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From: "Russell O'Connor" <roconnor@blockstream.io>
Date: Thu, 1 Jun 2017 11:10:56 -0400
Message-ID: <CAMZUoKm6Oh4fp3nK3sTkfX+cu2Nuf6gKRs87Cu4w9Tm+G5Jb5Q@mail.gmail.com>
To: Peter Todd <pete@petertodd.org>
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Cc: Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
Subject: Re: [bitcoin-dev] A Method for Computing Merkle Roots of Annotated
 Binary Trees
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On Mon, May 29, 2017 at 12:10 PM, Peter Todd <pete@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))                :=3D sha256Compress(sha256(t),
> > 0b0^512)
> >     merkleRoot (Unary (t, child))        :=3D sha256Compress(sha256(t),
> > merkleRoot(child) =E2=8B=85 0b0^256)
> >     merkleRoot (Binary (t, left, right)) :=3D sha256Compress(sha256(t),
> > merkleRoot(left) =E2=8B=85 merkleRoot(right))
> >
> > The Merkle--Damg=C3=A5rd property will still hold under the same condit=
ions
> > 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 wit=
h
> > 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 fir=
st
> 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 th=
e
> 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 en=
d
> 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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<div dir=3D"ltr"><br><div class=3D"gmail_extra"><br><div class=3D"gmail_quo=
te">On Mon, May 29, 2017 at 12:10 PM, Peter Todd <span dir=3D"ltr">&lt;<a h=
ref=3D"mailto:pete@petertodd.org" target=3D"_blank">pete@petertodd.org</a>&=
gt;</span> wrote:<br><blockquote class=3D"gmail_quote" style=3D"margin:0 0 =
0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><span class=3D"">On Mon=
, May 29, 2017 at 10:55:37AM -0400, Russell O&#39;Connor wrote:<br></span><=
span class=3D"">&gt; Some of this proposal can be salvaged, I think, by put=
ting the hash of the<br>
&gt; tags into Sha256Compress&#39;s first argument:<br>
&gt;<br>
&gt;=C2=A0 =C2=A0 =C2=A0merkleRoot : Tree BitString -&gt; Word256<br>
&gt;=C2=A0 =C2=A0 =C2=A0merkleRoot (Leaf (t))=C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 :=3D sha256Compress(sha256(t),<br>
&gt; 0b0^512)<br>
&gt;=C2=A0 =C2=A0 =C2=A0merkleRoot (Unary (t, child))=C2=A0 =C2=A0 =C2=A0 =
=C2=A0 :=3D sha256Compress(sha256(t),<br>
&gt; merkleRoot(child) =E2=8B=85 0b0^256)<br>
&gt;=C2=A0 =C2=A0 =C2=A0merkleRoot (Binary (t, left, right)) :=3D sha256Com=
press(sha256(t),<br>
&gt; merkleRoot(left) =E2=8B=85 merkleRoot(right))<br>
&gt;<br>
&gt; The Merkle--Damg=C3=A5rd property will still hold under the same condi=
tions<br>
&gt; about tags determining the type of node (Leaf, Unary, or Binary) while=
<br>
&gt; avoiding the need for SHA256&#39;s padding.=C2=A0 If you have a small =
number of<br>
&gt; tags, then you can pre-compute their hashes so that you only end up wi=
th<br>
&gt; one call to SHA256 compress per node. If you have tags with a large am=
ount<br>
&gt; of data, you were going to be hashing them anyways.<br>
<br>
</span>Notice how what you&#39;re proposing here is almost the same thing a=
s using SHA256<br>
directly, modulo the fact that you skip the final block containing the mess=
age<br>
length.<br>
<br>
Similarly, you don&#39;t need to compute sha256(t) - you can just as easily=
 compute<br>
the midstate sha256Compress(IV, t), and cache that midstate if you can reus=
e<br>
tags. Again, the only difference is the last block.<span class=3D""><br></s=
pan></blockquote><div><br></div><div>Yes, either way would be fine.<br></di=
v><div>=C2=A0</div><blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 =
.8ex;border-left:1px #ccc solid;padding-left:1ex"><span class=3D"">
&gt; Unfortunately we lose the ability to cleverly avoid collisions between=
 the<br>
&gt; Sha256 and MerkleRoot functions by using safe tags.<br>
<br>
</span>I think a better question to ask is why you want that property in th=
e first<br>
place?<br>
<br>
My earlier python-proofmarshal(1) library had a scheme of per-use-case tags=
,<br>
but I eventually realised that depending on tags being unique is a footgun.=
 For<br>
example, it&#39;s easy to see how two different systems could end up using =
the same<br>
tag due to designers forgetting to create new tags while copying and pastin=
g<br>
old code. Similarly, if two such systems have to be integrated, you&#39;ll =
end up<br>
with tags getting reused for two different purposes.<br>
<br>
Now, if you design a system where that doesn&#39;t matter, then by extensio=
n it&#39;ll<br>
also be true that collisions between the sha256 and merkleroot functions do=
n&#39;t<br>
matter either. And that system will be more robust to design mistakes, as t=
ags<br>
only need to be unique &quot;locally&quot; to distinguish between different=
 sub-types in<br>
a sum type (enum).<br></blockquote><div><br></div><div>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.<br></div></div></div></div>

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