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

[Peter Todd]

On Mon, May 29, 2017 at 10:55:37AM -0400, Russell O'Connor wrote:
> > This doesn't hold true in the case of pruned trees, as for the pruning to
> > be
> > useful, you don't know what produced the left merkleRoot, and thus you
> > can't
> > guarantee it is in fact a midstate of a genuine SHA256 hash.
> >
> 
> Thanks for the review Peter.  This does seem like a serious issue that I
> hadn't considered yet.  As far as I understand, we have no reason to think
> that the SHA-256 compression function will be secure with chosen initial
> values.

Well, it's an easy thing to forget, unless like me, you've written a general
purpose library to work with pruned data. :) (actually, soon to be two of
them!)

I also ran into the midstate issue with my OpenTimestamps protocol, as I was
looking into whether or not it was safe to have a SHA256 midstate commitment
operation, and couldn't find clear evidence that it was.

> 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.

> 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).


FWIW what I've done with my newer (and as yet unpublished) rust-proofmarshal
work is commitments are only valid for a specific type. Secondly, I use
blake2b, whose compression function processes up to 128 bytes of message on
each invocation.  That's large enough for four 32 byte hashes, which is by
itself more than sufficient for a summed merkle tree with three 32 byte hashes
(left right and sum) and a per-node-type tag.

Blake2b's documentations don't make it clear if it's resistant to collision if
the adversary can control the salt or personalization strings, so I don't
bother using them - the large block size by itself is enough to fit almost any
use-case into a single block, and it hashes blocks significantly faster than
SHA256. This also has the advantage that the actual primitive I'm using is 100%
standard blake2b, an aid to debugging and development.

1) https://github.com/proofchains/python-proofmarshal

-- 
https://petertodd.org 'peter'[:-1]@petertodd.org
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