Anonymous systems (e.g. anonymous cryptocurrencies and updatable anonymous credentials) often follow a construction template where an account can only perform a single anonymous action, which in turn potentially spawns new (and still single-use) accounts (e.g. UTXO with a balance to spend or session with a score to claim). Due to the anonymous nature of the action, no party can be sure which account has taken part in an action and, therefore, must maintain an ever-growing list of potentially unused accounts to ensure that the system keeps running correctly. Consequently, anonymous systems constructed based on this common template are seemingly not sustainable. In this work, we study the sustainability of ring-based anonymous systems, where a user performing an anonymous action is hidden within a set of decoy users, traditionally called a “ring”. On the positive side, we propose a general technique for ring-based anonymous systems to achieve sustainability. Along the way, we define a general model of decentralised anonymous systems (DAS) for arbitrary anonymous actions, and provide a generic construction which provably achieves sustainability. As a special case, we obtain the first construction of anonymous cryptocurrencies achieving sustainability without compromising availability. We also demonstrate the generality of our model by constructing sustainable decentralised anonymous social networks. On the negative side, we show empirically that Monero, one of the most popular anonymous cryptocurrencies, is unlikely to be sustainable without altering its current ring sampling strategy. The main subroutine is a sub-quadratic-time algorithm for detecting used accounts in a ring-based anonymous system.

Bitcoin and other cryptocurrencies have recently introduced support for Schnorr signatures whose cleaner algebraic structure, as compared to ECDSA, allows for simpler and more practical constructions of highly demanded ''t-of-n'' threshold signatures. However, existing Schnorr threshold signature schemes still fall short of the needs of real-world applications due to their assumption that the network is synchronous and due to their lack of robustness, i.e., the guarantee that t honest signers are able to obtain a valid signature even in the presence of other malicious signers who try to disrupt the protocol. This hinders the adoption of threshold signatures in the cryptocurrency ecosystem, e.g., in second-layer protocols built on top of cryptocurrencies.

In recent years, cryptocurrencies have increasingly been used in cybercrime and have become the key means of payment in darknet marketplaces, partly due to their alleged anonymity. Furthermore, the research attacking the anonymity of even those cryptocurrencies that claim to offer anonymity by design is growing and is being applied by law enforcement agencies in the fight against cybercrime. Their investigative measures require a certain degree of suspicion and it is unclear whether findings resulting from attacks on cryptocurrencies’ anonymity can indeed establish that required degree of suspicion. The reason for this is that these attacks are partly based upon uncertain assumptions which are often not properly addressed in the corresponding papers. To close this gap, we extract the assumptions in papers that are attacking Bitcoin, Monero and Zcash, major cryptocurrencies used in darknet markets which have also received the most attention from researchers. We develop a taxonomy to capture the different nature of those assumptions in order to help investigators to better assess whether the required degree of suspicion for specific investigative measures could be established. We found that assumptions based on user behaviour are in general the most unreliable and thus any findings of attacks based on them might not allow for intense investigative measures such as pre-trial detention. We hope to raise awareness of the problem so that in the future there will be fewer unlawful investigations based upon uncertain assumptions and thus fewer human rights violations.

In a ring-signature-based anonymous cryptocurrency, signers of a transaction are hidden among a set of potential signers, called a ring, whose size is much smaller than the number of all users. The ringmembership relations specified by the sets of transactions thus induce bipartite transaction graphs, whose distribution is in turn induced by the ring sampler underlying the cryptocurrency. Since efficient graph analysis could be performed on transaction graphs to potentially deanonymise signers, it is crucial to understand the resistance of (the transaction graphs induced by) a ring sampler against graph analysis. Of particular interest is the class of partitioning ring samplers. Although previous works showed that they provide almost optimal local anonymity, their resistance against global, e.g. graph-based, attacks were unclear. In this work, we analyse transaction graphs induced by partitioning ring samplers. Specifically, we show (partly analytically and partly empirically) that, somewhat surprisingly, by setting the ring size to be at least logarithmic in the number of users, a graph-analysing adversary is no better than the one that performs random guessing in deanonymisation up to constant factor of 2.

