to: % http://fc14.ifca.ai/papers/fc14_submission_124.pdf % Terminology: % - SEPA-transfer -- avoid 'SEPA transaction' as we use % 'transaction' already when we talk about taxable % transfers of Taler coins and database 'transactions'. % - wallet = coins at customer % - reserve = currency entrusted to exchange waiting for withdrawal % - deposit = SEPA to exchange % - withdrawal = exchange to customer % - spending = customer to merchant % - redeeming = merchant to exchange (and then exchange SEPA to merchant) % - refreshing = customer-exchange-customer % - dirty coin = coin with exposed public key % - fresh coin = coin that was refreshed or is new % - denomination key = exchange's online key used to (blindly) sign coin % - reserve key = key used to authorize withdrawals from a reserve % - message signing key = exchange's online key to sign exchange messages % - exchange master key = exchange's key used to sign other exchange keys % - owner = entity that knows coin private key % - transaction = coin ownership transfer that should be taxed % - sharing = coin copying that should not be taxed \title{Refreshing Coins for Giving Change and Refunds \\ in Chaum-style Anonymous Payment Systems} \begin{document} \mainmatter %\author{Florian Dold \and Sree Harsha Totakura \and Benedikt M\"uller \and Jeff Burdges \and Christian Grothoff} %\institute{The GNUnet Project} \maketitle % FIXME: As a general comment, I think we're mixing the crypto stuff and the systems % stuff too much. It might be more appropriate to have to systems stuff in a separate % section, and the "pure" crypto stuff for the crypto people? \begin{abstract} This paper introduces {\em Taler}, a Chaum-style digital payment system that enables anonymous payments while ensuring that entities that receive payments are auditable. In Taler, customers can never defraud anyone, merchants can only fail to deliver the merchandise to the customer, and payment service providers are audited. All parties receive cryptographic evidence for all transactions; still, each party only receives the minimum information required to execute transactions. Enforcement of honest behavior is timely, and is at least as strict as with legacy credit card payment systems that do not provide for privacy. The key technical contribution underpinning Taler is a new {\em refresh protocol} which allows fractional payments and refunds while maintaining untraceability of the customer and unlinkability of transactions. The refresh protocol combines an efficient cut-and-choose mechanism with a {\em link} step to ensure that refreshing is not abused for transactional payments. We argue that Taler provides a secure digital payment system for modern liberal societies as it is a flexible, libre and efficient protocol and adequately balances the state's need for monetary control with the citizen's needs for private economic activity. \end{abstract} \section{Introduction} The design of payment systems shapes economies and societies. Strong, developed nation states have adopted highly transparent payment systems, such as the MasterCard and VisaCard credit card schemes and computerized bank transactions such as SWIFT. These systems enable mass surveillance by both governments and private companies. Aspects of this surveillance sometimes benefit society by providing information about tax evasion or crimes like extortion. % %In particular, bribery and corruption are limited to elites who can %afford to escape the dragnet. % At the other extreme, weaker developing nation states have economic activity based largely on coins, paper money or even barter. Here, the state is often unable to effectively monitor or tax economic activity, and this limits the ability of the state to shape the society. % If we remove the sentence above, this one also needs to go as it % is the dual... % As bribery is virtually impossible to detect, corruption is % widespread and not limited to social elites. % % % SHORTER: Zerocash need not be mentioned so early? % Zerocash~\cite{zerocash} is an example for translating an % anarchistic economy into the digital realm. This paper describes Taler, a simple and practical payment system which balances accountability and privacy. The Taler protocol is an improvement over Chaum's original design~\cite{chaum1983blind} and also follows Chaum's basic architecture of customer, merchant and exchange (Figure~\ref{fig:cmm}). The two designs share the key first step where the {\em customer} withdraws digital {\em coins} from the {\em exchange} with unlinkability provided via blind signatures. The coins can then be spent at a {\em merchant} who {\em deposits} them at the exchange. Taler uses online detection of double-spending and provides fair exchange and exculpability via cryptographic proofs. % Thus merchants are instantly assured that a transaction is valid. \begin{figure}[h] \centering \begin{tikzpicture} \tikzstyle{def} = [node distance= 1em and 11em, inner sep=1em, outer sep=.3em]; \node (origin) at (0,0) {}; \node (exchange) [def,above=of origin,draw]{Exchange}; \node (customer) [def, draw, below left=of origin] {Customer}; \node (merchant) [def, draw, below right=of origin] {Merchant}; \node (auditor) [def, draw, above right=of origin]{Auditor}; \tikzstyle{C} = [color=black, line width=1pt] \draw [<-, C] (customer) -- (exchange) node [midway, above, sloped] (TextNode) {withdraw coins}; \draw [<-, C] (exchange) -- (merchant) node [midway, above, sloped] (TextNode) {deposit coins}; \draw [<-, C] (merchant) -- (customer) node [midway, above, sloped] (TextNode) {spend coins}; \draw [<-, C] (exchange) -- (auditor) node [midway, above, sloped] (TextNode) {verify}; \end{tikzpicture} \caption{Taler's system model for the payment system is based on Chaum~\cite{chaum1983blind}.