When Should Selfish Miners Double-Spend?

Computer Science > Cryptography and Security [Submitted on 6 Jan 2025 (v1), last revised 20 Mar 2026 (this version, v5)] When Should Selfish Miners Double-Spend? Mustafa Doger, Sennur Ulukus Conventional double-spending attack models ignore the revenue losses stemming from the orphan blocks. On the other hand, selfish mining literature usually ignores the chance of the attacker to double-spend at no-cost in each attack cycle. In this paper, we give a rigorous stochastic analysis of an attack where the goal of the adversary is to double-spend while mining selfishly. To do so, we first combine stubborn and selfish mining attacks, \textit{i.e.}, construct a strategy where the attacker acts stubborn until its private branch reaches a certain length and then switches to act selfish. We provide the optimal stubbornness for each parameter regime. Next, we provide the maximum stubbornness that is still more profitable than honest mining and argue a connection between the level of stubbornness and the k-confirmation rule. We show that, at each attack cycle, if the level of stubbornness is higher than k, the adversary gets a free shot at double-spending. At each cycle, for a given stubbornness level, we rigorously formulate how great the probability of double-spending is. We further modify the attack in the stubborn regime in order to conceal the attack and increase the double-spending probability. Subjects: Cryptography and Security (cs.CR); Distributed, Parallel, and Cluster Computing (cs.DC); Discrete Mathematics (cs.DM); Information Theory (cs.IT); Probability (math.PR) Cite as: arXiv:2501.03227 [cs.CR]   (or arXiv:2501.03227v5 [cs.CR] for this version)   https://doi.org/10.48550/arXiv.2501.03227 Focus to learn more Submission history From: Mustafa Doger [view email] [v1] Mon, 6 Jan 2025 18:59:26 UTC (729 KB) [v2] Tue, 7 Oct 2025 12:51:24 UTC (738 KB) [v3] Sat, 8 Nov 2025 23:39:16 UTC (738 KB) [v4] Wed, 24 Dec 2025 01:13:17 UTC (741 KB) [v5] Fri, 20 Mar 2026 04:05:22 UTC (775 KB) Access Paper: HTML (experimental) view license Current browse context: cs.CR < prev   |   next > new | recent | 2025-01 Change to browse by: cs cs.DC cs.DM cs.IT math math.IT math.PR References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)