lightning-bolts/03-transactions.md

BOLT #3: Bitcoin Transaction and Script Formats

This details the exact format of on-chain transactions, which both sides need to agree on to ensure signatures are valid. That is, the funding transaction output script, commitment transactions and the HTLC transactions.

Transaction input and output ordering

Lexicographic ordering as per BIP 69.

Use of segwit

Most transaction outputs used here are P2WSH outputs, the segwit version of P2SH. To spend such outputs, the last item on the witness stack must be the actual script that was used to generate the P2SWH output that is being spent. This last item has been omitted for brevity in the rest of this document.

Funding Transaction Output

• The funding output script is a pay-to-witness-script-hash^BIP141 to:
  • 0 2 <key1> <key2> 2 OP_CHECKMULTISIG
• Where <key1> is the numerically lesser of the two DER-encoded funding-pubkey and <key2> is the greater.

Commitment Transaction

• version: 2
• locktime: lower 24 bits are the obscured commitment transaction number.
• txin count: 1
  • txin[0] outpoint: txid and output_index from funding_created message
  • txin[0] sequence: lower 24 bits are upper 24 bits of the obscured commitment transaction number.
  • txin[0] script bytes: 0
  • txin[0] witness: <signature-for-key1> <signature-for-key-2>

The 48-bit commitment transaction number is obscured by XOR with the lower 48 bits of:

SHA256(payment-basepoint from open_channel || payment-basepoint from accept_channel)

This obscures the number of commitments made on the channel in the case of unilateral close, yet still provides a useful index for both nodes (who know the payment-basepoints) to quickly find a revoked commitment transaction.

Commitment Transaction Outputs

To allow an opportunity for penalty transactions in case of a revoked commitment transaction, all outputs which return funds to the owner of the commitment transaction (aka "local node") must be delayed for to-self-delay blocks. This delay is done in a second stage HTLC transaction (HTLC-success for HTLCs accepted by the local node, HTLC-timeout for HTLCs offered by the local node).

The reason for the separate transaction stage for HTLC outputs is so that HTLCs can time out or be fulfilled even though they are within the to-self-delay OP_CHECKSEQUENCEVERIFY delay. Otherwise the required minimum timeout on HTLCs is lengthened by this delay, causing longer timeouts for HTLCs traversing the network.

The amounts for each output are rounded down to whole satoshis. If this amount, minus the fees for the HTLC transaction is less than the dust-limit-satoshis set by the owner of the commitment transaction, the output is not produced (thus the funds add to fees).

To-Local Output

This output sends funds back to the owner of this commitment transaction, thus must be timelocked using OP_CSV. It can be claimed, without delay, by the other party if they know the revocation key. The output is a version 0 P2WSH, with a witness script:

OP_IF
    # Penalty transaction
    <revocation-pubkey>
OP_ELSE
    `to-self-delay`
    OP_CSV
    OP_DROP
    <local-delayedkey>
OP_ENDIF
OP_CHECKSIG

It is spent by a transaction with nSequence field set to to-self-delay (which can only be valid after that duration has passed), and witness script <local-delayedsig> 0.

If a revoked commit tx is published, the other party can spend this output immediately with the following witness script:

<revocation-sig> 1

To-Remote Output

This output sends funds to the other peer, thus is a simple P2PKH to <remotekey>.

Offered HTLC Outputs

This output sends funds to a HTLC-timeout transaction after the HTLC timeout, or to the remote peer on successful payment preimage. The output is a P2WSH, with a witness script:

<remotekey> OP_SWAP
    OP_SIZE 32 OP_EQUAL
OP_NOTIF
    # To me via HTLC-timeout tx (timelocked).
    OP_DROP 2 OP_SWAP <localkey> 2 OP_CHECKMULTISIG
OP_ELSE
    # To you with preimage.
    OP_HASH160 <ripemd-of-payment-hash> OP_EQUALVERIFY
    OP_CHECKSIG
OP_ENDIF

The remote node can redeem the HTLC with the scriptsig:

<remotesig> <payment-preimage>

Either node can use the HTLC-timeout transaction to time out the HTLC once the HTLC is expired, as show below.

Received HTLC Outputs

This output sends funds to the remote peer after the HTLC timeout, or to an HTLC-success transaction with a successful payment preimage. The output is a P2WSH, with a witness script:

<remotekey> OP_SWAP
    OP_SIZE 32 OP_EQUAL
OP_IF
    # To me via HTLC-success tx.
    OP_HASH160 <ripemd-of-payment-hash> OP_EQUALVERIFY
    2 OP_SWAP <localkey> 2 OP_CHECKMULTISIG
OP_ELSE
    # To you after timeout.
    OP_DROP <locktime> OP_CHECKLOCKTIMEVERIFY OP_DROP
    OP_CHECKSIG
OP_ENDIF

To timeout the htlc, the remote node spends it with the scriptsig:

<remotesig> 0

To redeem the HTLC, the HTLC-success transaction is used as detailed below.