} \label{fig:cmm} \end{figure} A key issue for an efficient Chaumian digital payment system is the need to provide change and existing systems for ``practical divisible'' electronic cash have transaction costs that are linear in the amount of value being transacted, sometimes hidden in the double spending detection logic of the payment service provider~\cite{martens2015practical}. The customer should also not be expected to withdraw exact change, as doing so reduces anonymity due to the obvious correlation. % FIXME: explain the logarithmic claim! It's only % true for a certain denomination structure. % This denomination structure potentially introduces privacy risks Taler solves the problem of giving change by introducing a new {\em refresh protocol} allowing for ``divisible'' transactions with amortized costs logarithmic in the amount of value being transacted. Using this protocol, a customer can obtain change or refunds in the form of fresh coins that other parties cannot link to the original transaction, the original coin, or each other. Additionally, the refresh protocol ensures that the change is owned by the same entity which owned the original coin. %\vspace{-0.3cm} \section{Related Work} %\vspace{-0.3cm} %\subsection{Blockchain-based currencies} % FIXME: SHORTEN. This is probably too much information for the audience, they % all know this In recent years, a class of decentralized electronic payment systems, based on collectively recorded and verified append-only public ledgers, have gained immense popularity. The most well-known protocol in this class is Bitcoin~\cite{nakamoto2008bitcoin}. The key contribution of blockchain-based protocols is that they dispense with the need for a central, trusted authority. Yet, there are several major irredeemable problems inherent in their designs: \begin{itemize} \item The computational puzzles solved by Bitcoin nodes with the purpose of securing the blockchain consume a considerable amount of energy. So Bitcoin is an environmentally irresponsible design. \item Bitcoin transactions have pseudonymous recipients, making taxation hard to systematically enforce. \item Bitcoin introduces a new currency, creating additional financial risks from currency fluctuation. \item Anyone can start an alternative Bitcoin transaction chain, called an AltCoin, and, if successful, reap the benefits of the low cost to initially create coins cheaply as the proof-of-work difficulty adjusts to the computation power of all miners in the network. As participants are de facto investors, AltCoins become a form of Ponzi scheme. % As a result, dozens of % AltCoins have been created, often without any significant changes to the % technology. A large number of AltCoins creates additional overheads for % currency exchange and exacerbates the problems with currency fluctuations. \end{itemize} Bitcoin also lacks anonymity, as all Bitcoin transactions are recorded for eternity, which can enable identification of users. Anonymous payment systems based on Bitcoin such as CryptoNote~\cite{cryptonote} (Monero), Zerocash~\cite{zerocash} (ZCash) and BOLT~\cite{BOLT} exacerbate the design issues we mention above. These systems exploit the blockchain's decentralized nature to escape anti-money laundering regulation~\cite{molander1998cyberpayments} as they provide anonymous, disintermediated transactions. %GreenCoinX\footnote{\url{https://www.greencoinx.com/}} is a more %recent AltCoin where the company promises to identify the owner of %each coin via e-mail addresses and phone numbers. While it is unclear %from their technical description how this identification would be %enforced against a determined adversary, the resulting payment system %would also merely impose a financial panopticon on a Bitcoin-style %money supply and transaction model. %\subsection{Chaum-style electronic cash} Chaum~\cite{chaum1983blind} proposed a digital payment system that would provide some customer anonymity while disclosing the identity of the merchants. DigiCash, a commercial implementation of Chaum's proposal ultimately failed to be widely adopted. In our assessment, key reasons for DigiCash's failure include: \begin{itemize} \item The use of patents to protect the technology; a payment system should be free software (libre) to have a chance for widespread adoption. \item Support for payments to off-line merchants, and thus deferred detection of double-spending, requires the exchange to attempt to recover funds from delinquent customers via the legal system. Any system that fails to be self-enforcing creates a major business risk for the exchange and merchants. % In 1983, there were merchants without network connectivity, making that % feature relevant, but today network connectivity is feasible for most % merchants, and saves both the exchange and merchants the business risks % associated with deferred fraud detection. \item % In addition to the risk of legal disputes wh fraudulent % merchants and customers, Chaum's published design does not clearly limit the financial damage a exchange might suffer from the disclosure of its private online signing key. \item Chaum did not support fractional payments or refunds without weakening customer anonymity. %, and Brand's % extensions for fractional payments broke unlinkability and thus % limited anonymity. % \item Chaum's system was implemented at a time where the US market % was still dominated by paper checks and the European market was % fragmented into dozens of currencies. Today, SEPA provides a % unified currency and currency transfer method for most of Europe, % significantly lowering the