Short Privacy-Preserving Proofs of Liabilities

In the wake of fraud scandals involving decentralized exchanges and the significant financial loss suffered by individuals, regulators are pressed to put mechanisms in place that enforce customer protections and capital requirements in decentralized ecosystems. Proof of liabilities (PoL) is such a mechanism: it allows a prover (e.g., an exchange) to prove its liability to a verifier (i.e., a customer). This paper introduces a fully privacy-preserving PoL scheme with short proofs. We store the prover's liabilities in a novel data structure, the sparse summation Verkle tree (SSVT), in which each internal node is a hiding vector commitment of its children and whose root commits to the sum of all the leaves in the tree. We leverage inner product arguments to prove that a user's liability is included in the total liabilities of the prover without leaking any information beyond the liability's inclusion. Our construction yields proofs of size O(log_n N) where n is the arity of the SSVT and N is an upper bound on the number of users. Additionally, we show how to further optimize the proof size using aggregation. We benchmark our scheme using an SSVT of size 2²⁵⁶ and one of size 10⁹ that covers the universe of all US social security numbers.