Mathematical Research for Blockchain Economy

The abilities of smart contracts today are confined to reading from their own state. It is useful for a smart contract to be able to react to events and read the state of other smart contracts. In this paper, we devise a mechanism by which a derivative smart contract can read data, observe the state evolution, and react to events that take place in one or more underlying smart contracts of its choice. Our mechanism works even if the underlying smart contract is not designed to operate with the derivative smart contract. Like in traditional finance, derivatives derive their value (and more generally state) through potentially complex dependencies. We show how derivative smart contracts can be deployed in practice on the Ethereum blockchain without any forks or additional assumptions. We leverage any NIPoPoWs mechanism (such as FlyClient or superblocks) to obtain succinct proofs for arbitrary events, making proving them inexpensive for users. The latter construction is of particular interest, as it forms the first introspective SPV client: an SPV client for Ethereum in Ethereum. Last, we describe applications of smart contract derivatives which were not possible prior to our work, in particular the ability to create decentralized insurance smart contracts which insure an underlying on-chain security such as an ICO, as well as futures and options.

With the advances in quantum computing taking place over the last few years, researchers have started considering the implications on cryptocurrencies. As most digital signature schemes would be impacted, it is somewhat reassuring that transition schemes to quantum resistant signatures are already being considered for Bitcoin. In this work, we stress the danger of public key reuse, as it prevents users from recovering their funds in the presence of a quantum enabled adversary despite any transition scheme the developers decide to implement. We emphasize this threat by quantifying the damage a functional quantum computer could inflict on Bitcoin (and Bitcoin Cash) by breaking exposed public keys.

We propose a novel modelling approach for the cryptocurrency ecosystem. We model on-chain and off-chain interactions as econophysical systems and employ methods from physical sciences to conduct interpretation of latent parameters describing the cryptocurrency ecosystem as well as to generate predictions. We work with an extracted dataset from the Ethereum blockchain which we combine with off-chain data from exchanges. This allows us to study a large part of the transaction flows related to the cryptocurrency ecosystem. From this aggregate system view we deduct that movements on the blockchain and price and trading action on exchanges are interrelated. The relationship is one directional: On-chain token flows towards exchanges have little effect on prices and trading volume, but changes in price and volume affect the flow of tokens towards the exchange.

Stress testing involves the use of simulation to assess the resilience of investment portfolios to changes in market regimes and extreme events. The quality of stress testing is a function of the realism of the market models employed, as well as the strategy used to determine the set of simulated scenarios. In this paper, we consider both of these parameters in the context of diversified portfolios, with a focus on the emerging class of cryptoasset-containing portfolios. Our analysis begins with univariate modelling of individual risk factors using ARMA and GJR–GARCH processes. Extreme Value Theory is applied to the tails of the standardised residuals distributions in order to account for extreme outcomes accurately. Next, we consider a family of copulas to represent the dependence structure of the individual risk factors. Finally, we combine the former approaches to generate a number of plausibility-constrained scenarios of interest, and simulate them to obtain a risk profile. We apply our methodology to the CoinShares Gold and Cryptoassets Index, a monthly-rebalanced index which comprises two baskets of risk-weighted assets: one containing gold and one containing cryptoassets. We demonstrate a superior risk-return profile as compared to investments in a traditional market-cap-weighted cryptoasset index.

We study selfish mining in Ethereum. The problem is combinatorially more complex than in Bitcoin because of major differences in the reward system and a different difficulty adjustment formula. Equivalent strategies in Bitcoin do have different profitabilities in Ethereum. The attacker can either broadcast his fork one block by one, or keep them secret as long as possible and publish them all at once at the end of an attack cycle. The first strategy is damaging for substantial hashrates, and we show that the second strategy is even worse. This confirms what we already proved for Bitcoin: Selfish mining is most of all an attack on the difficulty adjustment formula. We show that the current reward for signaling uncle blocks is a weak incentive for the attacker to signal blocks. We compute the profitabilities of different strategies and find out that for a large parameter space values, strategies that do not signal blocks are the best ones. We compute closed-form formulas for the apparent hashrates for these strategies and compare them. We use a direct combinatorial analysis with Dyck words to find these closed-form formulas.

Blockchain has the potential to accelerate the worldwide deployment of an emissions trading system (ETS) and improve the efficiency of existing systems. In this paper, we present a model for a permissioned blockchain implementation based on the successful European Union (EU) ETS and discuss its potential advantages over existing technology. The proposed ETS model is both backward compatible and future-proof, characterised by interconnectedness, transparency, tamper-resistance and continuous liquidity. Further, we identify key challenges to implementation of blockchain in ETS, as well as areas of future work required to enable a fully decentralised blockchain-based ETS.

Discrete event games are discrete time dynamical systems whose state transitions are discrete events caused by actions taken by agents within the game. The agents’ objectives and associated decision rules need not be known to the game designer in order to impose structure on a game’s reachable states. Mechanism design for discrete event games is accomplished by declaring desirable invariant properties and restricting the state transition functions to conserve these properties at every point in time for all admissible actions and for all agents, using techniques familiar from state-feedback control theory. Building upon these connections to control theory, a framework is developed to equip these games with estimation properties of signals which are private to the agents playing the game. Token bonding curves are presented as discrete event games and numerical experiments are used to investigate their signal processing properties with a focus on input-output response dynamics.

Collateral employed in cryptoeconomic protocols protects against the misbehavior of economically rational agents, compensating honest users for damages and punishing misbehaving parties. The introduction of collateral, however, carries three disadvantages: (i) requiring agents to lock up substantial amount of collateral can be an entry barrier, limiting the set of candidates to wealthy agents; (ii) affected agents incur ongoing opportunity costs as the collateral cannot be utilized elsewhere; and (iii) users wishing to interact with an agent on a frequent basis (e.g., with a service provider to facilitate second-layer payments), have to ensure the correctness of each interaction individually instead of subscribing to a service period in which interactions are secured by the underlying collateral. We present Promise, a subscription mechanism to decrease the initial capital requirements of economically rational service providers in cryptoeconomic protocols. The mechanism leverages future income (such as service fees) prepaid by users to reduce the collateral actively locked up by service providers, while sustaining secure operation of the protocol. Promise is applicable in the context of multiple service providers competing for users. We provide a model for evaluating its effectiveness and argue its security. Demonstrating Promise’s applicability, we discuss how Promise can be integrated into a cross-chain interoperability protocol, XCLAIM, and a second-layer scaling protocol, NOCUST. Last, we present an implementation of the protocol on Ethereum showing that all functions of the protocol can be implemented in constant time complexity and Promise only adds USD 0.05 for a setup per user and service provider and USD 0.01 per service delivery during the subscription period.

In the Ethereum network, miners are incentivized to include transactions in a block depending on the gas price specified by the sender. The sender of a transaction therefore faces a trade-off between timely inclusion and cost of his transaction. Existing recommendation mechanisms aggregate recent gas price data on a per-block basis to suggest a gas price. We perform an empirical analysis of historic block data to motivate the use of a predictive model for gas price recommendation. Subsequently, we propose a novel mechanism that combines a deep-learning based price forecasting model as well as an algorithm parameterized by a user-specific urgency value to recommend gas prices. In a comprehensive evaluation on real-world data, we show that our approach results on average in costs savings of more than 50% while only incurring an inclusion delay of 1.3 blocks, when compared to the gas price recommendation mechanism of the most widely used Ethereum client.