barrier to entry into this domain for % a larger market. \end{itemize} To our knowledge, the only publicly available effort to implement Chaum's idea is Opencoin~\cite{dent2008extensions}. However, Opencoin is neither actively developed nor used, and it is not clear to what degree the implementation is even complete. Only a partial description of the Opencoin protocol is available to date. % FIXME: ask OpenCoin dev's about this! Then make statement firmer! % FIXME: not only by brands. this formulation sounds like % we're unaware of the huge body of work in the area that is still growing. Chaum's original digital cash system~\cite{chaum1983blind} was extended by Brands~\cite{brands1993efficient} with the ability to {\em divide} coins and thus spend certain fractions of a coin using restrictive blind signatures. Restrictive blind signatures create privacy risks: if a transaction is interrupted, then any coins sent to the merchant become tainted, but may never arrive or be spent. It becomes tricky to extract the value of the tainted coins without linking to the aborted transaction and risking deanonymization. Ian Goldberg's HINDE system allowed the merchant to provide change, but the mechanism could be abused to hide income from taxation.\footnote{Description based on personal communication. HINDE was never published.} In~\cite{brands1993efficient}, $k$-show signatures were proposed to achieve divisibility for coins. However, with $k$-show signatures multiple transactions can be linked to each other. Performing fractional payments using $k$-show signatures is also rather expensive. In pure blind signature based schemes like Taler, withdrawal and spend operations require bandwidth logarithmic in the value being withdrawn or spent. In~\cite{Camenisch05compacte-cash}, there is a zero-knowledge scheme that improves upon this, requiring only constant bandwidth for withdrawals and spend operations, but unfortunately the exchanges' storage and search costs become linear in the total value of all transactions. %In principle, one could correct this by adding multiple denominations, %an open problem stated already in~\cite{Camenisch05compacte-cash}. % NO: he cannot give change, so that does not really work! As described, the scheme employs offline double spending protection, which inherently makes it fragile and creates an unnecessary deanonymization risk (see Section~\ref{sec:offline}). %We believe the offline protection from double %spending could be removed, thus switching the scheme to only protection %against online double spending, like Taler. % TOO much detail... % %Along with fixing these two issues, an interesting applied research project %would be to add partial spending and a form of Taler's refresh protocol. %At present, we feel these relatively new cryptographic techniques incur %unacceptable financial risks to the exchange, due to underdeveloped %implementation practice. % % SHORTER: Maybe some of the above could be thinned since % they do not know much about Taler's refresh protocol yet. % -- yeah, in particular the feeling/speculative parts are not needed... %In this vein, there are pure also zero-knowledge proof based schemes %like~\cite{ST99}, and subsequently Zerocash~\cite{zerocash}, and maybe %variations on BOLT~\cite{BOLT}, that avoid using any denomination-like %constructs, slightly reducing metadata leakage. At present, these all %incur excessive bandwidth or computational costs however. % -- commented out, seems excessive. %Some argue that the focus on technically perfect but overwhelmingly %complex protocols, as well as the the lack of usable, practical %solutions lead to an abandonment of these ideas by %practitioners~\cite{selby2004analyzing}. % FIXME: If we ever add peppercoin stuff, cite Matt Green paper % and talk about economics when encoding a punishment-coin % as the identity, with limited ticket lifespan %\subsection{Peppercoin} %Peppercoin~\cite{rivest2004peppercoin} is a microdonation protocol. %The main idea of the protocol is to reduce transaction costs by %minimizing the number of transactions that are processed directly by %the exchange. Instead of always paying, the customer ``gambles'' with the %merchant for each microdonation. Only if the merchant wins, the %microdonation is upgraded to a macropayment to be deposited at the %exchange. Peppercoin does not provide customer-anonymity. The proposed %statistical method by which exchanges detect fraudulent cooperation between %customers and merchants at the expense of the exchange not only creates %legal risks for the exchange, but would also require that the exchange learns %about microdonations where the merchant did not get upgraded to a %macropayment. It is therefore unclear how Peppercoin would actually %reduce the computational burden on the exchange. %\vspace{-0.3cm} \section{Design} %\vspace{-0.3cm} The Taler system comprises three principal types of actors (Figure~\ref{fig:cmm}): The \emph{customer} is interested in receiving goods or services from the \emph{merchant} in exchange for payment. To pay, the customer {\em spends} digital coins at the merchant. When making a transaction, both the customer and the merchant use the same \emph{exchange}, which serves as a payment service provider for the financial transaction between the two. The exchange is responsible for allowing the customer to withdraw anonymous digital coins from the customer's financial reserves, and for enabling the merchant to deposit digital coins in return for receiving credit at the merchant's financial reserve. In addition, Taler includes an \emph{auditor} who assures customers and merchants that the exchange operates correctly. %\vspace{-0.3cm} \subsection{Security