[bitcoin-dev] Capacity increases for the Bitcoin system.

Anthony Towns aj at erisian.com.au
Wed Dec 9 04:51:39 UTC 2015

On Wed, Dec 09, 2015 at 01:31:51AM +0000, Gregory Maxwell via bitcoin-dev wrote:
> On Wed, Dec 9, 2015 at 1:09 AM, Gavin Andresen <gavinandresen at gmail.com> wrote:
> > Create a 1-megabyte transaction, with all of it's inputs spending
> > segwitness-spending SIGHASH_ALL inputs.
> > Because the segwitness inputs are smaller in the block, you can fit more of
> > them into 1 megabyte. Each will hash very close to one megabyte of data.
> Witness size comes out of the 1MB at a factor of 0.25. It is not
> possible to make a block which has signatures with the full 1MB of
> data under the sighash while also having signatures externally.  So
> every byte moved into the witness and thus only counted as 25% comes
> out of the data being hashed and is hashed nInputs (*checksigs) less
> times.

So the worst case script I can come up with is:


which (if I didn't mess it up) would give you a redeem script of about
36B plus 4B per sigop, redeemable via a single signature that's valid
for precisely one of the checksigs.

Maxing out 20k sigops gives 80kB of redeemscript in that case; so you
could have to hash 19.9GB of data to fully verify the script with
current bitcoin rules.

Segwit with the 75% factor and the same sigop limit would make that very
slightly worse -- it'd up the hashed data by maybe 1MB in total. Without
a sigop limit at all it'd be severely worse of course -- you could fit
almost 500k sigops in 2MB of witness data, leaving 500kB of base data,
for a total of 250GB of data to hash to verify your 3MB block...

Segwit without the 75% factor, but with a 3MB of witness data limit,
makes that up to three times worse (750k sigops in 3MB of witness data,
with 1MB of base data for 750GB of data to hash), but with any reasonable
sigop limit, afaics it's pretty much the same.

However I think you could add some fairly straightforward (maybe
soft-forking) optimisations to just rule out that sort of (deliberate)
abuse; eg disallowing more than a dozen sigops per input, or just failing
checksigs with the same key in a single input, maybe. So maybe that's
not sufficiently realistic?

I think the only realistic transactions that would cause lots of sigs and
hashing are ones that have lots of inputs that each require a signature
or two, so might happen if a miner is cleaning up dust. In that case,
your 1MB transaction is a single output with a bunch of 41B inputs. If you
have 10k such inputs, that's only 410kB. If each input is a legitimate
2 of 2 multisig, that's about 210 bytes of witness data per input, or
2.1MB, leaving 475kB of base data free, which matches up. 20k sigops by
475kB of data is 9.5GB of hashing.

Switching from 2-of-2 multisig to just a single public key would prevent
you from hitting the sigop limit; I think you could hit 14900 signatures
with about 626kB of base data and 1488kB of witness data, for about
9.3GB of hashed data.

That's a factor of 2x improvement over the deliberately malicious exploit
case above, but it's /only/ a factor of 2x.

I think Rusty's calculation http://rusty.ozlabs.org/?p=522 was that
the worst case for now is hashing about 406kB, 3300 times for 1.34GB of
hashed data [0].

So that's still almost a factor of 4 or 5 worse than what's possible now?
Unless I messed up the maths somewhere?


[0] Though I'm not sure that's correct? Seems like with a 1MB
    transaction with i inputs, each with s bytes of scriptsig, that you're
    hashing (1MB-s*i), and the scriptsig for a p2pkh should only be about
    105B, not 180B.  So maximising i*(1MB-s*i) = 1e6*i - 105*i^2 gives i =
    1e6/210, so 4762 inputs, and hashing 500kB of data each time,
    for about 2.4GB of hashed data total.

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