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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2605.29651 |
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| _version_ | 1866917543324680192 |
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| author | Maleki, Homayoun Sainz, Nekane Legarda, Jon Santos-Grueiro, Igor |
| author_facet | Maleki, Homayoun Sainz, Nekane Legarda, Jon Santos-Grueiro, Igor |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29651 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Scarcity Is Not Enough: An Impossibility Result for Linear Sybil Cost Under Parallelizable Resources Maleki, Homayoun Sainz, Nekane Legarda, Jon Santos-Grueiro, Igor Cryptography and Security 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. |
| title | Scarcity Is Not Enough: An Impossibility Result for Linear Sybil Cost Under Parallelizable Resources |
| topic | Cryptography and Security |
| url | https://arxiv.org/abs/2605.29651 |