On Tue, May 26, 2015 at 01:13:05AM -0400, Peter Todd wrote:
> Case 1: Increasing the fee on a single tx
> -----------------------------------------
> We start with a 1-in-2-out P2PKH using transaction t1, 226 bytes in size
> with the minimal relay fee, 2.26uBTC. Increasing the fee while
> respecting FSS-RBF rules requires the addition of one more txin, with
> the change output value increased appropriately, resulting in
> transaction t2, size 374 bytes. If the change txout is sufficient for
> the fee increase, increasing the fee via CPFP requires a second
> 1-in-1-out transaction, 192 bytes, for a total of 418 bytes; if another
> input is required, CPFP requires a 2-in-1-out tx, 340 bytes, for a total
> of 566 bytes.
> Benefits: 11% to 34%+ cost savings, and RBF can increase fees even in
>           cases where the original transaction didn't have a change
>           output.

To clarify a point raised(1) on the pull-req itself:

The replacement transaction is allowed to not only add new txin's, but
also replace txins. Suppose t1 is a 2-in-2-out P2PKH using transaction,
374 bytes in size. With CPFP accomplished by a 1-in-1-out tx, 192 bytes,
you have 566 bytes total. With FSS RBF if you have an unspent output
greater in value than one of the outputs spent by t1, you can replace
that output in t1's vin txin set and rebroadcast the transaction, still
374 bytes in size. This gives you a 34% cost savings vs. CPFP.

> Case 2: Paying multiple recipients in succession
> ------------------------------------------------
> We have a 1-in-2-out P2PKH transaction t1, 226 bytes, that pays Alice.
> We now need to pay Bob. With plain RBF we'd just add a new outptu and
> reduce the value of the change address, a 90% savings. However with FSS
> RBF, decreasing the value is not allowed, so we have to add an input.
> If the change of t1 is sufficient to pay Bob, a second 1-in-2-out tx can
> be created, 2*226=452 bytes in total. With FSS RBF we can replace t1
> with a 2-in-3-out tx paying both, increasing the value of the change
> output appropriately, resulting in 408 bytes transaction saving 10%
> Similar to the above example in the case where the change address of t1
> is insufficient to pay Bob the end result is one less transaction output
> in the wallet, defragmenting it. Spending these outputs later on would
> require two 148 byte inputs compared to one with RBF, resulting in an
> overall savings of 25%

Similarly in the multiple recipients case, if sufficiently large
outputs are available the additional funds can be obtained by swapping
one input for another.

For instance if Alice has three outputs, 1.0, 0.5, and 0.2 BTC, and
needs to pay Bob 1.1 BTC, she can create t1:

    1.0 -> Bob   1.1
    0.2 -> Alice 0.1

If she then needs to pay Charlie 0.2 BTC she can doublespend that with:

    1.0 -> Bob     1.1
    0.5 -> Charlie 0.2
        -> Alice   0.2

Note that care does need to be taken to ensure that multiple rounds of
this always leave at least one input unchanged.

1) https://github.com/bitcoin/bitcoin/pull/6176#issuecomment-105630255


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