Mathematical Research for Blockchain Economy

This work targets unfairness in Nakamoto, Bitcoin’s distinguished permissionless consensus protocol, towards miners with relatively small computational powers, and miners which participate during relatively unrewarding mining periods. We propose a set of computationally-grounded metrics for measuring miner expenditures, miner compensation, and coin value. Using our metrics, we quantitatively bring to light the sources of inequity in Nakamoto using Bitcoin as a real-world example. Furthermore, we propose a set of reward issuance constraints for mining incentive mechanisms to achieve equitable rewards, and argue for the efficacy of applying our constraints.

We examine vote delegation on blockchains where preferences of agents are private information. One group of agents (delegators) does not want to participate in voting and either abstains under conventional voting or can delegate its votes to a second group (voters) who decides between two alternatives. We show that free delegation favors minorities, that is, alternatives that have a lower chance of winning ex-ante. The same occurs if the number of voting rights that actual voters can exert is capped. When the number of delegators increases, the probability that the ex-ante minority wins under free and capped delegation converges to the one under conventional voting—albeit non-monotonically.

We model incentive security in non-custodial stablecoins and derive conditions for participation in a stablecoin system across risk absorbers (vaults/CDPs) and holders of governance tokens. We apply option pricing theory to derive closed form solutions to the stakeholders’ problems, and to value their positions within the capital structure of the stablecoin. We derive the optimal interest rate that is incentive compatible, as well as conditions for the existence of equilibria without governance attacks, and discuss implications for designing secure protocols.

We revisit the standard game-theoretic model of blockchain mining and identify two sources of instabilities for its unique Nash equilibrium. In our first result, we show that griefing, a practice according to which participants of peer-to-peer networks harm other participants at some lesser cost to themselves, is a plausible threat that may lead cost-efficient miners to allocate more resources than predicted. The proof relies on the evaluation of griefing factors, ratios that measure network losses relative to an attacker’s own losses and leads to a generalization of the notion of evolutionary stability to non-homogeneous populations which may be of independent game-theoretic interest. From a practical perspective, this finding provides explains the over-dissipation of mining resources, consolidation of power and high entry barriers that are currently observed in many mining networks. We, then, turn to the natural question of whether dynamic adjustments of mining allocations may, in fact, lead to the Nash equilibrium prediction. By studying two common learning rules, gradient ascent and best response dynamics, we provide evidence for the contrary. Thus, along with earlier results regarding in-protocol attacks, these findings paint a more complete picture about the various inherent instabilities of permissionless mining networks.

In this paper, we use a variety of machine learning methods to quantify the extent to which economic and technological factors are predictive of the progression of Central Bank Digital Currencies (CBDC) within a country, using as our measure of this progression the CBDC project index (CBDCPI). By extracting and aggregating cross country data provided by several international organisations, we find that the financial development index is the most important feature for our model, followed by the GDP per capita and an index of the voice and accountability of the country’s population. Our results are consistent with previous qualitative research which finds that countries with a high degree of financial development or digital infrastructure have more developed CBDC projects. Further, we obtain robust results when predicting the CBDCPI at different points in time.

The meteoric rise of Decentralized Finance (DeFi) has been accompanied by a number of financially devastating attacks on its protocols. There have been over 70 exploits of DeFi protocols, with the total of lost funds amounting to approximately 1.5bn USD. In this paper, we introduce a new approach to minimizing the frequency and severity of such attacks: dissimilar redundancy for smart contracts. In a nutshell, the idea is to implement a program logic more than once, ideally using different programming languages. Then, for each implementation, the results should match before allowing the state of the blockchain to change. This is inspired by and has clear parallels to the field of avionics, where on account of the safety-critical environment, flight control systems typically feature multiple redundant implementations. We argue that the high financial stakes in DeFi protocols merit a conceptually similar approach, and we provide a novel algorithm for implementing dissimilar redundancy for smart contracts.

We propose a decentralized finance (DeFi) survival analysis approach for discovering and characterizing user behavior and risks in lending protocols. We demonstrate how to gather and prepare DeFi transaction data for survival analysis. We demonstrate our approach using transactions in AAVE, one of the largest lending protocols. We develop a DeFi survival analysis pipeline which first prepares transaction data for survival analysis through the selection of different index events (or transactions) and associated outcome events. Then we apply survival analysis statistical and visualization methods such as median survival times, Kaplan–Meier survival curves, and Cox hazard regression to gain insights into usage patterns and risks within the protocol. We show how by varying the index and outcome events, we can utilize DeFi survival analysis to answer three different questions. What do users do after a deposit? How long until borrows are first repaid or liquidated? How does coin type influence liquidation risk? The proposed DeFi survival analysis can easily be generalized to other DeFi lending protocols. By defining appropriate index and outcome events, DeFi survival analysis can be applied to any cryptocurrency protocol with transactions.

