Abstract The traditional Byzantine quorum-system model assumes a pre-existing, global agreement on the set of quorums (typically defined as the sets consisting of more than two-thirds of the participants). This assumption is problematic in permissionless systems, which strive to allow anyone to join or leave the system dynamically. While proof-of-stake permissionless systems like Ethereum require newly joining participants to register into the system, other permissionless systems like the Ripple Ledger or the Stellar network allow participants to join the system without synchronization by forgoing agreement on the set of quorums. This results in what we call a heterogeneous quorum system, where each participant has its own, personal set of quorums. An important question is to determine under what condition is it possible to solve synchronization problems like reliable broadcast or consensus in a heterogeneous quorum system. In this work, we show that the traditional quorum intersection and quorum availability conditions are not sufficient in heterogeneous quorum systems. Moreover, we propose quorum subsumption, a new condition which, together with quorum availability and quorum intersection, is sufficient to allow solving reliable broadcast and consensus. Finally, we propose protocols for reliable broadcast and consensus in heterogeneous quorum systems that satisfy quorum subsumption. In particular, we present a practical consensus protocol called Satrapy which in contrast to abstract consensus protocols uses finite state and messages.

Optimistic replication of objects avoids coordination and brings higher responsiveness and availability. However, when clients issue concurrent operations, conflicts naturally arise which can lead the replicated states to diverge or lose integrity. When conflicts occur, existing approaches resort to pessimism or abortion. This paper characterizes ORDTs (Optimistically Replicated Data Types), objects that can be optimistically replicated with convergence and integrity, and without aborting calls. It shows that ORDTs subsume CRDTs and transformed relational schema, and presents techniques to convert objects to ORDTs. It further proves that optimistic replication for objects that fall out of ORDTs is aborting and NP-Complete. Further, it presents an optimistic replication protocol for ORDTs called Frashokereti . It uses a statically decided order to efficiently order calls. The paper proves that Frashokereti is sound for every ORDT, i.e., Frashokereti is optimistic and non-aborting, and preserves convergence, integrity, and liveness properties. Experimental results show that Frashokereti significantly outperforms previous optimistic protocols.

Extreme valuation and volatility of cryptocurrencies require investors to diversify often which demands secure exchange protocols. A cross-chain swap protocol allows distrusting parties to securely exchange their assets. However, the current models and protocols assume predefined user preferences for acceptable outcomes. This paper presents a generalized model of swaps that allows each party to specify its preferences on the subsets of its incoming and outgoing assets. It shows that the existing swap protocols are not necessarily a strong Nash equilibrium in this model. It characterizes the class of swap graphs that have protocols that are safe, live and a strong Nash equilibrium, and presents such a protocol for this class. Further, it shows that deciding whether a swap is in this class is NP-hard through a reduction from 3SAT, and further is$\Sigma_{2}^{\mathsf{P}}$-complete through a reduction from$\exists\forall \mathsf{DNF}$.

Byzantine quorum systems provide higher throughput than proof-of-work and incur modest energy consumption. Further, their modern incarnations incorporate personalized and heterogeneous trust. Thus, they are emerging as an appealing candidate for global financial infrastructure. However, since their quorums are not uniform across processes anymore, the properties that they should maintain to support abstractions such as reliable broadcast and consensus are not well-understood. It has been shown that the two properties quorum intersection and availability are necessary. In this paper, we prove that they are not sufficient. We then define the notion of quorum subsumption, and show that the three conditions together are sufficient: we present reliable broadcast and consensus protocols, and prove their correctness for quorum systems that provide the three properties.

In recent years, many different cryptocurrencies have risen in popularity. Since coins vary in fiat value and functionality, it has become important to securely exchange between them. A common exchange method is hashed timelock contracts (HTLC). However, this method did not support brokerage transactions that allow parties to leverage assets they gain during the transaction. We consider HTLC with brokering. The transaction fees for HTLC is a direct function of the size of the leader set. Thus, brokers are interested in finding the minimum leader set of a given transaction graph. We show that finding the minimum leader set on general transaction graphs with brokering is NP-hard. We then introduce flower transaction graphs, a common type of transaction graphs with brokering, and show that finding the minimum leader set of a flower graph is also NP-hard through a reduction from the knapsack problem.