arXiv 2008.082082020-08-19cs.DCcs.CR

一种处理跨区块链交易的代数拓扑方法

An Algebraic-Topological Approach to Processing Cross-Blockchain Transactions

Dongfang Zhao

摘要：

用于处理跨区块链交易的最先进技术采用简单的集中式方法：当区块链上的资产$X$（例如$X$ -硬币）与区块链上的资产$Y$（$Y$ -硬币）交换时，这些$X$ -硬币需要交换到“中间”介质（例如比特币），然后交换到$Y$ -硬币。如果在一个全局交易中涉及到两个以上的交易方，则全局交易被分成多个本地两方交易，每个交易都遵循上述中央交换协议。不幸的是，全局事务的原子性与中心交换方法相违背：这些本地两方事务一旦提交，如果全局事务决定中止，就不能回滚。从更一般的意义上说，基于图的（双方）交易模型很难扩展到跨区块链交易中的任意数量的交易方。%从为什么到如何在本文中，我们介绍了跨区块链交易的更高级别抽象。我们采用了\textit{abstract simplicial complex}，一个广泛研究的数学对象在代数拓扑，代表任意数量的参与区块链交易的各方。全局事务中的每一方都被建模为一个顶点，$n+1$（$n \in \mathbb{Z}$，$n > 0$）方之间的全局事务构成一个$n$维单纯形.虽然这种更高级别的抽象似乎微不足道，但我们将展示这种简单的扩展如何导致一系列新的建模方法和协议，以更好地处理跨区块链交易。

英文摘要：

The state-of-the-art techniques for processing cross-blockchain transactions take a simple centralized approach: when the assets on blockchain $X$, say $X$-coins, are exchanged with the assets on blockchain $Y$---the $Y$-coins, those $X$-coins need to be exchanged to a "middle" medium (such as Bitcoin) that is then exchanged to $Y$-coins. If there are more than two parties involved in a single global transaction, the global transaction is split into multiple local two-party transactions, each of which follows the above central-exchange protocol. Unfortunately, the atomicity of the global transaction is violated with the central-exchange approach: those local two-party transactions, once committed, cannot be rolled back if the global transaction decides to abort. In a more general sense, the graph-based model of (two-party) transactions can hardly be extended to an arbitrary number of parties in a cross-blockchain transaction. %from why to how In this paper, we introduce a higher-level abstraction of cross-blockchain transactions. We adopt the \textit{abstract simplicial complex}, an extensively-studied mathematical object in algebraic topology, to represent an arbitrary number of parties involved in the blockchain transactions. Essentially, each party in the global transaction is modeled as a vertex and the global transaction among $n+1$ ($n \in \mathbb{Z}$, $n > 0$) parties compose a $n$-dimensional simplex. While this higher-level abstraction seems plausibly trivial, we will show how this simple extension leads to a new line of modeling methods and protocols for better processing cross-blockchain transactions.

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