HTLC-Timeout and HTLC-Success Transaction

These HTLC transactions are almost identical, except the HTLC-Timeout transaction is timelocked. This is also the transaction which can be spent by a valid penalty transaction.

• version: 2
• txin: the commitment transaction HTLC output.
• locktime: 0 for HTLC-Success, htlc-timeout for HTLC-Timeout.
• txin count: 1
  • txin[0] outpoint: txid of the commitment transaction and output_index of the matching HTLC output for the HTLC transaction.
  • txin[0] sequence: 0
  • txin[0] script bytes: 0
  • txin[0] witness stack: 0 <remotesig> <localsig> 0 (HTLC-Timeout) or 0 <remotesig> <localsig> <payment-preimage> (HTLC-success).
• txout count: 1
  • txout[0] amount: the HTLC amount minus fees (see Fee Calculation).
  • txout[0] script: version 0 P2WSH with witness script as below.

The witness script for the output is:

OP_IF
    # Penalty transaction
    <revocation-pubkey>
OP_ELSE
    `to-self-delay`
    OP_CSV
    OP_DROP
    <local-delayedkey>
OP_ENDIF
OP_CHECKSIG

To spend this via penalty, the remote node uses a witness stack <revocationsig> 1 and to collect the output the local node uses an input with nSequence to-self-delay and a witness stack <local-delayedsig> 0

Fee Calculation

The fee calculation for both commitment transactions and HTLC transactions is based on the current feerate-per-kw and the expected weight of the transaction.

The actual and expected weight vary for several reasons:

• Bitcoin uses DER-encoded signatures which vary in size.
• Bitcoin also uses variable-length integers, so a large number of outputs will take 3 bytes to encode rather than 1.
• The to-local output may be below the dust limit once fees are extracted.

Thus we use a simplified formula for expected weight, which assumes:

• Signatures are 73 bytes long (the maximum length)
• There is a small number of outputs (thus 1 byte to count them)
• There is always a to-local output.

The expected weight of a commitment transaction is calculated as follows:

transaction core: 4 + 1 + 1 + 4
transaction input: 32 + 4 + 1 + 4
transaction input witness: 1 + 74 + 74 + 1 + 1 + 34 + 34 + 1 + 1
transaction output: 8 + 1
transaction htlc output: 34
transaction to-local output: 34
transaction to-remote output: 25

Multiplying non-witness data by 4, this gives a weight of:

597 + 136*num-htlc-outputs + 100*to-remote

Where to-remote is 0 if the amount is below the local node's dust-limit-satoshis, or 1 otherwise. num-htlc-outputs is the number of HTLCs whose amount (minus HTLC transaction fee) is greater or equal to the local dust-limit-satoshis.

The expected weight of an HTLC transaction is calculated as follows:

transaction core: 4 + 1 + 1 + 4
transaction input: 32 + 4 + 1 + 4
transaction input witness: 1 + 74 + 74 + (1 for HTLC-timeout or 33 for HTLC-success)
transaction output: 8 + 1 + 34

Multiplying non-witness data by 4, this gives a weight of:

526 (HTLC-timeout)
558 (HTLC-success)

Requirements

The fee for an HTLC-timeout transaction MUST BE calculated to match:

1. Multiply feerate-per-kw by 526 and divide by 1024 (rounding down).

The fee for an HTLC-success transaction MUST BE calculated to match:

1. Multiply feerate-per-kw by 558 and divide by 1024 (rounding down).

The fee for a commitment transaction MUST BE calculated to match:

1. Start with weight = 597, and fee = 0.

2. If the amount to the remote node is greater or equal to the local node's dust-limit-satoshis, add 136 to weight.

3. For every offered HTLC, if the HTLC amount plus the HTLC-timeout transaction fee is greater or equal to the local node's dust-limit-satoshis, then add 136 to weight, otherwise add the HTLC amount to fee.

4. For every accepted HTLC, if the HTLC amount plus the HTLC-success transaction fee is greater or equal to the local node's dust-limit-satoshis, then add 136 to weight, otherwise add the HTLC amount to fee.

5. Multiply feerate-per-kw by weight, divide by 1024 (rounding down), and add to fee.

Key Derivation

Each commitment transaction uses a unique set of keys; <localkey> and <remotekey>. The HTLC-success and HTLC-timeout transactions use <local-delayedkey> and <revocationkey>. These are changed every time depending on the per-commitment-point.

Keys change because of the desire for trustless outsourcing of watching for revoked transactions; a "watcher" should not be able to determine what the contents of commitment transaction is, even if given the transaction ID to watch for and can make a resonable guess as to what HTLCs and balances might be included. Nonetheless, to avoid storage for every commitment transaction, it can be given the per-commit-secret values (which can be stored compactly) and the revocation-basepoint and delayed-payment-basepoint to regnerate the scripts required for the penalty transaction: it need only be given (and store) the signatures for each penalty input.

