Communication cost of consensus for nodes with limited memory

Motivated by applications in blockchains and sensor networks, we consider a model of $n$ nodes trying to reach consensus on their majority bit. Each node $i$ is assigned a bit at time zero, and is a finite automaton with $m$ bits of memory (i.e., $2^m$ states) and a Poisson clock. When the clock of $i$ rings, $i$ can choose to communicate, and is then matched to a uniformly chosen node $j$. The nodes $j$ and $i$ may update their states based on the state of the other node. Previous work has focused on minimizing the time to consensus and the probability of error, while our goal is minimizing the number of communications. We show that when $m>3 \log\log\log(n)$, consensus can be reached at linear communication cost, but this is impossible if $m<\log\log\log(n)$. We also study a synchronous variant of the model, where our upper and lower bounds on $m$ for achieving linear communication cost are $2\log\log\log(n)$ and $\log\log\log(n)$, respectively. A key step is to distinguish when nodes can become aware of knowing the majority bit and stop communicating. We show that this is impossible if their memory is too low.Comment: 62 pages, 5 figure

Privacy in Cross-border Digital Currency. A Transatlantic Approach

This paper is one of four publications launched at the inaugural Frankfurt Forum on US-European GeoEconomics held in Germany from September 27 – 29, 2022. Co-hosted by the Atlantic Council GeoEconomics Center and Atlantik-Brücke, the Frankfurt Forum anchors critical work on transatlantic economic cooperation. The war in Ukraine, and the G7 response, reminded the world of the impact of transatlantic coordination. As part of the Frankfurt Forum, this new research aims to advance transatlantic dialogue from crisis response to addressing the key economic issues that will underpin the US-EU partnership over the next decade. The goal of the Frankfurt Forum is to deliver a blueprint for cooperation in four key areas: digital currencies, monetary policy, international trade, and economic statecraft

Deconstructing the Blockchain to Approach Physical Limits

Transaction throughput, confirmation latency and confirmation reliability are fundamental performance measures of any blockchain system in addition to its security. In a decentralized setting, these measures are limited by two underlying physical network attributes: communication capacity and speed-of-light propagation delay. Existing systems operate far away from these physical limits. In this work we introduce Prism, a new proof-of-work blockchain protocol, which can achieve 1) security against up to 50% adversarial hashing power; 2) optimal throughput up to the capacity C of the network; 3) confirmation latency for honest transactions proportional to the propagation delay D, with confirmation error probability exponentially small in CD ; 4) eventual total ordering of all transactions. Our approach to the design of this protocol is based on deconstructing the blockchain into its basic functionalities and systematically scaling up these functionalities to approach their physical limits.Comment: Computer and Communications Security, 201