Subject: Re: [Bitcoin-development] Ultimate Blockchain Compression w/ trust-free lite nodes

From: Peter Todd <[email-masked]>
Date: Mon, 18 Jun 2012 06:14:41 -0400

On Mon, Jun 18, 2012 at 12:46:47AM +0200, Alberto Torres wrote:
> Hi,
> 
> I did describe a very similar thing back in January (also illustrated,
> and, if I'm not mistaken, more simple and efficient to recalculate),
> and I wanted to do a prototype, but I have been very busy with other
> projects since then.
> 
> https://en.bitcoin.it/wiki/User:DiThi/MTUT
> 
> I just saw Gavin left a comment in the talk page, I'm sorry I haven't
> seen it earlier.
> 
> I think armory is the perfect client to implement such an idea. I sort
> of waited it to be able to run in my laptop with 2 GB of RAM before
> being sucked into other projects. I even lost track of its
> development.

I strongly disagree on that point. What you're proposing needs miner
support to work, and miners generally run either the satoshi client as a
daemon, or some other custom code. Implementing the idea in armory
doesn't give those miners a nice upgrade path.

That said, *using* the hash tree is something that can be implemented in
any client, but a lot of the code will be shared between calculating it
and using it anyway, so again implementing in the satoshi client makes
sense.

> I hope this gets developed. I will be able to help after summer if
> this is still not done.
> 
> DiThi
> 
> P.S: Sorry Peter, I've sent you the message privately by mistake.
> Also, I don't quite understand your concern of "unbalancing" the tree.

Lets suppose we're trying to make a tree consisting of real numbers:

    /\
   /  \
   *   \
  / \   \
 /   \   \
 *   *   *
/ \ / \ / \
1 2 3 4 5 6

If the numbers are evenly distributed, as will happen with hashes of
arbitrary data, any number will be at most log(n) steps away from the
head of the tree.

Suppose though some malicious actor adds the following numbers to that
tree: 3.001 3.002 3.003

    /\
   /  \
   *   \
  / \   \
 /   \   \
 *   *   *
/ \ / \ / \
1 2 * 4 5 6
   / \
   |  \
   *   *
  / \ / \
  0 1 2 3 <- (3.000 to 3.003)

Ooops, the tree suddenly became a lot higher, with an associated
decrease in retrieval performance and an increase in memory usage.

Of course the exact details depend on what rules there are for
constructing the tree, but essentially the attacker can either force the
a big increase in the depth of the tree, or a large number of vertexes
to be re-organizationed to create the tree, or both.

Now, to be exact, since the key of each vertex is a transaction hash,
this malicious actor will need to brute chosen prefix hash collisions,
but this is bitcoin: the whole system is about efficiently brute forcing
chosen prefix hash collisions. Besides, you would only need something
like k*n collisions to product an n increase in tree depth, with some
small k.

My solution was to simply state that vertexes that happened to cause the
tree to be unbalanced would be discarded, and set the depth of inbalance
such that this would be extremely unlikely to happen by accident. I'd
rather see someone come up with something better though.

Another naive option would be to hash each vertex key (the transaction
hash) with a nonce known only to the creator of that particular merkle
tree, but then the whole tree has to be recreatred from scratch each
time, which is worse than the problem... Interestingly in a
*non-distributed* system this idea is actually quite feasible feasible,
as the nonce could be kept secret.

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