A Framework for Blockchain Architecture Design

TL;DR

The paper studies how different blockchain architectures behave under random network delays by introducing an asynchronous recursion model for the evolving data structure, namely $G_{t+1} = f(G_t, G_{t-\xi_t})$, to formalize the impact of delays on consensus. It defines one-endedness as a limiting graph property that guarantees infinitely many confirmed blocks and uses ends of infinite graphs to formalize consensus; this yields a rigorous framework for architecture design beyond Bitcoin. The authors prove existence and one-endedness of asynchronous limits for Bitcoin’s Nakamoto attachment $f_{\text{Nak}}$ and for Iota’s $f_k$ with $k\ge 2$ (while $k=1$ is not one-ended), and they extend the framework to mixtures and generalized delays, including forward-backward delay models. These results provide a robust, architecture-agnostic basis for designing blockchains in applications requiring frequent updates (e.g., supply chains, IoT) by clarifying when consensus-like behavior emerges and how many blocks become confirmed in the limit.

Abstract

Emerging applications of blockchains, such as grocery supply chains, require frequent updates to the data structure. This is in contrast with typical analyses of the Bitcoin blockchain, in which updates occur infrequently. With more frequent updates, the spread of blocks among participants in the blockchain protocol becomes complicated; thus, the structure of the blockchain data structure itself can differ significantly from the structure without the presence of network delays. In addition, emerging blockchain applications such as internet-of-things or supply chain warrant different architectures of the blockchain data structure, and so one needs a general understanding of how the data structure works rather than focusing on the specific architecture of Bitcoin. In this paper, we develop a new model to study the dynamics of the blockchain data structure in the presence of i.i.d.~network delays. Specifically, we consider an asymptotic design criterion called one-endedness, which should be satisfied by all blockchain architectures. We develop techniques to show that the one-endedness property holds for some of the leading blockchain architectures.

Figures (2)

• Figure 1: Stochastic domination in the proof of Proposition \ref{['prop:tau-xi']} with $\ell=15,V_{i}=t_{i-1}-t_{i}, i\geqslant 1$.
• Figure 2: Confirmed blocks in a regeneration interval.

Theorems & Definitions (53)

• Theorem 1.1
• Theorem 1.2
• Theorem 1.3
• Theorem 1.4
• Theorem 1.5
• Definition 2.1: aldous2007processes
• Definition 2.2: See halin1964unendliche
• Definition 2.3: See halin1964unendliche
• Definition 2.4
• Lemma 2.5: gopalan2020stability