About

This repo contains experimental prototypes of ring signature algorithms that we intend to use for zero-knowledge proofs.

Notes

0xPARC (Program for Applied Research in Cryptography) is actively developing methods to prove public key derivation from secret keys, verifying ECDSA signatures, etc. in zk snarks. They use circom for this which is a fairly low level language for writing zk snark circuits. Problem is, that these circuits contain millions of constraints and require a significant amount of computational resources (tens of gigabytes of RAM). StealthDrop is a prototype implementation making use of such circuits.

We are looking for alternative solutions (more lightweight) to prove that someone has the corresponding private key for a given public key without disclosing their public key. So far, ring signatures are quite promising, as our usecase is exactly that we need to prove that we are part of a group of addresses that hold some kind of tokens. Through Balancy we are able to construct such address groups publicly. An entry-level (mathematical) introduction of how ring signatures work can be found in Monero's handbook. There is a Rust repo that implements the math in this handbook which helped constructing our prototype.

There are some further practical issues to solve though. StealthDrop uses ECDSA verification circom scripts that are way more bulkier than just proving secret/public key derivation because there's no way to extract the bare private key from a wallet like Metamask. You can read an interesting twitter thread about this here.

Ring signatures also make use of direct access to the secret key when generating the proof. However, there might exist a solution where EDCSA signature verification happens via masking the public key via Pedersen commitments. The whitepaper describing the algorithm can be found here, and it builds on Groth's seminal paper. The advantage of this method is that it doesn't seem to require direct access to the user's private key. Thus, the user only signs a message (using Metamask for example), commits a Pedersen commitment masking their public key and generates the proof based on these values.

Proposed flow

• I. Balancy generates a list of eligible (Ethereum) addresses for a given guild.
• II. Users whose address is found in this array (ring) may provide a ring signature that proves they are eligible to enter the guild.
• III. The guild backend receives the ring signature (proof) along with the ID of the guild and (Discord) ID of the user and verifies the proof.