**Home Edition**

# Discussion notes #1: Distributed Auditing Proofs of Liabilities
Presenter: Kostas Chalkias

Authors:
* Konstantinos Chalkias (Calibra / Facebook) <[e-mail]>
* Kevin Lewi (Calibra / Facebook) <[e-mail]>
* Payman Mohassel (Calibra / Facebook) <[e-mail]>
* Valeria Nikolaenko (Calibra / Facebook) <[e-mail]>

To be presented on 2020-04-20.

Resources:
* [Latest PDF version](https://docs.zkproof.org/pages/standards/accepted-workshop3/proposal-dapol.pdf)
* [Miro Whiteboard](https://zkproof.org/workshop3-board)
* [ZKProof WG_DAPOL working group](https://community.zkproof.org/g/WG_DAPOL) (open to joining)
* [Additional related links](https://hackmd.io/@HtwXZr-PTFCniCs7fWFSmQ/B1AwbdI_8)
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## Real-time notes
_Note taker: Daira Hopwood_.

> Others are welcome to augment/annotate using notes. Add your name. ---EranTromer

Problem statement:
* auditing of some quantity where audited entity doesn't have incentive to increase liabilities/obligations.
* i.e. we have a number where the auditor doesn't have incentive to increase it.
* users should be able to verify inclusion of their contribution to the number.
* Examples: solvency, disapproval voting, number of COVID-19 cases.

Purpose is to agree on one or two suitable schemes that are transparent, secure, interoperable, and have some privacy properties (to be decided?)

Current problems:
* no standards (e.g. for proofs of solvency), everyone must redesign/implement

Want to have a reference proof-of-concept implementation with test vectors.

Can be used for benchmarking.

What is proof of solvency?
* prove that liabilities <= assets (or ratio is below a threshold)
* focus on liabilities. Reason is: different blockchains have different privacy properties, different ways to prove assets.
* Example of MtGox as insolvency.

Option A:
* expose everything publically (wallet balances, identities, performance, zero balance customers, total liabilities). Obviously not ok.

Option B:
* expose to auditors (information as above). Wallet-auditor collusion?

Option C:
* summation Merkle trees (parent node holds sum of child nodes)
* privacy leaks to customers:
* from siblings in Merkle path
* total liabilities, wallet performance
* still in use. Improvement over previous approaches.

Option D:
* random denomination trees. randomly split balances over coins, shuffle and put those in the tree as in Option C
* some obfuscation of balances
* still expose to customers the total liabilities and sibling denominations.

Option E:
* trusted enclaves (SGX)
* potential problems: difficult to make stateful, serious side channel attacks, need to trust the vendor, decapping attacks.

Option F:
* "ZK proofs to the rescue"
* hide numbers using homomorphic encryption/commitments
* use homomorphism to add up commitments (e.g. Pedersen)
* each node also holds hash of user id || audit id (salt)
* Pedersen commitments also need range proofs to avoid overflow
* this is the tree version of the Provisions proposal
* cannot hide size of the tree, can only add fake users / leaves
* if we had small number of clients (100s), tree would need to be huge to hide this
* if you have to increase the tree size, you leak the number of users at that point.
* Provisions proposal originally used Bulletproofs. Aggregation property helps efficiency.
* use KDF instead of hash
* company can manipulate audit ids, might be subtrees that no-one checks
* solved by deterministically generating IDs, e.g. using VRF or KDF with audit sequence id. Now company can't manipulate users' position in the tree.
* can use the same audit ID for multiple audits, so blinding factors can be derived deterministically / without interaction
* improvement of padding: use padding nodes for subtrees, not leaves. Don't need to add too many padding nodes to hide number of users.
* Discussion of auditor sampling: can give a proof that the requested index is in a padding subtree, because we derive that deterministically.

Can have a tree of contributors that reflects the organisation of reporting (e.g. COVID reporting by hospitals).