model} %\vspace{-0.3cm} As a payment system, Taler naturally needs to make sure that coins are unforgeable and prevent double-spending. More precisely, as the same coin is allowed to be involved in multiple operations, Taler needs to ensure that the amounts spent per coin remain below the denomination value and amounts credited to the coin from refunds. Furthermore, transactions should be unlinkable; in particular, if a coin has been partially spent or if a transaction was aborted, Taler must provide a mechanism for customers to spend the remaining value in another transaction that remains unlinkable to the first transaction. Finally, this mechanism must not introduce a new loophole that might be used to hide transactions in a way that would enable tax-evasion. As a practical system, Taler needs to be concerned with transient network failures or loss of power. Thus, it must be possible to resume protocols and recover from such failures at any point in time, without any party suffering financial losses. We require that parties are able to securely persist information and assume that after errors they can resume from the previous state that was persisted. We will explicitly state in the protocol when what state has to be persisted. Participants that fail to recover data they were expected to persist may suffer financial losses in proportion to the value of the transactions involved. Taler assumes that each participant has full control over their system. We assume the contact information of the exchange is known to both customer and merchant from the start, including that the customer can authenticate the merchant, for example by using X.509 certificates~\cite{rfc6818}. A Taler 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 the customer receives cryptographic evidence of the contract and the associated payment. We assume each Taler customer has an anonymous bi-directional channel, such as Tor, to communicate with both the exchange and the merchant. A Taler exchange is trusted to hold funds of its customers and to forward them when receiving the respective deposit instructions from the merchants. Customer and merchant can have assurances about the exchange's liquidity and operation though published audits by financial regulators or other trusted third parties. An exchange's signing keys expire regularly, allowing the exchange to eventually destroy the corresponding accumulated cryptographic proofs, and limiting the exchange's financial liability. On the cryptographic side, a Taler exchange demands that coins use a full domain hash (FDH) to make so-called ``one-more forgery'' attacks provably hard, assuming the RSA known-target inversion problem is hard~\cite[Theorem 12]{RSA-HDF-KTIvCTI}. For a withdrawn coin, violating the customers anonymity cryptographically requires recognizing a random blinding factor from a random element of the group of integers modulo the denomination key's RSA modulus, which appears impossible even with a quantum computers. For a refreshed coin, unlinkability requires the hardness of the discrete logarithm for Curve25519. The cut-and-choose protocol prevents merchants and customers from conspiring to conceal a merchants income. We assume that the maximum tax rate is below $1/\kappa$, and that expected transaction losses of a factor of $\kappa$ for tax evasion are thus unacceptable. \subsection{Taxability and Entities} Taler ensures that the state can tax {\em transactions}. We must, however, clarify what constitutes a transaction that can be taxed. % As we believe citizens should be in control of their computing, as well as for 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 even more extreme measures. % SHORTER: % including preventing them from communicating with anyone but % the exchange terminal during withdrawal. % FIXME: Oddly phrased: % 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. % SHORTER: There might be a shorter way to say this and the previous % paragraph together, but now I see why they were kept apart. 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 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 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 who withdrew enough coin of given denominations. There are naturally risks that the business operation that the merchant runs on behalf of the customer may require the merchant to learn 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 untraceability 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 the full domain hash (FDH) of the coin's public key. The exchange has multiple RSA {\em denomination key} pairs available for blind-signing coins of different values. 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. If a private denomination key were to be compromised, the exchange can detect this once more coins are redeemed than the total that was signed into existence using that denomination key. In this case, the exchange can allow authentic customers to redeem their unspent coins that were signed with the compromised private key, while refusing further deposits involving coins signed by the compromised denomination key. As a result, the financial damage of losing a private signing key is limited to at most the amount originally signed with that key, and denomination key rotation can be used to bound that risk. We 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 with validity periods that imply sufficiently strong anonymity sets. 