Scarcity Is Not Enough: An Impossibility Result for Linear Sybil Cost Under Parallelizable Resources

Computer Science > Cryptography and Security [Submitted on 28 May 2026] Scarcity Is Not Enough: An Impossibility Result for Linear Sybil Cost Under Parallelizable Resources Homayoun Maleki, Nekane Sainz, Jon Legarda, Igor Santos-Grueiro Permissionless systems resist Sybil attacks by binding influence to scarce resources. We show that scarcity alone is insufficient: the structural properties of the resource determine whether influence can be concentrated at sublinear cost through identity replication, delegation, or pooling. We model this through the adversarial cost C(s,T): the minimum expenditure required to achieve influence proportional to s independent participation units over T windows. We prove that any resource satisfying divisibility, additivity of influence, temporal reusability, and identity transferability admits influence amortization: C(s,T)=o(sT), regardless of protocol design. This is an impossibility result: no protocol rule can enforce linear cost of influence concentration over a structurally parallelizable resource. We further prove that throughput-bounded, non-transferable, window-local resources enforce C(s,T)=Omega(sT): each additional unit of sustained influence incurs marginal cost Delta(s,T)=Omega(T), growing with the time horizon. The two resource classes are asymptotically separated. As a direct design consequence, any mechanism targeting linear cost of influence concentration must ground participation in a resource that violates at least one parallelizability property. Comments: 14 pages, 5 figures Subjects: Cryptography and Security (cs.CR) Cite as: arXiv:2605.29651 [cs.CR]   (or arXiv:2605.29651v1 [cs.CR] for this version)   https://doi.org/10.48550/arXiv.2605.29651 Focus to learn more Submission history From: Homayoun Maleki [view email] [v1] Thu, 28 May 2026 09:15:34 UTC (582 KB) Access Paper: HTML (experimental) view license Current browse context: cs.CR < prev   |   next > new | recent | 2026-05 Change to browse by: cs 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?)