Changing the <localkey> and <remotekey> every time ensures that commitment transaction id cannot be guessed: Every commitment transaction uses one of these in its output script. Splitting the <local-delayedkey> which is required for the penalty transaction allows that to be shared with the watcher without revealing <localkey>; even if both peers use the same watcher, nothing is revealed.

Finally, even in the case of normal unilateral close, the HTLC-success and/or HTLC-timeout transactions do not reveal anything to the watcher, as it does not know the corresponding per-commit-secret and cannot relate the <local-delayedkey> or <revocationkey> with their bases.

For efficiency, keys are generated from a series of per-commitment secrets which are generated from a single seed, allowing the receiver to compactly store them (see below).

localkey, remotekey, local-delayedkey and remote-delayedkey Derivation

These keys are simply generated by addition from their base points:

pubkey = basepoint + SHA256(per-commit-point || basepoint)*G

The localkey uses the local node's payment-basepoint, remotekey uses the remote node's payment-basepoint, the local-delayedkey uses the local node's delayed-payment-basepoint, and the remote-delayedkey uses the remote node's delayed-payment-basepoint.

The correspoding private keys can be derived similarly if the basepoint secrets are known (ie. localkey and local-delayedkey only):

secretkey = basepoint-secret + SHA256(basepoint || commit-number)

revocationkey Derivation

The revocationkey is a blinded key: the remote node provides the base, and the local node provides the blinding factor which it later reveals, so the remote node can use the secret revocationkey for a penalty transaction.

The per-commit-point is generated using EC multiplication:

per-commit-point = per-commit-secret * G

And this is used to derive the revocation key from the remote node's revocation-basepoint:

revocationkey = revocation-basepoint * SHA256(revocation-basepoint || per-commit-point) + per-commit-point*SHA256(per-commit-point || revocation-basepoint)

This construction ensures that neither the node providing the basepoint nor the node providing the per-commit-point can know the private key without the other node's secret.

Per-commitment Secret Requirements

A node MUST select an unguessable 256-bit seed for each connection, and MUST NOT reveal the seed. Up to 2^48-1 per-commitment secrets can be generated; the first secret used MUST be index 281474976710655, and then the index decremented.

The I'th secret P MUST match the output of this algorithm:

generate_from_seed(seed, I):
    P = seed
    for B in 0 to 47:
        if B set in I:
            flip(B) in P
            P = SHA256(P)
    return P

Where "flip(B)" alternates the B'th least significant bit in the value P.

The receiving node MAY store all previous per-commitment secrets, or MAY calculate it from a compact representation as described below.

Efficient Per-commitment Secret Storage

The receiver of a series of secrets can store them compactly in an array of 49 (value,index) pairs. This is because given a secret on a 2^X boundary, we can derive all secrets up to the next 2^X boundary, and we always receive secrets in descending order starting at 0xFFFFFFFFFFFF.

In binary, it's helpful to think of any index in terms of a prefix, followed by some trailing zeroes. You can derive the secret for any index which matches this prefix.

For example, secret 0xFFFFFFFFFFF0 allows us to derive secrets for 0xFFFFFFFFFFF1 through 0xFFFFFFFFFFFF inclusive. Secret 0xFFFFFFFFFF08 allows us to derive secrets 0xFFFFFFFFFF09 through 0xFFFFFFFFFF0F inclusive.

We do this using a slight generalization of generate_from_seed above:

# Return I'th secret given base secret whose index has bits..47 the same.
derive_secret(base, bits, I):
    P = base
    for B in 0 to bits:
        if B set in I:
            flip(B) in P
            P = SHA256(P)
    return P

We need only save one secret for each unique prefix; in effect we can count the number of trailing zeros, and that determines where in our storage array we store the secret:

# aka. count trailing zeroes
where_to_put_secret(I):
	for B in 0 to 47:
		if testbit(I) in B == 1:
			return B
    # I = 0, this is the seed.
	return 48

We also need to double-check that all previous secrets derive correctly, otherwise the secrets were not generated from the same seed:

insert_secret(secret, I):
	B = where_to_put_secret(secret, I)

    # This tracks the index of the secret in each bucket as we traverse.
	for b in 0 to B:
		if derive_secret(secret, B, known[b].index) != known[b].secret:
			error The secret for I is incorrect
			return

    # Assuming this automatically extends known[] as required.
	known[B].index = I
	known[B].secret = secret

Finally, if we are asked to derive secret at index I, we need to figure out which known secret we can derive it from. The simplest method is iterating over all the known secrets, and testing if we can derive from it:

derive_old_secret(I):
	for b in 0 to len(secrets):
	    # Mask off the non-zero prefix of the index.
	    MASK = ~((1 << b)-1)
		if (I & MASK) == secrets[b].index:
			return derive_secret(known, i, I)
    error We haven't received index I yet.

This looks complicated, but remember that the index in entry b has b trailing zeros; the mask and compare is just seeing if the index at each bucket is a prefix of the index we want.

References

Authors

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