In the past few years blockchains have been a major focus for security research, resulting in significant progress in the design, formalization, and analysis of blockchain protocols. However, the more general class of distributed ledgers, which includes not just blockchains but also prominent non-blockchain protocols, such as Corda and OmniLedger, cannot be covered by the state-of-the-art in the security literature yet. These distributed ledgers often break with traditional blockchain paradigms, such as block structures to store data, system-wide consensus, or global consistency. In this paper, we close this gap by proposing the first framework for defining and analyzing the security of general distributed ledgers, with an ideal distributed ledger functionality, called Fledger, at the core of our contribution. This functionality covers not only classical blockchains but also non-blockchain distributed ledgers in a unified way. To illustrate Fledger, we first show that the prominent ideal block-chain functionalities Gledger and GPL realize (suitable instantiations of) Fledger, which captures their security properties. This implies that their respective implementations, including Bitcoin, Ouroboros Genesis, and Ouroboros Crypsinous, realize Fledger as well. Secondly, we demonstrate that Fledger is capable of precisely modeling also non-blockchain distributed ledgers by performing the first formal security analysis of such a distributed ledger, namely the prominent Corda protocol. Due to the wide spread use of Corda in industry, in particular the financial sector, this analysis is of independent interest. These results also illustrate that Fledger not just generalizes the modular treatment of blockchains to distributed ledgers, but moreover helps to unify existing results.

A ring signature scheme allows the signer to sign on behalf of an ad hoc set of users, called a ring. The verifier can be convinced that a ring member signs, but cannot point to the exact signer. Ring signatures have become increasingly important today with their deployment in anonymous cryptocurrencies. Conventionally, it is implicitly assumed that all ring members are equally likely to be the signer. This assumption is generally false in reality, leading to various practical and devastating deanonymizing attacks in Monero, one of the largest anonymous cryptocurrencies. These attacks highlight the unsatisfactory situation that how a ring should be chosen is poorly understood.

In their celebrated work, Groth and Sahai [EUROCRYPT'08, SICOMP' 12] constructed non-interactive zero-knowledge (NIZK) proofs for general bilinear group arithmetic relations, which spawned the entire subfield of structure-preserving cryptography. This branch of the theory of cryptography focuses on modular design of advanced cryptographic primitives. Although the proof systems of Groth and Sahai are a powerful toolkit, their efficiency hits a barrier when the size of the witness is large, as the proof size is linear in that of the witness. In this work, we revisit the problem of proving knowledge of general bilinear group arithmetic relations in zero-knowledge. Specifically, we construct a succinct zero-knowledge argument for such relations, where the communication complexity is logarithmic in the integer and source group components of the witness. Our argument has public-coin setup and verifier and can therefore be turned non-interactive using the Fiat-Shamir transformation in the random oracle model. For the special case of non-bilinear group arithmetic relations with only integer unknowns, our system can be instantiated in non-bilinear groups. In many applications, our argument system can serve as a drop-in replacement of Groth-Sahai proofs, turning existing advanced primitives in the vast literature of structure-preserving cryptography into practically efficient systems with short proofs.

Monero is the largest cryptocurrency with built-in cryptographic privacy features. The transactions are authenticated using zero-knowledge spend proofs, which provide a certain level of anonymity by hiding the source accounts from which the funds are sent among a set of other accounts. Due to its similarities to ring signatures, this core cryptographic component is called Ring Confidential Transactions (RingCT). Because of its practical relevance, several works attempt to analyze the security of RingCT. Since RingCT is rather complex, most of them are either informal, miss fundamental functionalities, or introduce undesirable trusted setup assumptions. Regarding efficiency, Monero currently deploys a scheme in which the size of the spend proof is linear in the ring size. This limits the ring size to only a few accounts, which in turn limits the acquired anonymity significantly and facilitates de-anonymization attacks. As a solution to these problems, we present the first rigorous formalization of RingCT as a cryptographic primitive. We then propose a generic construction of RingCT and prove it secure in our formal security model. By instantiating our generic construction with new efficient zero-knowledge proofs, we obtain Omniring, a fully-fledged RingCT scheme in the discrete logarithm setting that provides the highest concrete and asymptotic efficiency as of today. Omniring is the first RingCT scheme which 1) does not require a trusted setup or pairing-friendly elliptic curves, 2) has a proof size logarithmic in the size of the ring, and 3) allows to share the same ring between all source accounts in a transaction, thereby enabling significantly improved privacy level without sacrificing performance. Our zero-knowledge proofs rely on novel enhancements to the Bulletproofs framework (S&P 2018), which we believe are of independent interest.