Transaction Fee in Confidential Transactions

Question

Is there any transaction fee for Confidential Transactions in the Liquid Network?

In the UTXO model, Alice has 10 btc. She sends 1 btc to Bob, 8.999 btc as return change, and 0.001 as fee.

Input :  10     btc (Alice)  
Outputs:  1     btc (Bob)  
          8.999 btc (Alice)

The remaining balance of 0.001 is considered the fee but not recorded as a transaction output.

Is this the same for Confidential Transaction?

Input : C1 = Commit (10btc)
Output: C2 = Commit (1 btc)
        C3 = Commit (8.999 btc)
        C4 = Commit (0.001 btc)

C1 = C2 + C3 + C4

If C4 is not there, then can we assume C4 = C1 - C2 - C3.

But is there any coinbase tx in Liquid to take the C4 fee? I 'm confused.

Answer 1

In Confidental Transactions, like they are implemented in Blockstream Liquid, transactions have an explicit (plain text) fee field, and the rule is that sum(output_commitments) + commit(fee) = sum(input_commitments).

Without clear text fee field, miners indeed would not be able to claim the difference between outputs and inputs.

Answer 2

Fees in liquid are explicitly defined as an output, as describing them as the deficit between input and output is impossible when the values are unknown to the validator.