Unspent note handling

Processing of multiple unspent notes in a single outgoing operation can result in additional fees

Multiple transactions are sometimes required when there are many unspent notes in an account.

zkBob uses an Unspent Transaction Output (UTXO) model with strict ordering. Incoming zkAccount transfers are ordered and referred to as 'notes'. About notes:

• Notes are received as incoming transfers within the zkBob pool. They are collected in the receiver's zkAccount and displayed as part of the account's BOB balance.

• Notes are collected in a FIFO (first-in-first-out) order.

• Collected (unspent) notes are automatically aggregated and added to any outgoing transfer/ withdrawal transaction. A maximum of 3 notes can be included in 1 transaction.

When an account has many incoming and outgoing transactions, notes are aggregated regularly (collected and spent) and do not build up.

However, in certain scenarios there may be a large number of unspent notes which are requested for processing in a single operation. In this case, multiple transactions are performed by the zkBob application for a single operation. Each transaction requires a separate 0.10 (Polygon) or 0.50 (Optimism) BOB fee.

Example: Carl withdraws 20 BOB on Optimism

Carl starts with a zkBob account funded with 10 BOB. He then receives 10 separate transfers through zkBob of 1 BOB each (ie 10 notes) from his friends. Now, Carl's total account balance displays 20 BOB. He decides to withdraw the entire 20 BOB.

In this scenario there are 10 unspent notes that need to be processed to complete the entire operation. They are automatically processed in a series of 4 transactions.

1. Tx #1: Aggregates the first 3 notes of 1 BOB each and increases the account balance. The account balance becomes: 10 + 3x1 - 0.1(fee) = 12.9 BOB

2. Tx #2: Aggregates next 3 notes -> acc = 12.9 + 3x1 - 0.1(fee) = 15.8 BOB

3. Tx #3: Aggregates next 3 notes -> acc = 15.8 + 3x1 - 0.1(fee) = 18.7 BOB

4. Tx #4: Aggregates the last note -> acc = 18.7 + 1 - 0.1(fee) = 19.6 BOB and simultaneously makes an outgoing withdrawal for the full account balance, i.e. 19.6 BOB

When the operation is complete, Carl receives 19.6 BOB, and 0.4 BOB is spent as fees for the 4 transactions. His new zkAccount balance is 0.

Example: Carl withdraws 15 BOB on Optimism

If Carl wants to withdraw 15 BOB, the operation only requires 2 txs.

1. Tx #1: Aggregates first 3 notes -> acc = 10 + 3x1 - 0.1(fee) = 12.9 BOB

2. Tx #2: Aggregates next 3 notes -> acc = 12.9 + 3x1 - 0.1(fee) = 15.8 BOB and makes a simultaneous withdrawal of 15 BOB acc = 15.8 - 15 = 0.8 BOB . The account also contains 4 unspent notes of 1 BOB each.

Carl receives 15 BOB, and 0.2 BOB is used to pay the transaction fees. His new zkAccount balance displays 4.8 BOB. His account consists of 4 unspent notes of 1 BOB each and 0.8 account balance, however this is abstracted for Carl so he only sees the total account balance of 4.8.