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

[Antares Chen]

Hi everyone,

Just wanted to forward a message from Francesca following up on some
discussion from this past Wednesday's lunch.

Thank you again to everyone for your help in making theory lunch a success
this year, and hope you all enjoy the summer!

Best,
Antares


---

Hi all,

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 (https://eprint.iacr.org/2017/1066.pdf) -- 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).

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.

Best,
Francesca

On Wed, May 31, 2023 at 12:05 AM Christopher Kang <ctkang at uchicago.edu>
wrote:

>
> ------------------------------
> *From:* noreply+automations at airtableemail.com <
> noreply+automations at airtableemail.com>On Behalf OfTheoryBot (via
> Airtable) <noreply+automations at airtableemail.com>
> *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.
> Sent via Automations on [image: Airtable]
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