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 P2WSH 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<sup>[BIP141](https://github.com/bitcoin/bips/blob/master/bip-0141.mediawiki#witness-program)</sup> 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](#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-remote` output may be below the dust limit.
* 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 both a to-local output and a to-remote output.

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

	p2wsh: 34 bytes
		- OP_0: 1 byte
		- OP_DATA: 1 byte (witness_script_SHA256 length)
		- witness_script_SHA256: 32 bytes

	p2wpkh: 22 bytes
		- OP_0: 1 byte
		- OP_DATA: 1 byte (public_key_HASH160 length)
		- public_key_HASH160: 20 bytes

	multi_sig: 71 bytes
		- OP_2: 1 byte
		- OP_DATA: 1 byte (pub_key_alice length)
		- pub_key_alice: 33 bytes
		- OP_DATA: 1 byte (pub_key_bob length)
		- pub_key_bob: 33 bytes
		- OP_2: 1 byte
		- OP_CHECKMULTISIG: 1 byte

	witness: 222 bytes
		- number_of_witness_elements: 1 byte
		- nil_length: 1 byte
		- sig_alice_length: 1 byte
		- sig_alice: 73 bytes
		- sig_bob_length: 1 byte
		- sig_bob: 73 bytes
		- witness_script_length: 1 byte
		- witness_script (multi_sig)
		
	funding_input: 41 bytes
		- previous_out_point: 36 bytes
			- hash: 32 bytes
			- index: 4 bytes
		- var_int: 1 byte (script_sig length)
		- script_sig: 0 bytes
		- witness <----	we use "witness" instead of "script_sig" for
	 			transaction validation, but "witness" is stored
	 			separately and cost for it size is smaller. So
	 			we separate the calculation of ordinary data
	 			from witness data.
		- sequence: 4 bytes

	output_paying_to_us: 43 bytes
		- value: 8 bytes
		- var_int: 1 byte (pk_script length)
		- pk_script (p2wsh): 34 bytes

	output_paying_to_them: 31 bytes
		- value: 8 bytes
		- var_int: 1 byte (pk_script length)
		- pk_script (p2wpkh): 22 bytes

	 htlc_output: 43 bytes
		- value: 8 bytes
		- var_int: 1 byte (pk_script length)
		- pk_script (p2wsh): 34 bytes

	 witness_header: 2 bytes
		- flag: 1 byte
		- marker: 1 byte

	 commitment_transaction: 125 + 43 * num-htlc-outputs bytes
		- version: 4 bytes
		- witness_header <---- part of the witness data
		- count_tx_in: 1 byte
		- tx_in: 41 bytes
			funding_input
		- count_tx_out: 1 byte
		- tx_out: 74 + 43 * num-htlc-outputs bytes
			output_paying_to_them,
			output_paying_to_us,
			....htlc_output's...
		- lock_time: 4 bytes
	
Multiplying non-witness data by 4, this gives a weight of:
	
	// 500 + 172 * num-htlc-outputs weight
	commitment_transaction_weight = 4 * commitment_transaction

	// 224 weight
	witness_weight = witness_header + witness

	overall_weight = 500 + 172 * num-htlc-outputs + 224 weight 

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

    accepted_htlc_script: 109 bytes
	    - OP_DATA: 1 byte (remotekey length)
		- remotekey: 33 bytes
		- OP_SWAP: 1 byte
		- OP_SIZE: 1 byte
		- 32: 1 byte
		- OP_EQUAL: 1 byte
		- OP_IF: 1 byte
		- OP_HASH160: 1 byte
		- OP_DATA: 1 byte (ripemd-of-payment-hash length)
		- ripemd-of-payment-hash: 20 bytes
		- OP_EQUALVERIFY: 1 byte
		- 2: 1 byte
		- OP_SWAP: 1 byte
		- OP_DATA: 1 byte (localkey length)
		- localkey: 33 bytes
		- 2: 1 byte
		- OP_CHECKMULTISIG: 1 byte
		- OP_ELSE: 1 byte
		- OP_DROP: 1 byte
		- OP_PUSHDATA2: 1 byte (locktime length)
		- locktime: 2 bytes
		- OP_CHECKLOCKTIMEVERIFY: 1 byte
		- OP_DROP: 1 byte
        - OP_CHECKSIG: 1 byte
		- OP_ENDIF: 1 byte

