<div dir="ltr">Hi everyone,<div><br></div><div>Just wanted to forward a message from Francesca following up on some discussion from this past Wednesday's lunch. </div><div><br></div><div>Thank you again to everyone for your help in making theory lunch a success this year, and hope you all enjoy the summer!<br></div><div><br></div><div>Best, </div><div>Antares</div><div><br></div><div><br></div><div>---</div><div><br></div><div><div dir="auto"><div dir="ltr" style="font-family:-apple-system,"Helvetica Neue";word-spacing:1px;border-color:rgb(49,49,49);color:rgb(49,49,49)"><div style="font-size:1rem;border-color:rgb(49,49,49)">Hi all,</div><div style="border-color:rgb(49,49,49)"><br></div><div style="font-size:1rem;border-color:rgb(49,49,49)">Thanks again for coming! I wanted to just follow up on my commentary on the range proof. I didn't do it justice and I needed at least another 30 minutes to explain it properly! In any case, for those interested, our work builds off of Bulletproofs (<a href="https://eprint.iacr.org/2017/1066.pdf" target="_blank" style="font-size:1rem;border-color:rgb(66,133,244)">https://eprint.iacr.org/2017/1066.pdf</a>) -- the difference being that they prove ranges for individual values (committed to via Pedersen commitments) whereas we prove ranges for a vector of values (committed to via Vector Commitments).</div><div style="border-color:rgb(49,49,49)"><br></div><div style="font-size:1rem;border-color:rgb(49,49,49)">I'm not sure I'm able to share our paper at the moment due to company policy, but once public I'd be happy to share it with anyone interested. <br></div><div style="border-color:rgb(49,49,49)"><br></div><div style="font-size:1rem;border-color:rgb(49,49,49)">Best,</div><div style="font-size:1rem;border-color:rgb(49,49,49)">Francesca</div></div></div></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Wed, May 31, 2023 at 12:05 AM Christopher Kang <<a href="mailto:ctkang@uchicago.edu">ctkang@uchicago.edu</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div class="msg3182623264966858052">
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<font face="Tahoma" size="2"><b>From:</b> <a href="mailto:noreply%2Bautomations@airtableemail.com" target="_blank">noreply+automations@airtableemail.com</a> <<a href="mailto:noreply%2Bautomations@airtableemail.com" target="_blank">noreply+automations@airtableemail.com</a>>On Behalf OfTheoryBot (via Airtable) <<a href="mailto:noreply%2Bautomations@airtableemail.com" target="_blank">noreply+automations@airtableemail.com</a>><br>
<b>Sent:</b> Wednesday, May 31, 2023 12:04:55 AM (UTC-06:00) Central Time (US & Canada)<br>
<b>To:</b> Antares Chen <<a href="mailto:antaresc@uchicago.edu" target="_blank">antaresc@uchicago.edu</a>><br>
<b>Cc:</b> Christopher Kang <<a href="mailto:ctkang@uchicago.edu" target="_blank">ctkang@uchicago.edu</a>><br>
<b>Subject:</b> Theory Lunch 2023-05-31T17:30:00.000Z<br>
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<p style="margin-top:0px"><span>Today's Theory Lunch talk:</span></p>
<p><em><span>Francesca Falzon (University of Chicago): Short Privacy-Preserving Proofs of Liabilities</span></em></p>
<p><span><a href="https://urldefense.com/v3/__https://uchicago.zoom.us/j/91616319229?pwd=dDdXQnFXeGNubFRkZy9hTDQrcWlXdz09__;!!BpyFHLRN4TMTrA!5abFbtcTaqZY29pSCqKT9useOuz-70Utcc2E-Ck-JSG-xUPBgF2bJEabszWzfR8uVL5A1MN_MGJaidoSCUbQiaxaiOa-hzoPyQw$" target="_blank">https://uchicago.zoom.us/j/91616319229?pwd=dDdXQnFXeGNubFRkZy9hTDQrcWlXdz09</a></span></p>
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<p><span>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.</span></p>
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