2

Let's take the classical example of Alice and Bob with 0.5BTC each. Commitment Txs are exchanged for a new balance sheet: Alice has 0.6BTC, and Bob 0.4BTC.

If Alice loses Bob's Breach Remedy Tx, she can still publish a Commitment Tx and get her 0.6BTC, but if Bob acts maliciously, she is not able to defraud him. Is that correct?

3

Yes that is correct. Bob's revocation secret is used as an insurance policy for Alice. If she loses it, Bob will be able to act maliciously and get away with it.

However, I want to add two things:

  1. At least in c-lightning, there is the HSM secret. This serves as a 256-bit seed for an HD wallet from which all key pairs (for Commitment Txs as well as for Breach Remedy Txs) are being derived. Since the derivation in the lightning network is also deterministic, Alice should be able to reconstruct her keys (which she still needs in order to spend the output of her Commitment Tx).
  2. If eltoo gets implemented (which requires a bitcoin soft-fork and acceptance of BIP118), the situation changes since there are no revocation keys needed anymore.

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