[Theory] FW: Theory Lunch 2023-05-31T17:30:00.000Z

[Christopher Kang]

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Sent: Wednesday, May 31, 2023 12:04:55 AM (UTC-06:00) Central Time (US & Canada)
To: Antares Chen <antaresc at uchicago.edu>
Cc: Christopher Kang <ctkang at uchicago.edu>
Subject: Theory Lunch 2023-05-31T17:30:00.000Z


Today's Theory Lunch talk:

Francesca Falzon (University of Chicago): Short Privacy-Preserving Proofs of Liabilities

https://uchicago.zoom.us/j/91616319229?pwd=dDdXQnFXeGNubFRkZy9hTDQrcWlXdz09<https://urldefense.com/v3/__https://uchicago.zoom.us/j/91616319229?pwd=dDdXQnFXeGNubFRkZy9hTDQrcWlXdz09__;!!BpyFHLRN4TMTrA!5abFbtcTaqZY29pSCqKT9useOuz-70Utcc2E-Ck-JSG-xUPBgF2bJEabszWzfR8uVL5A1MN_MGJaidoSCUbQiaxaiOa-hzoPyQw$>

Description: 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 tree 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 then leverage inner product arguments to prove that a liability of a user is included in the total liabilities of the prover without leaking any information beyond the liability’s inclusion. The privacy of the scheme follows from the history independence of the SSVT, the zero-knowledge of the inner product arguments, and the hiding property of the vector commitments. 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. Finally, we benchmark our scheme using an SSVT of size 2^256 and an another of size 10^9 that covers the universe of all US social security numbers.

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