Mathematical Research for Blockchain Economy

Payment channel networks (PCNs) are a layer-2 blockchain scalability solution, with its main entity, the payment channel, enabling transactions between pairs of nodes “off-chain,” thus reducing the burden on the layer-1 network. Nodes with multiple channels can serve as relays for multihop payments by providing their liquidity and withholding part of the payment amount as a fee. Relay nodes might after a while end up with one or more unbalanced channels, and thus need to trigger a rebalancing operation. In this paper, we study how a relay node can maximize its profits from fees by using the rebalancing method of submarine swaps. We introduce a stochastic model to capture the dynamics of a relay node observing random transaction arrivals and performing occasional rebalancing operations, and express the system evolution as a Markov Decision Process. We formulate the problem of the maximization of the node’s fortune over time over all rebalancing policies, and approximate the optimal solution by designing a Deep Reinforcement Learning (DRL)-based rebalancing policy. We build a discrete event simulator of the system and use it to demonstrate the DRL policy’s superior performance under most conditions by conducting a comparative study of different policies and parameterizations. Our work is the first to introduce DRL for liquidity management in the complex world of PCNs.

Many protocols in distributed computing rely on a source of randomness, usually called a random beacon, both for their applicability and security. This is especially true for proof-of-stake blockchain protocols in which the next miner or set of miners have to be chosen randomly and each party’s likelihood to be selected is in proportion to their stake in the cryptocurrency. The chosen miner is then allowed to add a block to the chain. Current random beacons used in proof-of-stake protocols, such as Ouroboros and Algorand, have two fundamental limitations: Either (i) they rely on pseudorandomness, e.g. assuming that the output of a hash function is uniform, which is a widely used but unproven assumption, or (ii) they generate their randomness using a distributed protocol in which several participants are required to submit random numbers which are then used in the generation of a final random result. However, in this case, there is no guarantee that the numbers provided by the parties are uniformly random and there is no incentive for the parties to honestly generate uniform randomness. Most random beacons have both limitations. In this work, we provide a protocol for distributed generation of randomness. Our protocol does not rely on pseudorandomness at all. Similar to some of the previous approaches, it uses random inputs by different participants to generate a final random result. However, the crucial difference is that we provide a game-theoretic guarantee showing that it is in everyone’s best interest to submit uniform random numbers. Hence, our approach is the first to incentivize honest behavior instead of just assuming it. Moreover, the approach is trustless and generates unbiased random numbers. It is also tamper-proof and no party can change the output or affect its distribution. Finally, it is designed with modularity in mind and can be easily plugged into existing distributed protocols such as proof-of-stake blockchains.

We design and analyze attention games that incentivize validators to check computation results. We show that no pure strategy Nash equilibrium of the game without outside parties exists by a simple argument. We then proceed to calculate the security of the system in the mixed Nash equilibrium, as a function of the number of validators and their stake sizes. Our results provide lower and upper bounds on the optimal number of validators. More concretely, a minimal feasible number of validators minimizes the probability of failure. The framework also allows to calculate optimum stake sizes, depending on the target function. In the end, we discuss optimal design of rewards by the protocol for validators.

The emerging decentralized financial ecosystem (DeFi) is comprised of numerous protocols, one type being lending protocols. People make transactions in lending protocols, each of which is attributed to a specific blockchain address which could represent an externally-owned account (EOA) or a smart contract. Using Aave, one of the largest lending protocols, we summarize the transactions made by each address in each quarter from January 1, 2021, through December 31, 2022. We cluster these quarterly summaries to identify and name common patterns of quarterly behavior in Aave. We then use these clusters to glean insights into the dominant behaviors in Aave. We show that there are three kinds of keepers, i.e., a specific type of users tasked with the protocol’s governance, but only one kind of keeper finds consistent success in making profits from liquidations. We identify the largest-scale accounts in Aave and the highest-risk kinds of behavior on the platform. Additionally, we use the temporal aspect of the clusters to track how common behaviors change through time and how usage has shifted in the wake of major events that impacted the crypto market, and we show that there seem to be problems with user retention in Aave as many of the addresses that perform transactions do not remain in the market for long.

The ecosystem around blockchain and Decentralized Finance (DeFi) is seeing more and more interest from centralized regulators. For instance, recently, the US government placed sanctions on the largest DeFi mixer, Tornado.Cash (TC). To our knowledge, this is the first time that centralized regulators sanction a decentralized and open-source blockchain application. It has led various blockchain participants, e.g., miners/validators and DeFi platforms, to censor TC-related transactions. The blockchain community has extensively discussed that censoring transactions could affect users’ privacy. In this work, we analyze the efficiency and possible security implications of censorship on the different steps during the life cycle of a blockchain transaction, i.e., generation, propagation, and validation. We reveal that fine-grained censorship will reduce the security of block validators and centralized transaction propagation services, and can potentially cause Denial of Service (DoS) attacks. We also find that DeFi platforms adopt centralized third-party services to censor user addresses at the frontend level, which blockchain users could easily bypass. Moreover, we present a tainting attack whereby an adversary can prevent users from interacting normally with DeFi platforms by sending TC-related transactions.