    offered_htlc_script: 104 bytes
		- OP_DATA: 1 byte (remotekey length)
		- remotekey: 33 bytes
		- OP_SWAP: 1 byte
		- OP_SIZE: 1 byte
		- 32: 1 byte
		- OP_EQUAL: 1 byte
		- OP_NOTIF: 1 byte
		- OP_DROP: 1 byte
		- 2: 1 byte
		- OP_SWAP: 1 byte
		- OP_DATA: 1 byte (localkey length)
		- localkey: 33 bytes
		- 2: 1 byte
		- OP_CHECKMULTISIG: 1 byte
		- OP_ELSE: 1 byte
		- OP_HASH160: 1 byte
		- OP_DATA: 1 byte (ripemd-of-payment-hash length)
		- ripemd-of-payment-hash: 20 bytes
		- OP_EQUALVERIFY: 1 byte
		- OP_CHECKSIG: 1 byte
		- OP_ENDIF: 1 byte

    timeout_witness: 256 bytes
		- number_of_witness_elements: 1 byte
		- nil_length: 1 byte
		- sig_alice_length: 1 byte
		- sig_alice: 73 bytes
		- sig_bob_length: 1 byte
		- sig_bob: 73 bytes
		- nil_length: 1 byte
		- witness_script_length: 1 byte
		- witness_script (offered_htlc_script)

    success_witness: 293 bytes
		- number_of_witness_elements: 1 byte
		- nil_length: 1 byte
		- sig_alice_length: 1 byte
		- sig_alice: 73 bytes
		- sig_bob_length: 1 byte
		- sig_bob: 73 bytes
		- preimage_length: 1 byte
		- preimage: 32 bytes
		- witness_script_length: 1 byte
		- witness_script (accepted_htlc_script)

    commitment_input: 41 bytes
		- previous_out_point: 36 bytes
			- hash: 32 bytes
			- index: 4 bytes
		- var_int: 1 byte (script_sig length)
		- script_sig: 0 bytes
		- witness (success_witness or timeout_witness)
		- sequence: 4 bytes

    htlc_tx_output: 43 bytes
		- value: 8 bytes
		- var_int: 1 byte (pk_script length)
		- pk_script (p2wsh): 34 bytes

	htlc_transaction: 
		- version: 4 bytes
		- witness_header <---- part of the witness data
		- count_tx_in: 1 byte
		- tx_in: 41 bytes
			commitment_input
		- count_tx_out: 1 byte
		- tx_out: 43
			htlc_tx_output
		- lock_time: 4 bytes

Multiplying non-witness data by 4, this gives a weight of 376.  Adding
the witness data for each case (256 + 2 for HTLC-timeout, 293 + 2 for
HTLC-success) gives a weight of:

	634 (HTLC-timeout)
	671 (HTLC-success)

### Requirements

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

1. Multiply `feerate-per-kw` by 634 and divide by 1024 (rounding down).

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

1. Multiply `feerate-per-kw` by 671 and divide by 1024 (rounding down).

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

1. Start with `weight` = 724, and `fee` = 0.

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 172 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 172 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-commitment-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-commitment-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](#efficient-per-commitment-secret-storage)).

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

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

	pubkey = basepoint + SHA256(per-commitment-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(per-commitment-point || basepoint)

## `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-commitment-point` is generated using EC multiplication:

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

This construction ensures that neither the node providing the
basepoint nor the node providing the `per-commitment-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

FIXME

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