[bitcoin-dev] A Method for Computing Merkle Roots of Annotated Binary Trees

Russell O'Connor roconnor at blockstream.io
Thu Jun 1 15:10:56 UTC 2017

On Mon, May 29, 2017 at 12:10 PM, Peter Todd <pete at petertodd.org> wrote:

> On Mon, May 29, 2017 at 10:55:37AM -0400, Russell O'Connor wrote:
> > Some of this proposal can be salvaged, I think, by putting the hash of
> the
> > tags into Sha256Compress's first argument:
> >
> >     merkleRoot : Tree BitString -> Word256
> >     merkleRoot (Leaf (t))                := sha256Compress(sha256(t),
> > 0b0^512)
> >     merkleRoot (Unary (t, child))        := sha256Compress(sha256(t),
> > merkleRoot(child) ⋅ 0b0^256)
> >     merkleRoot (Binary (t, left, right)) := sha256Compress(sha256(t),
> > merkleRoot(left) ⋅ merkleRoot(right))
> >
> > The Merkle--Damgård property will still hold under the same conditions
> > about tags determining the type of node (Leaf, Unary, or Binary) while
> > avoiding the need for SHA256's padding.  If you have a small number of
> > tags, then you can pre-compute their hashes so that you only end up with
> > one call to SHA256 compress per node. If you have tags with a large
> amount
> > of data, you were going to be hashing them anyways.
> Notice how what you're proposing here is almost the same thing as using
> SHA256
> directly, modulo the fact that you skip the final block containing the
> message
> length.
> Similarly, you don't need to compute sha256(t) - you can just as easily
> compute
> the midstate sha256Compress(IV, t), and cache that midstate if you can
> reuse
> tags. Again, the only difference is the last block.

Yes, either way would be fine.

> > Unfortunately we lose the ability to cleverly avoid collisions between
> the
> > Sha256 and MerkleRoot functions by using safe tags.
> I think a better question to ask is why you want that property in the first
> place?
> My earlier python-proofmarshal(1) library had a scheme of per-use-case
> tags,
> but I eventually realised that depending on tags being unique is a
> footgun. For
> example, it's easy to see how two different systems could end up using the
> same
> tag due to designers forgetting to create new tags while copying and
> pasting
> old code. Similarly, if two such systems have to be integrated, you'll end
> up
> with tags getting reused for two different purposes.
> Now, if you design a system where that doesn't matter, then by extension
> it'll
> also be true that collisions between the sha256 and merkleroot functions
> don't
> matter either. And that system will be more robust to design mistakes, as
> tags
> only need to be unique "locally" to distinguish between different
> sub-types in
> a sum type (enum).

I was looking to add the property mostly because it was free to do with my
original design when the set of tags was small and could make some
applications more robust and/or easier to debug.
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