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On the Unfairness of Blockchain

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Networked Systems (NETYS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 11028))

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Abstract

The success of Bitcoin relies on the perception of a fair underlying peer-to-peer protocol: blockchain. Fairness here means that the reward (in bitcoins) given to any participant that helps maintain the consistency of the protocol by mining, is proportional to the computational power devoted by that participant to the mining task. Without such perception of fairness, honest miners might be disincentivized to maintain the protocol, leaving the space for dishonest miners to reach a majority and jeopardize the consistency of the entire system.

We prove that blockchain is unfair, even in a distributed system of only two honest miners. In a realistic setting where message delivery is not instantaneous, the ratio between the (expected) number of blocks committed by two miners is actually lower bounded by a term exponential in the product of the message delay and the difference between the two miners’ hashrates. To obtain our result, we model the growth of blockchain, which may be of independent interest. We also apply our result to explain recent empirical observations and vulnerabilities.

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Notes

  1. 1.

    In the case of two honest miners, GHOST is equivalent to Bitcoin blockchain [15].

  2. 2.

    Algorithm 1 is a simplified variant of the algorithm of [6, 19]. After a chain is updated, while the original mining algorithm exchanges the data and inventories of newly created blocks [20] for performance reasons, Algorithm 1 sends the whole new chain. The two algorithms are equivalent for the purpose of establishing our results.

  3. 3.

    Decker and Wattenhofer’s experiment [17] on blockchain supported such model, which was also adopted in the analysis of selfish mining [9, 11].

  4. 4.

    The probability distribution of \(\tau _{k}\) cannot be expressed by a cumulative distribution function because \(\tau _{k} - \tau _{k-1}\) is neither continuous nor discrete.

  5. 5.

    Eyal and Sirer [11] showed a lower bound \(\mathcal {L}\) (on \(\alpha \)) as a function of parameter \(\gamma \) which represents the percentage of miners in the honest majority \(\mathcal {M}_1\) that adopt the selfish minority \(\mathcal {M}_2\)’s chain, and did not consider exact message delay u. The sufficient condition (i.e., an upper bound on \(\mathcal {L}\)) in [11] is obtained when \(\gamma = 0\), which implies \(u=0\).

  6. 6.

    If we consider \(\gamma \) and u as two parameters of the lower bound, then when \(u > 0\), for all \(\gamma \), the case where \(\gamma = 0\) requires the highest computational power th from the selfish minority. As a result, we consider here parameter \(\gamma = 0\) for \(u>0\), and \(\alpha > th\) is still a sufficient condition.

  7. 7.

    This setting neglects the variable relation between mining and time, e.g., when a message is delayed, a miner may have more time (more increments) to mine a block.

  8. 8.

    Lewenberg et al. [14] proposed inclusive blockchain as an alternative, which stores all possible blockchains in a directed acyclic graph, and then still observed disproportionate rewards among honest miners. Eyal et al. [13] proposed Bitcoin-NG, where a leader (a special miner that is entitled to include transaction blocks) is elected based on blockchain (and its companion mining algorithm); the leader election could still suffer from the unfairness of blockchain as shown in this paper.

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Acknowledgement

This work has been supported in part by the European ERC Grant 339539 - AOC.

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Authors and Affiliations

  1. École Polytechnique Fédérale de Lausanne, IC, Lausanne, Switzerland

    Rachid Guerraoui & Jingjing Wang

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  1. Rachid Guerraoui
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  2. Jingjing Wang
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Correspondence to Jingjing Wang .

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Editors and Affiliations

  1. Universität Freiburg, Freiburg, Germany

    Andreas Podelski

  2. University of Rennes 1, Rennes, France

    François Taïani

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Guerraoui, R., Wang, J. (2019). On the Unfairness of Blockchain. In: Podelski, A., Taïani, F. (eds) Networked Systems. NETYS 2018. Lecture Notes in Computer Science(), vol 11028. Springer, Cham. https://doi.org/10.1007/978-3-030-05529-5_3

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  • DOI: https://doi.org/10.1007/978-3-030-05529-5_3

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