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Edited 07_payment_channels.asciidoc with Atlas code editor

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kristen@oreilly.com 2021-10-19 12:25:48 -07:00
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07_payment_channels.asciidoc
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@ -548,9 +548,17 @@ The first clause allows the output to be spent by anyone who can sign for +<revo
****
Each side sends a `revocation_basepoint` during the initial channel negotiation messages as well as a `first_per_commitment_point`. The `revocation_basepoint` is static for the lifetime of the channel, while each new channel state will be based off a new `first_per_commitment_point`.
Given this information, the `revocationpubkey` for each channel state is derived via the following series of elliptic curve and hashing operations: `revocationpubkey = revocation_basepoint * sha256(revocation_basepoint || per_commitment_point) + per_commitment_point * sha256(per_commitment_point || revocation_basepoint)`.
Given this information, the `revocationpubkey` for each channel state is derived via the following series of elliptic curve and hashing operations:
Due to the commutative property of the abelian groups that elliptic curves are defined over, once the `per_commitment_secret` (the private key for the `per_commitment_point`) is revealed by the remote party, self can derive the private key for the `revocationpubkey` with the following operation: `revocation_priv = (revocationbase_priv * sha256(revocation_basepoint || per_commitment_point)) + (per_commitment_secret * sha256(per_commitment_point || revocation_basepoint)) mod N`.
----
revocationpubkey = revocation_basepoint * sha256(revocation_basepoint || per_commitment_point) + per_commitment_point * sha256(per_commitment_point || revocation_basepoint)
----
Due to the commutative property of the abelian groups that elliptic curves are defined over, once the `per_commitment_secret` (the private key for the `per_commitment_point`) is revealed by the remote party, self can derive the private key for the `revocationpubkey` with the following operation:
----
revocation_priv = (revocationbase_priv * sha256(revocation_basepoint || per_commitment_point)) + (per_commitment_secret * sha256(per_commitment_point || revocation_basepoint)) mod N
----
To see why this works in practice, notice that we can _reorder_ (commute) and expand the public key computation of the original formula for `revocationpubkey`:
```