On Profitability of Trailing Mining

Grunspan, Cyril; Pérez-Marco, Ricardo

doi:10.48550/arxiv.1811.09322

Cited by 9 publications

(16 citation statements)

References 4 publications

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“…from [10] (See Corollary 2.5) which is a consequence of Stern's formula [17]. So, using Proposition 3.2 we compute,…”

Section: Probability Of Successmentioning

confidence: 94%

“…This computation is classical and can be found in Appendix A of [10] for example (see Theorem A.1). So, we have using Proposition 3.2 together with ( 7) and ( 8),…”

Section: Probability Of Successmentioning

confidence: 99%

“…As in the original article [8], and subsequent application to other block withholding strategies [8], [9], [10], the main tool in the proof of this Theorem are martingale techniques and the application of Doob's Stopping Time Theorem. Previous techniques using Markov chains do not allow the computation of the expected duration of the attack, which is critical for the profitability analysis.…”

Section: Introductionmentioning

confidence: 99%

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On Profitability of Nakamoto double spend

Grunspan,

Pérez-Marco

2019

Preprint

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Nakamoto double spend strategy, described in Bitcoin foundational article, leads to total ruin with positive probability and does not make sense from the profitability point of view. The simplest strategy that can be profitable incorporates a stopping threshold when success is unlikely. We solve and compute the exact profitability for this strategy. We compute the minimal amount of the double spend that is profitable. For a given amount of the transaction, we determine the minimal number of confirmations to be requested by the recipient such that this double spend strategy is non-profitable. We find that this number of confirmations is only 1 or 2 for average transactions and a small hashrate of the attacker. This is substantially lower than the original Nakamoto numbers that are widely used and are only based on the success probability instead of the profitability.

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“…from [10] (See Corollary 2.5) which is a consequence of Stern's formula [17]. So, using Proposition 3.2 we compute,…”

Section: Probability Of Successmentioning

confidence: 94%

“…This computation is classical and can be found in Appendix A of [10] for example (see Theorem A.1). So, we have using Proposition 3.2 together with ( 7) and ( 8),…”

Section: Probability Of Successmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On Profitability of Nakamoto double spend

Grunspan,

Pérez-Marco

2019

Preprint

Self Cite

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“…Other blockwithholding strategies were presented in Sapirshtein et al [23] and Nayak et al [20] leading to an optimized relative revenue. These strategies imply a lower revenue, even for the malicious nodes, which led Grunspan and Marco-Pérez in a series of contributions [14,11,13,12] to label them as not profitable. The authors pointed out that the time required to implement such a scheme can be rather long and the time before it becomes profitable even longer exposing them to a significant risk of going bankrupt.…”

Section: Introductionmentioning

confidence: 99%

On the profitability of selfish blockchain mining under consideration of ruin

Albrecher,

Goffard

2020

Preprint

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Mining blocks on a blockchain equipped with a proof of work consensus protocol is well-known to be resource-consuming. A miner bears the operational cost, mainly electricity consumption and IT gear, of mining, and is compensated by a capital gain when a block is discovered. This paper aims at quantifying the profitability of mining when the possible event of ruin is also considered. This is done by formulating a tractable stochastic model and using tools from applied probability and analysis, including the explicit solution of a certain type of advanced functional differential equation. The expected profit at a future time point is determined for the situation when the miner follows the protocol as well as when he/she withholds blocks. The obtained explicit expressions allow to analyze the sensitivity with respect to the different model ingredients and to identify conditions under which selfish mining is a strategic advantage.

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“…After a difficulty adjustment, this mean duration time becomes equal to E[L] • τ B where L is the number of blocks added to the official blockchain by the network per attack cycle and τ B = 600 sec. [6]. Thus, the objective function becomes proportional to the long-term apparent hashrate of the strategy q…”

Section: Introductionmentioning

confidence: 99%

Bitcoin Selfish Mining and Dyck Words

Grunspan,

Pérez-Marco

2019

Preprint

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We give a straightforward proof for the formula giving the long-term apparent hashrate of the Selfish Mining strategy in Bitcoin using only elementary probabilities and combinatorics, and more precisely, Dyck words. There is no need to compute stationary probabilities on Markov chain nor stopping times for Poisson processes as it was previously done. We consider also several other block withholding strategies.

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On Profitability of Trailing Mining

Cited by 9 publications

References 4 publications

On Profitability of Nakamoto double spend

On Profitability of Nakamoto double spend

On the profitability of selfish blockchain mining under consideration of ruin

Bitcoin Selfish Mining and Dyck Words

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