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 reserve 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 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 and the signature over the coin's public key by an exchange's denomination key enables spending 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} \def\KDF{\textrm{KDF}} \def\FDH{\textrm{FDH}} % 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. We avoid asking either customers or merchants to make trust decisions about individual exchanges. Instead, they need only select the auditors. Auditors must sign all the exchange's keys including, the individual denomination keys. As we are dealing with financial transactions, we explicitly describe whenever entities need to safely write data to persistent storage. As long as the data persists, the protocol can be safely resumed at any step. Persisting data is cumulative, that is an additional persist operation does not erase the previously stored information. Keys and thus coins always have a well-known expiration date; information persisted 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. % FIXME: Auditor? $S_K$ denotes RSA signing with denomination key $K$ and EdDSA over elliptic curve $\mathbb{E}$ for other types of keys. $G$ denotes the generator of elliptic curve $\mathbb{E}$. \subsection{Withdrawal} To withdraw anonymous digital coins, the customer first selects an exchange and one of its public denomination public keys $K_p$ whose value $K_v$ corresponds to an amount the customer wishes to withdraw. We let $K_s$ denote the exchange's private key corresponding to $K_p$. We use $FDH_K$ to denote a full-domain hash where the domain is the public key $K_p$. Now the customer carries out the following interaction with the exchange: % FIXME: These steps occur at very different points in time, so probably % they should be restructured into more of a protocol description. % It does create some confusion, like is a reserve key semi-ephemeral % like a linking key? \begin{enumerate} \item The customer randomly generates: \begin{itemize} \item reserve key $W := (w_s,W_p)$ with private key $w_s$ and public key $W_p := w_sG$, \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 persists $\langle W, C, b \rangle$. \end{itemize} The customer then transfers an amount of money corresponding to at least $K_v$ to the exchange, with $W_p$ in the subject line of the transaction. \item The exchange receives the transaction and credits the reserve $W_p$ with the respective amount in its database. \item The customer computes $B := B_b(\FDH_K(C_p))$ and sends $S_W(B)$ 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 a Chaum-style blind signature $S_K(B)$ with private key $K_s$ to the customer. \\ 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 $\langle S_W(B), S_K(B) \rangle$ in its database for future reference, \item deducts the amount corresponding to $K$ from the reserve, \end{enumerate} and then sends $S_K(B)$ 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 the unblinded signature $U_b(S_K(B))$ and verifies that $S_K(\FDH_K(C_p)) = U_b(S_K(B))$. Finally the customer persists the coin $\langle S_K(\FDH_K(C_p)), c_s \rangle$ in their local wallet. \end{enumerate} \subsection{Exact and partial spending} A customer can spend coins at a merchant, under the condition that the merchant trusts the exchange that issued the coin. % FIXME: Auditor here? Merchants are identified by their public key $M_p$ which the customer's wallet learns through the merchant's Web page, which itself should be authenticated with X.509c. % FIXME: Is this correct? 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 $\widetilde{C} := S_K(\FDH_K(C_p))$ where $K$ is the exchange's denomination 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 $\vec{X} := \langle X_1, \ldots, X_n \rangle$ denote the list of exchanges accepted by the merchant where each $X_j$ is a exchange's public key. \item The merchant creates a signed contract $\mathcal{A} := S_M(m, f, a, H(p, r), \vec{X})$ where $m$ is an identifier for this transaction, $f$ is the price of the offer, and $a$ is data relevant to the contract indicating which services or goods the merchant will deliver to the customer, including the merchant specific URI for the payment. $p$ is the merchant's payment information (e.g. his IBAN number), and $r$ is a random nonce. The merchant persists $\langle \mathcal{A} \rangle$ and sends $\mathcal{A}$ to the customer. \item The customer should already possess a coin $\widetilde{C}$ issued by a exchange that is accepted by the merchant, meaning $K$ of $\widetilde{C}$ should be publicly signed by some $X_j$ from $\vec{X}$, and has a value $\geq f$. % \item Let $X_j$ be the exchange which signed $\widetilde{C}$ with $K$. The customer generates a \emph{deposit-permission} $$\mathcal{D} := S_c(\widetilde{C}, m, f, H(a), H(p,r), M_p)$$ and sends $\langle \mathcal{D}, X_j\rangle$ to the merchant. \label{step:first-post} \item The merchant gives $(\mathcal{D}, p, r)$ to the exchange, thereby 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 persists $\langle \mathcal{D} \rangle$ and signs a message affirming the deposit operation was successful. \item The merchant persists the response 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{step:first-post}, subsequent transactions with the same coin could be linked to this operation. 