In recent years, we have witnessed a dramatic increase in the adoption and application of smart contracts in a variety of contexts. However, security vulnerabilities pose a significant challenge to the continued adoption of smart contracts. An important and pervasive class of security vulnerabilities that afflicts Ethereum smart contracts is the gas limit DoS on a contract via unbounded operations. These vulnerabilities result in a failed transaction with an “out-of-gas” error and are often present in contracts containing loops whose bounds are affected by end-user input. To address this issue, we present Gas Gauge, a tool aimed at detecting Out-of-Gas DoS vulnerabilities in Ethereum smart contracts. The Gas Gauge tool has three major components: The Detection Phase, Identification Phase, and Correction Phase. The Detection Phase component consists of an accurate static analysis approach that finds and summarizes all the loops in a smart contract. The Identification Phase component uses a white-box fuzzing approach to generate a set of inputs that causes the contract to run out of gas. Lastly, the Correction Phase component uses static analysis and run-time verification to predict the maximum loop bounds consistent with allowable gas usage and suggest appropriate repairs to the tool’s users. Each part of Gas Gauge can be used separately or all together to detect, identify and help repair contracts vulnerable to Out-of-Gas DoS vulnerabilities. Gas Gauge was tested on 1,000 real-world solidity smart contracts. When compared to seven state-of-the-art tools, we show that Gas Gauge is the most effective (i.e., has no false positives and false negatives) while being competitive in terms of efficiency.

Recently, Chaum et al. (ACNS’21) introduced \(\mathcal {S}_{\text{ leeve }}\), which describes an extra security layer for signature schemes, i.e., ECDSA. This distinctive feature is a new key generation mechanism, allowing users to generate a “back up key” securely nested inside the secret key of a signature scheme. Using this novel construction, the “back up key”, which is secret, can be used to generate a “proof of ownership”, i.e., only the rightful owner of this secret key can generate such a proof. This design offers a quantum secure fallback, i.e., a brand new quantum resistant signature, ready to be used, nested in the ECDSA secret key. In this work, we rely on the original \(\mathcal {S}_{\text{ leeve }}\) definition to generalize the construction to a modular design based on Tweakable Hash Functions, thus yielding a cleaner design of the primitive. Furthermore, we provide a thorough security analysis taking into account the security of the ECDSA signature scheme, which is lacking in the original work. Finally, we provide an analysis based on formal methods using Verifpal assuring the security guarantees our construction provides.

Distributed ledger are maintained through consensus protocols which have inherent limitations to their scalability. Layer-2 protocols operate on channels and allow parties to interact with another without going through the consensus protocol albeit relying on its security as fall-back. Channels can be concatenated into networks using techniques such as Hash Timelock Contracts (HTLC) to execute payments or virtual state channels as introduced by Dziembowski et al. [CCS’18] to execute state machines across a path of channels. This is realized by utilizing intermediaries, which are the parties on the channel path between both endpoints, who have to pay collateral to ensure security of the constructions. Dziembowski et al. [Eurocrypt’19] introduced multi-party state channels based on a virtual channel construction and more recently Hydra heads [FC’21] is a channel construction that allows multiple parties the execution of Constraint Emitting Machines (CEM). While existing protocols such as HTLCs can be extended such that two parties can interact with another across channels, there are no dedicated constructions that utilize multi-party channels and similarly allow more than two parties to interact across a network of channels. This work addresses this gap by extending Hydra and introducing the Interhead construction that allows for the iterative creation of virtual Hydra heads. Our construction is the first that (1) supports and utilizes multi-party channels and (2) allows for collateral to be paid by multiple intermediaries.

This paper compares mathematical models for automated market makers (AMM) including logarithmic market scoring rule (LMSR), liquidity sensitive LMSR (LS-LMSR), constant product/mean/sum, and others. It is shown that though LMSR may not be a good model for Decentralized Finance (DeFi) applications, LS-LMSR has several advantages over constant product/mean based AMMs. This paper proposes and analyzes constant ellipse based cost functions for AMMs. The proposed cost functions are computationally efficient (only requires multiplication and square root calculation) and have certain advantages over widely deployed constant product cost functions. For example, the proposed market makers are more robust against slippage based front running attacks. In addition to the theoretical advantages of constant ellipse based cost functions, our implementation shows that if the model is used as a cryptographic property swap tool over Ethereum blockchain, it saves up to 46.88% gas cost against Uniswap V2 and saves up to 184.29% gas cost against Uniswap V3 which has been launched in April 2021. The source codes related to this paper are available at https://​github.​com/​coinswapapp and the prototype of the proposed AMM is available at http://​coinswapapp.​io/​.

Curve Finance invented the first stableswap-focused algorithm. However, its algorithm involves (1) solving complex polynomials and (2) requiring assets in the pool to have the same size of liquidity. This paper introduces a new stableswap algorithm–Wombat, to address these issues. Wombat uses a closed-form solution, so it is more gas efficient and adds the concept of asset-liability management to enable single-side liquidity provision, which increases capital efficiency. Furthermore, we derive efficient algorithms from calculating withdrawal or deposit fees as an arbitrage block. Wombat is named after the short-legged, muscular quadrupedal marsupials native to Australia. As Wombats are adaptable and habitat-tolerant animals, the invariant created is also adaptable and tolerant to liquidity changes.

Data cooperatives allow their members—the data owners—to pool their digital assets together for processing and access management. In this context, reputation is an important measure of trust, which can effectively complement financial assets in the decentralized scenario, also providing incentives for users’ honest behavior. We present a decentralized data cooperative system based on the Proof-of-Reputation and Proof-of-Stake blockchains. In order to provide inclusivity for low-reputation (newly joined) users, which is required in our community-based scenario, we use the tier-based committee selection introduced by Kleinrock et al. at Indocrypt 2020. As the underlying Proof-of-Stake system, we use Snow White due to its convenient properties such as flexible committee selection and user participation.