arXiv subjects

Jon Legarda

Publications and source records attributed to Jon Legarda.

6 recordsLinked to original sources

arXiv2026

Beyond Identity Creation: Bilinear Sybil Cost in Identities and Time

Sybil defenses price the creation of an identity, yet influence goes, again and again, to active identities. We study the cost of maintaining influence. A defense has a bilinear Sybil cost with ratio $A$ if keeping $s$ identities active for $T$ periods costs at least $sT/A$ honest units: the average cost per identity-window is at least $1/A$ times an honest participant's cost. Recurrence alone does not guarantee this cost. The cost can be carried over from earlier periods, shared among many identities, or be negligible when fast hardware does the work of thousands of honest devices. We give four sufficient conditions for a defense that checks every identity each period to achieve bilinear Sybil cost: identity binding, freshness, a shared deadline, and sequential, non-batchable work. They yield two guarantees: a bilinear total cost, with $A$ the speed advantage of the adversary's fastest hardware, and, because the work must be fresh and finished by a common deadline, a bound on the identities active in a period by the processors running at that time. We prove that none of the four follows from the other three. A verifiable delay function on an identity-bound input meets all four without payments, with $A$ of 2 to 8 for CPUs and about 28 for a hypothetical ASIC, against $10^3$ to $10^7$ for hash puzzles. We measure one active identity per core per period against about 80,000 under a signed heartbeat, no gain from batching up to 1,000 identities, and rejection of all tested attacks.

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arXiv2026

Identity Amortization: Shared Resources and the Cost of Sybil Attacks

Sybil defenses commonly price identities by requiring a resource for each one. When one resource can support several identities, an adversary can pay less per identity than the defense intends. We call this identity amortization: a strict reduction in the minimum cost of provisioning identities when resources may be shared, relative to provisioning each one independently. It is a second route to the gap that a Sybil attack exploits. When influence is assigned per identity, a defense calibrated to the nominal price can overestimate the cost of a Sybil threshold by up to the number of identities one resource supports. For any resource catalogue, we give exact tests for when identity amortization occurs, where it begins, and its largest error; a sharing cap below the onset removes it. Because the tests need only prices and capacities, they apply to any defense that admits identities against a shareable resource, telling designers whether the assumed per-identity cost is paid, how wrong it can be, and which intervention restores it most cheaply for honest participants. On published phone-verification prices, per-account estimates overstate provisioning cost 1.6 to 4.3 times; Tor's raised per-address relay limit cut modeled attack cost by 8 to 72%, depending on the address-to-relay price ratio.

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arXiv2026

Sustained Participation as a Security Resource: The Bounded Participation Channel

Can sustained, per-identity participation be engineered into a security resource? Most anti-Sybil defenses price identity creation rather than identity survival. Once admitted, an adversary may sustain many identities without paying a recurring cost. We introduce the Bounded Participation Channel (BPC), a formal primitive for repeatedly verifying participation window by window. BPC issues fresh, identity-bound challenges under a strict deadline and enforces four structural properties: identity binding, freshness, real-time response, and bounded per-channel throughput. Together, these yield a provable cost theorem: sustaining $s$ identities over $T$ windows requires $C(s,T) \geq sT/τ_h$ participation channel-windows. The guarantee is solver-agnostic: a channel may be operated by a human, an AI system, or a hybrid. We give a hash-based construction with publicly verifiable participation proofs, characterize four admissible challenge families, and evaluate two against GPT-4o, Gemini 2.5 Flash, and Claude Sonnet 4.5 across 600 trials. Despite near-perfect accuracy (97--100%) on the perceptual tasks, the evaluated automated channels remain throughput-bounded under the tested deployment conditions. The results illustrate a key distinction: solvability does not imply unlimited throughput. By requiring participation to be re-earned by every identity in every time window, BPC turns sustained participation into a measurable security resource with a linear structural cost floor, independent of whether the participation is supplied by humans, AI systems, or hybrids.