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 following 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 $\widetilde{C}$. To simplify the description, this section describes the case where one {\em unspent} dirty coin (for example, from an aborted transaction) is exchanged for a fresh coin of the same denomination. In practice, Taler uses a natural extension where multiple fresh coins of possibly many different denominations are generated at the same time. For this, the wallet simply specifies an array of coins wherever the protocol below specifies only a single coin. The different denominations of the fresh coins must be chosen by the wallet such that their value adds up to the remaining balance of the dirty coin. This way, refreshing enables giving precise change matching any amount, assuming the exchange offers an adequate value range in its denominations. In the protocol, $\kappa \ge 2$ is a security parameter for the cut-and-choose part of the protocol. $\kappa = 3$ is actually perfectly sufficient in most cases in practice, as the cut-and-choose protocol does not need to provide cryptographic security: If the maximum applicable tax is less than $\frac{2}{3}$, then $\kappa = 3$ ensures that cheating results in a negative financial return on average as $\kappa - 1$ out of $\kappa$ attempts to hide from taxation are detected and penalized by a total loss. This makes our use of cut-and-choose practical and efficient, and in particular faster than the comparable use of zk-SNARKs in ZeroCash~\cite{zerocash}. % FIXME: I'm explicit about the rounds in postquantum.tex \begin{enumerate} \item %[POST {\tt /refresh/melt}] For each $i = 1,\ldots,\kappa$, the customer randomly generates a transfer private key $t^{(i)}_s$ and computes \begin{enumerate} \item the transfer public key $T^{(i)}_p := t^{(i)}_s G$ and \item the new coin secret seed $L^{(i)} := H(c'_s T_p^{(i)})$. \end{enumerate} We have computed $L^{(i)}$ as a Diffie-Hellman shared secret between the transfer key pair $T^{(i)} := \left(t^{(i)}_s,T^{(i)}_p\right)$ and old coin key pair $C' := \left(c_s', C_p'\right)$; as a result, $L^{(i)} = H(t^{(i)}_s C'_p)$ also holds. Now the customer applies key derivation functions $\KDF_{\textrm{blinding}}$ and $\KDF_{\textrm{Ed25519}}$ to $L^{(i)}$ to generate \begin{enumerate} \item a blinding factor $b^{(i)} = \FDH_K(\KDF_{\textrm{blinding}}(L^{(i)}))$. \item $c_s^{(i)} = \KDF_{\textrm{Ed25519}}(L^{(i)})$ \end{enumerate} Now the customer can compute her new coin key pair $C^{(i)} := \left(c_s^{(i)}, C_p^{(i)}\right)$ where $C^{(i)}_p := c^{(i)}_s G$. The customer persists $\langle C', \vec{t}\rangle$ where $\vec{t} = \langle t^{(1)}_s, \ldots, t^{(\kappa)}_s \rangle$. We observe that $t^{(i)}_s$ suffices to regenerate $C^{(i)}$ and $b^{(i)}$ using the same key derivation functions. % \item The customer computes $B^{(i)} := B_{b^{(i)}}(\FDH_K(C^{(i)}_p))$ for $i \in \{1,\ldots,\kappa\}$ and sends a signed commitment $S_{C'}(\vec{B}, \vec{T_p})$ to the exchange. \item % [200 OK / 409 CONFLICT] The exchange generates a random $\gamma$ with $1 \le \gamma \le \kappa$ and marks $C'_p$ as spent by persisting $\langle C', \gamma, S_{C'}(\vec{B}, \vec{T_p}) \rangle$. Auditing processes should assure that $\gamma$ is unpredictable until this time to prevent the exchange from assisting tax evasion. \\ % The exchange sends $S_{K'}(C'_p, \gamma)$ to the customer where $K'$ is the exchange's message signing key, thereby committing the exchange to $\gamma$. \item % [POST {\tt /refresh/reveal}] The customer persists $\langle C', S_K(C'_p, \gamma) \rangle$. Also, the customer assembles $\mathfrak{R} := \left(t_s^{(i)}\right)_{i \ne \gamma}$ and sends $S_{C'}(\mathfrak{R})$ to the exchange. \item %[200 OK / 400 BAD REQUEST] % \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{L^{(i)}} :&= H(t_s^{(i)} C_p') \\ \overline{c_s^{(i)}} :&= \KDF_{\textrm{Ed25519}}(\overline{L^{(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)}} :&= \FDH_K(\KDF_{\textrm{blinding}}(\overline{L^{(i)}})) \\ \overline{B^{(i)}} :&= B_{\overline{b^{(i)}}}(\FDH_K\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[200 OK / 409 CONFLICT] % \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} % FIXME: Maybe explain why we don't need n-m refreshing? % FIXME: What are the privacy implication of not having n-m refresh? % What about the resulting number of large coins, doesn't this reduce the anonymity set? %\subsection{N-to-M Refreshing} % %TODO: Explain, especially subtleties regarding session key / the spoofing attack that requires signature. \subsection{Linking}\label{subsec:linking} % FIXME: What is \mathtt{link} ? For a coin that was successfully refreshed, the exchange responds to a request $S_{C'}(\mathtt{link})$ with $(T^{(\gamma)}_p, \widetilde{C})$. % This allows the owner of the melted coin to derive 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 secretly 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 mismatch 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 should 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 are 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{Experimental results} %\begin{figure}[b!] % \begin{subfigure}{0.45\columnwidth} % \includegraphics[width=\columnwidth]{bw_in.png} % \caption{Incoming traffic at the exchange, in bytes per 5 minutes.} % \label{fig:in} % \end{subfigure}\hfill % \begin{subfigure}{0.45\columnwidth} % \includegraphics[width=\columnwidth]{bw_out.png} % \caption{Outgoing traffic from the exchange, in bytes per 5 minutes.} % \label{fig:out} % \end{subfigure} % \begin{subfigure}{0.45\columnwidth} % \includegraphics[width=\columnwidth]{db_read.png} % \caption{DB read operations per second.} % \label{fig:read} % \end{subfigure} % \begin{subfigure}{0.45\columnwidth} % \includegraphics[width=\columnwidth]{db_write.png} % \caption{DB write operations per second.} % \label{fig:write} % \end{subfigure} % \begin{subfigure}{0.45\columnwidth} % \includegraphics[width=\columnwidth]{cpu_balance.png} % \caption{CPU credit balance. Hitting a balance of 0 shows the CPU is % the limiting factor.