# Mitigating Collusion in Proofs of Liabilities Source: [Mitigating Collusion in Proofs of Liabilities]() Collection index: [llms.txt]() Data updated: 2026-03-17T05:00:04.157Z Authors: Malcom Mohamed, Ghassan Karame Published: 2026-03-13T13:45:23.000Z ## Abstract Cryptocurrency exchanges use proofs of liabilities (PoLs) to prove to their customers their liabilities committed on-chain, thereby enhancing their trust in the service. Unfortunately, a close examination of currently deployed and academic PoLs reveals significant shortcomings in their designs. For instance, existing schemes cannot resist realistic attack scenarios in which the provider colludes with an existing user. In this paper, we propose a new model, dubbed permissioned PoL, that addresses this gap by not requiring cooperation from users to detect a dishonest provider's potential misbehavior. At the core of our proposal lies a novel primitive, which we call Permissioned Vector Commitment (PVC), to ensure that a committed vector only contains values that users have explicitly signed. We provide an efficient PVC and PoL construction that carefully combines homomorphic properties of KZG commitments and BLS-based signatures. Our prototype implementation shows that, despite the stronger security, our proposal also improves server performance (by up to $10\\times$) compared to prior PoLs. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Proof of Liabilities Evaluation on Synthetic Proof of Liabilities (PoL) Environment](): Proof of Liabilities Evaluation; Synthetic Proof of Liabilities (PoL) Environment; Throughput (Updates/s): 369. ## Original sources and implementation [Original paper]() [PDF]()