The always-available liquidity of automated market makers (AMMs) has been one of the most important catalysts in early cryptocurrency adoption. However, it has become increasingly evident that AMMs in their current form are not viable investment options for passive liquidity providers. This is large part due to the cost incurred by AMMs providing stale prices to arbitrageurs against external market prices, formalized as loss-versus-rebalancing (LVR) (Milionis et al. 2022). In this paper, we present Diamond, an automated market making protocol that aligns the incentives of liquidity providers and block producers in the protocol-level retention of LVR. In Diamond, block producers effectively auction the right to capture any arbitrage that exists between the external market price of a Diamond pool, and the price of the pool itself. The proceeds of these auctions are shared by the Diamond pool and block producer in a way that is proven to remain incentive compatible for the block producer. Given the participation of competing arbitrageurs to capture LVR, LVR is minimized in Diamond. We formally prove this result, and detail an implementation of Diamond. We also provide comparative simulations of Diamond to relevant benchmarks, further evidencing the LVR-protection capabilities of Diamond. With this new protection, passive liquidity provision on blockchains can become rationally viable, beckoning a new age for decentralized finance.

For a mining strategy we define “profit lag” as the minimum time it takes to be profitable after that moment. We compute closed forms for the profit lag and the revenue ratio for the strategies “selfish mining” and “intermittent selfish mining”. This corroborates prior numerical simulations and provides further elucidation regarding the issue of profitability as discussed in the existing literature. We also study mining pairs of PoW cryptocurrencies, often coming from a fork, with the same mining algorithm. This represents a vector of attack that can be exploited using the “alternate network mining” strategy that we define. We compute closed forms for the profit lag and the revenue ratio for this strategy that is more profitable than selfish mining and intermittent selfish mining. It is also harder to counter since it does not rely on a flaw in the difficulty adjustment formula that is the reason for profitability of the other strategies.

We investigate the theoretical and empirical relationships between activity in on-chain markets and pricing in off-chain cryptocurrency markets (e.g., ETH/USD prices). The motivation is to develop methods for proxying off-chain market data using data and computation that is in principle verifiable on-chain and could provide an alternative approach to blockchain price oracles. We explore relationships in PoW mining, PoS validation, block space markets, network decentralization, usage and monetary velocity, and on-chain Automated Market Makers (AMMs). We select key features from these markets, which we analyze through graphical models, mutual information, and ensemble machine learning models to explore the degree to which off-chain pricing information can be recovered entirely on-chain. We find that a large amount of pricing information is contained in on-chain data, but that it is generally hard to recover precise prices except on short time scales of retraining the model. We discuss how even noisy information recovered from on-chain data could help to detect anomalies in oracle-reported prices on-chain.

This research proposes a methodology which can be used for measuring governance decentralization in a Decentralized Autonomous Organization (DAO). DAOs, commonly, have the ambition to become more decentralized as time progresses. Such ambitions led to the creation of decentralized governance models that use governance tokens to represent voting power. Relevant research suggests that the distribution of the governance tokens follows centralized accumulations in a few wallets. By studying the accumulations of voting power from a DeFi protocol, this research presents a framework for identifying and measuring decentralization via analyzing all the various governance sub-systems instead of focusing on one or a small group. Governance within a DAO is a multi-layered process. By examining the decentralization of each layer or subsystem within the overarching governance structure, we can compose a comprehensive understanding of the entire protocol. To demonstrate this method, this paper uses the Compound Finance protocol as a case study. The first sub-system that this research discusses is the delegated and self-delegated wallets which are the only entities that can participate in the voting process in the Compound platform. The second sub-system is the actual proposals and votes that have taken place in the protocol’s governance. Data is derived directly from the protocol’s web data and for two time periods.

In this paper, we propose the modelling of patterns of financial transactions - with a focus on the domain of cryptocurrencies - as splittings and present a method for generating such splittings utilizing integer partitions. We further exemplify that, by having these partitions fulfill certain criteria derived from financial policies, the splittings generated from them can be used for modelling illicit transactional behavior as seen in smurfing.

The prosperous development of Ethereum has bred many illegal activities by malefactors, such as Ponzi schemes, theft of funds from exchanges, and attacks on service providers. Aiming to expedite the realization of their gains, criminals will launder illicit money, making it as difficult as possible for security companies or agencies to recover those illicit funds. In this paper, we focus on a typical security event on Upbit exchange and explore the scale of the gang behind the security event. Specifically, We construct a rough suspicious money laundering transaction network by crawling downstream transactions of 815 accounts marked as Upbit hacks. Then, in order to refine a more accurate gang of Upbit hacks, we design a suspiciousness indicator for money laundering and modify an existing general risk assessment framework based on propagation models to assess the money laundering risk of accounts. Based on the risks, we acquire an accurate gang for Upbit hacks. In the end, we find that the size of the Upbit hack gang is much bigger than we thought. We also present several interesting analyses of the Upbit hack gang.