Features of DAPOL protocol:
* hide total value, balance values, identities, size of population
* allow larger ranges
* deterministic tree
* allow selective auditor sampling
* can be hierarchical
* reusable audit key
* applications outside solvency

Recommendations:
* need to publish root to an unforgeable/equivocable channel (e.g. blockchain)
* use PIR to hide who downloaded proofs
* users provide their own audit_key (devices can be equipped with trusted enclaves)

More applications beside solvency:
* Finance:
* syndicated loans (splitting risk with minimal info disclosure)
* taxable income (users can check their purchase was taxed)
* credit scoring (avoid centralized credit reference agencies)
* fundraising (check your donation included in accounts)
* Voting:
* count dislikes, disapproval voting
* decentralized elections
* Reporting:
* disease outbreak reporting (user can verify their case was included in a count)
* unemployment
* accidents

Q. Is there a deterministic number of times verification has to be done by verifiers to ensure that none of the users are missed out?
A. Have probabilitic model. Usually 15-20% of users sufficient. But users with large balances are more likely to check. Could improve by automating checks.

Q. About attack model: untrusted prover, honest but curious auditor, honest users, no collusion between parties?
A. Yes this is accurate. E.g. prominent past cases of colluding auditors. But better than nothing.

Q. Is there a way of linking a physical asset like cash (via a proof of assets) to the number that is reported? In other words, is there a way to prove that the number 'measured' is the same that is reported?

Q. Does it effectively take an "atomic snapshot" of everyone's asset status, or could they game proofs by making concurrent transactions? Money can be circulated in order to hide it. In a fully working system, there are big distributed systems problems.
A. This is why we don't deal with proof of assets, only liabilities. We use signatures for the transaction processing so that we can timestamp reports. There is no good solution to snapshotting assets.
A. (Daira Hopwood) We considered this in the context of stake-weighted voting in Zcash. Basically do a ZK proof that you held a coin at a given time (identified by an anchor, in the case of Zcash). This didn't handle payment channels.
A. (Kostas) Payment channels are very hard, because there can be risk-free collusion.

Q. How would you propose to handle identity data? Would need to both keep privacy and prove test result in COVID case. Can you change identity over time (e.g. by mixing)?
A. (by Kevin Lewi) Protocol doesn't handle identities, leaves that to another layer.
A. Some of this is specific to the contract tracing case. Useful to investigate but not the main focus of this protocol.
A. (Lera Nikola) Different audits can use different ids.
A. (Kostas) Users can give pseudonyms (although they could multiple-report). Need ids to be unique.

Q. Do you have a flip-side of the asset problem on the liability side (if someone challenges a proof)?
A. No obvious solution to dispute resolution unless you have bilateral agreements on contracts. Similarly for hospitals, there could be a signature that you have to prove a test result.

----
Daniel -

Should we standardize top to bottom or bottom to top?
Q: If we standardize the protocol, what other standards are we missing when it comes to the primitives?
A: may take existing standards for the primtives that exist, and build other independent standards for those that do not exist.

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Charter Ideas

Goals:

- fix application / flow
- outline the privacy / security requirements
- standardize protocol abstracted from the primitives
-
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## Discussion topics

_Suggestions welcome! Please append at the end, and the moderators will incorporate into the schedule._

~15 minutes each, by default.

### 1. **Epidemiology applications:** How would transparent reporting be useful for virus outbreaks: could it help with issues such as government underreporting, misinformation, contact tracing or others?

Was discussed partially in Q&A.

### 2. **Other applications?**

Skipped due to lack of time.

### 3. **What should we standardize:** one or two specific constructions or a set of rules that outline the requirements that any acceptable solutions should satisfy, in particular existing general ZK solutions provide solutions to the described functionalities?

(Mariana) Should we standardize this proposal as-is? Or spend more time to crystalize requirements? Add new features/fixes?

(Kostas) Want to provide consistency. Problem has existed for 6-7 years with no solution. Let's make a start on standardizing something usable now. Open to feedback.

(Daniel Bennaroch) Important to have requirements clearly defined, necessary for people not to mess up usage.

(Kostas) How are we going to agree on which scheme to use, before we have standardized the schemes?

(Daira) Specify required security and functionality from proof scheme.

(Mariana) There are many schemes that would provide those properties.

(Eran) Proposals like zkInterface are in scope for this event.

Much discussion of how to proceed with getting interoperability to work.

### 4. **What set of functionalities** would be sufficient for real applications that need proofs of liabilities - is the proposed set of functionalities here all we need as a starting point, or do people think more is needed?

### X. Enter yours here