On Mon, Jan 18, 2016 at 10:02:51PM +1000, Anthony Towns via bitcoin-dev wrote:
> I think these numbers are slightly mistaken -- I was only aware of version
> 1 segwit scripts at the time, and assumed 256 bit hashes would be used
> for all segwit transaction, however version 0 segwit txns would be more
> efficient for p2pkh, with the same security as bitcoin currently has
> (which seems fine).

Latest segwit code just has version 0 witness format, and treats a 32
byte push as the sha256 of a script, and a 20 byte push as the hash of
the pub key. Also, the witness scriptPubKey format uses "OP_0 [hash]" to
push the version and hash to the script separately, rather than "[0x00
script]" or "[0x01 hash]" (this changes allows segwit transactions to
be encoded backwards compatibly as a p2sh payment).

> p2pkh:
>   segwit: 10+41i+36o + 0.25*105*i [1]

> [0] 10 bytes for version (4), input count (1), output count (1) and
>     locktime (4); 146 bytes per input consisting of tx hash (32), txout
>     index (4), script length (1), scriptsig (signature and pubkey =
>     105), CHECKSIG = 25), and sequence number (4); 34 bytes per output
>     consisting of value (8), script length (1) and scriptpubkey (DUP

> [1] Same as [0], except two extra bytes per output script (segwit push
>     and segwit version byte), and moving the 105 bytes of signature
>     script directly into the segregated witness

So this change means segwit p2pkh needs 31 bytes per output not 36 bytes (value,
length stay the same, scriptpubkey becomes "OP_0 PUSH20" for 22 bytes
instead of 25+2 bytes). This gives another couple of percent gain, so:

    segwit: 10+41i+31o + 0.25*105*i [1]

Setting i=o makes:

>         p2pkh           2-of-2 msig
> now     10+180i         10+286i
> segwit  10+104i         10+140i


segwit    10+99i          10+140i

and therefore,

>         p2pkh           2-of-2 msig
> now     100%            100%
> segwit  166%-173%       197%-204%


segwit    174%-181%       197%-204%

Constantly creeping up! Pretty nice.

Also, p2pkh with segwit-via-p2sh is probably interesting, those numbers
work out as:

segwit:   10+41i+31o + 0.25*105*i (for comparison)
segp2sh:  10+60i+32o + 0.25*105*i [0]
  ->      10+119i
  ->      147%-151%

So that still looks like a reasonable improvement even if (eg) in the
short term merchants are the only ones that upgrade, and customers just
use non-segwit-aware wallets with a p2sh address that's only redeemable
by a segwit-aware wallet.


[0] 10 bytes standard. For each input, tx hash (32) plus index (4),
    script length (1) and scriptsig which is a push of the standard segwit
    pubscript (22+1) totaling to 60, and witness data is the same as for
    normal segwit (105). Each output is standard p2sh, which is value
    (8), length (1) and script (23) for a total of 32.


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