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arXiv2026

Scarcity Is Not Enough: Structural Limits of Linear Sybil Cost Under Parallelizable Resources

Permissionless systems resist Sybil attacks by binding influence to scarce resources. Yet influence concentration persists across systems built on computation, capital, and other reusable resources despite substantial differences in protocol design. This raises a fundamental question: is concentration primarily a consequence of protocol rules, or of the structural properties of the underlying resource itself? We address this through the adversarial cost function $C(s,T)$, the minimum expenditure to sustain influence equivalent to controlling $s$ independent participants over a horizon of length $T$. We develop an axiomatic resource taxonomy connecting resource structure to adversarial cost scaling. We show that resource-mechanism pairs satisfying divisibility, additivity of influence, temporal reusability, and identity transferability admit influence amortization, yielding $C(s,T)=o(sT)$. Conversely, throughput-bounded, non-transferable, window-local resources enforce $C(s,T)=Ω(sT)$, with marginal cost $Δ(s,T)=Ω(T)$ increasing with time. These results reveal a fundamental asymptotic separation between resource classes that admit amortization and those that enforce linear cost. These results shift the focus of decentralization from protocol design to resource design. If concentration is a structural consequence of the properties that make resources parallelizable, redesigning consensus rules alone cannot eliminate it. The same properties enable concentrated control to be projected across many nominally distinct participants through delegation, pooling, or identity replication, obscuring the relationship between visible identities and underlying control. The search for stronger decentralization must therefore begin with the choice of the underlying resource.

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arXiv2026

Proof of Commitment: A Human-Centric Resource for Permissionless Consensus

Permissionless consensus protocols require a scarce resource to regulate leader election and provide Sybil resistance. Existing paradigms such as Proof of Work and Proof of Stake instantiate this scarcity through parallelizable resources like computation or capital. Once acquired, these resources can be subdivided across many identities at negligible marginal cost, making linear Sybil cost fundamentally unattainable. We introduce Proof of Commitment (PoCmt), a consensus primitive grounded in a non-parallelizable resource: real-time human engagement. Validators maintain a commitment state capturing cumulative human effort, protocol participation, and online availability. Engagement is enforced through a Human Challenge Oracle that issues identity-bound, time-sensitive challenges, limiting the number of challenges solvable within each human window. Under this model, sustaining multiple active identities requires proportional human-time effort. We establish a cost-theoretic separation showing that protocols based on parallelizable resources admit zero marginal Sybil cost, whereas PoCmt enforces a strictly linear cost profile. Using a weighted-backbone analysis, we show that PoCmt achieves safety, liveness, and commitment-proportional fairness under partial synchrony. Simulations complement the analysis by isolating human-time capacity as the sole adversarial bottleneck and validating the predicted commitment drift and fairness properties. These results position PoCmt as a new point in the consensus design space, grounding permissionless security in sustained human effort rather than computation or capital.

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arXiv2026

Human Challenge Oracle: Designing AI-Resistant, Identity-Bound, Time-Limited Tasks for Sybil-Resistant Consensus

Sybil attacks remain a fundamental obstacle in open online systems, where adversaries can cheaply create and sustain large numbers of fake identities. Existing defenses, including CAPTCHAs and one-time proof-of-personhood mechanisms, primarily address identity creation and provide limited protection against long-term, large-scale Sybil participation, especially as automated solvers and AI systems continue to improve. We introduce the Human Challenge Oracle (HCO), a new security primitive for continuous, rate-limited human verification. HCO issues short, time-bound challenges that are cryptographically bound to individual identities and must be solved in real time. The core insight underlying HCO is that real-time human cognitive effort, such as perception, attention, and interactive reasoning, constitutes a scarce resource that is inherently difficult to parallelize or amortize across identities. We formalize the design goals and security properties of HCO and show that, under explicit and mild assumptions, sustaining s active identities incurs a cost that grows linearly with s in every time window. We further describe abstract classes of admissible challenges and concrete browser-based instantiations, and present an initial empirical study illustrating that these challenges are easily solvable by humans within seconds while remaining difficult for contemporary automated systems under strict time constraints.

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