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Applying simple transactions inside SNARKs

In this part of the tutorial, we will look into how a simple account-based payment system can be designed on top of arkworks APIs in Rust. At the end of this step, you should be familiar with APIs for cryptographic primitives in arkworks.

High-level architecture

Our payment system maintains a ledger consisting of accounts with corresponding balances. In more detail, an "account" is a (AccountID, SigPubKey, Balance) triple. The ledger maintains a Merkle tree atop this list of accounts, so that the i-th leaf corresponds to the i-th AccountID. For simplicity and efficiency, in this tutorial we fix the number of accounts to be a small number (say, 256).

To register an account via ledger::State::register, a user provides their signature public key to the ledger, and receives a unique AccountID in return. The ledger stores the public key and an initial balance of 0 for this identifier. AccountIDs are generated sequentially. That is, if n accounts have been registered so far, then the next registration will return AccountID = n+1.

To transfer value from their account to another account, the user first creates a Transaction consisting of the following pieces of information:

  • Sender's account identifier
  • Recipient's account identifier
  • Transaction amount
  • Signature on the previous three parts, using the signature public key associated with the sender's account.

The user then publishes this to the ledger, which applies the transaction via ledger::State::apply_transaction.

The latter method updates the ledger's information if the following conditions are satisfied:

  • The sender's account exists
  • The recipient's account exists
  • The sender's account contains a balance greater than or equal to the transaction amount
  • The signature is valid with respect to the public key stored in the sender's account

To enforce this logic, Transaction::verify performs the following steps on input a transaction tx and existing ledger state State.

  • Look up the (SigPubKey, Balance) tuple corresponding to the sender's ID in the Merkle tree in State.
  • Verify the transaction signature with respect to SigPubKey.
  • Check that the tx.amount <= Balance.
  • Check that the Merkle tree in State contains a path corresponding to the current recipient's ID.

If these checks pass, the ledger decrements the sender's account balance by tx.amount, increments the recipient's balance by tx.amount, and updates the appropriate paths in the Merkle tree.

Cryptographic primitives

Signature scheme

We use a simple custom implementation of Schnorr signatures over the prime order subgroup of the Jubjub curve. This curve is implemented in the ark-ed-on-bls12-381 crate. Our Schnorr signature implementation can be found in src/signature/schnorr/mod.rs.

Merkle tree

Our implementation uses the Merkle tree of ark-crypto-primitives. This is the same tree that we saw in the merkle-tree-example step. In our system, the concrete underlying hash function is the Pedersen hash function, as implemented in the ark-crypto-primitives crate. This hash is implemented over the prime-order subgroup of the Jubjub curve.

Code walk-through

To get an overview of important data structures as well as their associated methods, run cargo doc --open --no-deps.