} % \label{fig:cpu} % \end{subfigure}\hfill % \begin{subfigure}{0.45\columnwidth} % \includegraphics[width=\columnwidth]{cpu_usage.png} % \caption{CPU utilization. The t2.micro instance is allowed to use 10\% of % one CPU.} % \label{fig:usage} % \end{subfigure} % \caption{Selected EC2 performance monitors for the experiment in the EC2 % (after several hours, once the system was ``warm'').} % \label{fig:ec2} %\end{figure} We ran the Taler exchange v0.0.2 on an Amazon EC2 t2.micro instance (10\% of a Xeon E5-2676 at 2.4 GHz) based on Ubuntu 14.04.4 LTS, using a db.t2.micro instance with Postgres 9.5 for the database. We used 1024-bit RSA keys for blind signatures, Curve25519 for DH, EdDSA for non-blind signatures and SHA-512 for hashing. For the KDF and FDH operations we used~\cite{rfc5869} with SHA-512 as XTR and SHA-256 for PRF as suggested in~\cite{rfc5869}. Using 16 concurrent clients performing withdraw, deposit and refresh operations we then pushed the t2.micro instance to the resource limit %(Figure~\ref{fig:cpu}) from a network with $\approx$ 160 ms latency to the EC2 instance. At that point, the instance managed about 8 HTTP requests per second, which roughly corresponds to one full business transaction (as a full business transaction is expected to involve withdrawing and depositing several coins). The network traffic was modest at approximately 50 kbit/sec from the exchange %(Figure~\ref{fig:out}) and 160 kbit/sec to the exchange. %(Figure~\ref{fig:in}). At network latencies above 10 ms, the delay for executing a transaction is dominated by the network latency, as local processing virtually always takes less than 10 ms. Database transactions are dominated by writes% %(Figure~\ref{fig:read} vs. Figure~\ref{fig:write}) , as Taler mostly needs to log transactions and occasionally needs to read to guard against double-spending. Given a database capacity of 2 TB---which should suffice for more than one year of full transaction logs---the described setup has a hosting cost within EC2 of approximately USD 252 per month, or roughly 0.0001 USD per full business transaction. This compares favorably to the $\approx$ USD 10 per business transaction for Bitcoin and the \EUR{0.35} plus 1.9\% charged by Paypal for domestic transfers within Germany. In the Amazon EC2 billing, the cost for the database (using SSD storage) dominates the cost with more than USD 243 per month. We note that these numbers are approximate, as the frontend and backend in our configuration uses systems from the AWS Free Usage Tier and is not perfectly balanced in between frontend and backend. Nevertheless, these experimental results show that computing-related business costs will only marginally contribute to the operational costs of the Taler payment system. \section{Discussion} \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} \label{sec:offline} Anonymous digital cash schemes since Chaum were frequently designed to allow the merchant to be offline during the transaction, by providing a means to deanonymize customers involved in double-spending. We consider this problematic as either the exchange or the merchant still requires an out-of-band means to recover funds from the customer, an expensive and unreliable proposition. Worse, there are unacceptable risks that a customer may accidentally deanonymize herself, 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, they 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 $10^{-2}$ 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 free software 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} We thank people (anonymized). %This work benefits from the financial support of the Brittany Region %(ARED 9178) and a grant from the Renewable Freedom Foundation. %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. \newpage \bibliographystyle{alpha} \bibliography{taler,rfc} %\vfill %\begin{center} % \Large Demonstration available at \url{https://demo.taler.net/} %\end{center} %\vfill \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 persisted 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[$X_j$]{Public key of a exchange (not used to sign coins)} \item[$\vec{X}$]{Vector of $X_j$ 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 $t^{(i)}_s$} \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[$L^{(i)}$]{Link secret derived from ECDH operation via hashing} % \item[$E_{L^{(i)}}()$]{Symmetric encryption using key $L^{(i)}$} % \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[$\overline{L^{(i)}}$]{Link secrets 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} \section{Taxability arguments} We assume the exchange operates honestly when discussing taxability. We feel this assumption is warratned mostly because a Taler exchange requires liscenses to operate as a financial institution, which it risks loosing if it knowingly facilitates tax evasion. We also expect an auditor monitors the exchange similarly to how government regulators monitor financial institutions. In fact, our auditor software component gives the auditor read access to the exchange's database, and carries out test operations anonymously, which expands its power over conventional auditors. \begin{proposition} Assuming the exchange operates the refresh protocol honestly, a customer operating the refresh protocol dishonestly expects to loose $1 - {1 \over \kappa}$ of the value of thei coins. \end{proposition} \begin{proof} An honest esxchange keeps any funds being refreshed if the reveal phase is never carried out, does not match the commitment, or shows an incorrect commitment. As a result, a customer dishonestly refreshing a coin looses their money if they have more than one dishonet commitment. They have a $1 \over \kappa$ chance of their dishonest commitment being selected for the