A. Cullen, P. Ferraro, C. King, and R. Shorten

Abstract—Directed Acyclic Graph (DAG) based Distributed Ledgers can be useful in a number of applications in the IoT domain. A distributed ledger should serve as an immutable and irreversible record of transactions, however, a DAG structure is amore complicated mathematical object than its blockchain counterparts, and as a result, providing guarantees of immutabilityand irreversibility is more involved. In this paper, we analyse a commonly discussed attack scenario known as a parasite chainattack for the IOTA Foundation’s DAG based ledger. We analysethe efficacy of IOTA’s core MCMC algorithm using a matrixmodel and present an extension which improves the ledger’s resistance to these attacks.

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Distributed Ledger has attracted a great deal of attention in recent years, initially as a peer-to-peer electronic cash system [1], but more recently, distributed ledgers have been applied to problems in the IoT domain, as discussed in detail in[2]. Not all distributed ledgers are suited to IoT applications: often the necessity of transaction fees and the manner in which low value transactions are dealt with makes some DLTs unsuitable. We areparticularly interesting in DLTs based on Directed Acyclic Graphs (DAGs) in this work, and more specifically, one DAG based ledger known as the IOTA Tangle [3] which seems to posess properties that make it suitable for the use-cases of interest.

The security of distributed ledgers is still much disputed—the immutability and irreversibility of the ledger rely on cryptographic hashing and the consensus protocols built around this, but guarantees are generally probabilistic and subject to many network conditions being met [4]–[7]. In this paper, we analyse a commonly discussed attack scenario known as a parasite chain attack which aims to reverse a transaction that has been accepted by the network and spend the same coin again. We analyse this attack in the context of the IOTA Tangle and investigate the efficacy of IOTA’s core algorithm using an explicit model and present an extension of the algorithm which improves the ledger’s resistance to these attacks.

In Section II we describe the Tangle DAG in detail and introduce a double spending mechanism known as a parasite chain attack. Section III begins with the stochastic model for the Tangle presented in [2]. We extend this model by providing an explicit formulation for the Markov Chain Monte Carlo (MCMC) tip selection algorithm and use this model to simulate the algorithm’s resistance to parasite chain attacks. Section IV introduces a modification to the MCMC which makes use of the growth of the cumulative weight in the Tangle and we present thecorresponding results for a parasite chain attack.

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