refresh. \end{proof} We say a coin is {\em controlled} by a user if the user's wallet knows its secret scalar $c_s$, the signature $S$ of the appropriate denomination key on its public key $C_s$, and the residual value of the coin. We assume the wallet cannot loose knowledge of a particular coin's key material, and the wallet can query the exchange to learn the residual value of the coin, so a wallet cannot loose control of a coin. A wallet may loose the monetary value associated with a coin if another wallet spends it however. We say a user Alice {\em owns} a coin $C$ if only Alice's wallets can gain control of $C$ using standard interactions with the exchange. In other words, ownership means exclusive control not just in the present, but in the future even if another user interacts with the exchange. \begin{theorem} Let $C$ denote a coin controlled by users Alice and Bob. Suppose Bob creates a coin $C'$ from $C$ using the refresh protocol. Assuming the exchange and Bob operated the refresh protocol correctly, and that they continue to operate the linking protocol \S\ref{subsec:linking} correctly, then Alice can gain control of $C'$ using the linking protocol. \end{theorem} \begin{proof} Alice may run the linking protocol to obtain all transfer keys $T^i$, blindings $B^i$ associated to $C$, and those coins denominations, including the $T'$ for $C'$. We assumed both the exchange and Bob operated the refresh protocol correctly, so now $c_s T'$ is the seed from which $C'$ was generated. Alice rederives both $c_s$ and the blinding factor to unblind the denomination key signature on $C'$. Alice finally asks the exchange for the residual value on $C'$ and runs the linking protocol to determine if it was refreshed too. \end{proof} At a result, there is no way for a user to loose control over a coin, \section{Privacy arguments} The {\em linking problem} for blind signature is, if given coin creation transcrips and possibly fewer coin deposit transcripts for coins from the creation transcripts, then produce a corresponding creation and deposit transcript. We say a probabilistic polynomial time (PPT) adversary $A$ {\em links} coins if it has a non-negligable advantage in solving the linking problem, when given the private keys of the exchange. In Taler, there are two forms of coin creation transcrips, withdrawal and refresh. \begin{lemma} If there are no refresh operations, any adversary with an advantage in linking coins is polynomially equivelent to an advantage with the same advantage in recognizing blinding factors. \end{lemma} \begin{proof} Let $n$ denote the RSA modulous of the denomination key. Also let $d$ and $e$ denote the private and public exponents, respectively. In effect, coin withdrawal transcripts consist of numbers $b m^d \mod n$ where $m$ is the FDH of the coin's public key and $b$ is the blinding factor, while coin deposits transcripts consist of only $m^d \mon n$. Of course, if the adversary can link coins then they can compute the blinding factors as $b m^d / m^d \mod n$. Conversely, if the adversary can recognize blinding factors then they link coins after first computing $b_{i,j} = b_i m_i^d / m_j^d \mod n$ for all $i,j$. \end{proof} We now know the following because Taler used SHA512 adopted to be a FDH to breat the blinding factor. \begin{corollary} Assuming no refresh opeeration, any PPT adversary with an advantage for linking Taler coins gives rise to an adversary with an advantage for recognizing SHA512 output. \end{corollary} There was an earlier encryption-based version of the Taler protocol in which refresh operated consisted of $\kappa$ normal coin withdrawals encrypted using the secret $t^{(i)} C$ where $C = c G$ is the coin being refreshed and $T^{(i)} = t^{(i)} G$ is the transfer key. \begin{proposition} Assuming the encryption used is ??? secure, and that the independence of $c$, $t$, and the new coins key materials, then any PPT adversary with an advantage for linking Taler coins gives rise to an adversary with an advantage for recognizing SHA512 output. \end{proposition} We now apply \cite[??]{??} to deduce : \begin{theorem} In the random oracle model, any PPT adversary with an advantage in linking Taler coins has an advantage in breaking elliptic curve Diffie-Hellman key exchange on curve25519. \end{theorem} \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:} $\langle S_M(m, f), \vec{X} \rangle$ containing the price of the offer $f$, a transaction ID $m$ and the list of exchanges $\vec{X} = \langle X_1, \ldots, X_n \rangle$ accepted by the merchant, where each $X_j$ is an 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 $X_j$ 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 $\langle \mathcal{L}, X_j\rangle$ to the merchant, where $X_j$ 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 persists $\langle \mathcal{L} \rangle$ 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 persists $\langle \mathcal{A} \rangle$ and sends it to the customer. \item The customer creates a \emph{deposit-permission} $\mathcal{D} := S_c(\widetilde{C}, \widetilde{L}, f, m, M_p, H(a), H(p, r))$, persists $\langle \mathcal{A}, \mathcal{D} \rangle$ and sends $\mathcal{D}$ to the merchant. \item\label{invoice_paid2} The merchant persists the received $\langle \mathcal{D} \rangle$. \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, the exchange performs the following transaction: \begin{enumerate} \item $\langle \mathcal{D}, p, r \rangle$ is persisted. \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 ,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 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 "Speculation 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}