Subject: [bitcoin-dev] Why sharding the blockchain is difficult

From: Peter Todd <[email-masked]>
Date: Wed, 25 Nov 2015 16:37:47 -0500

https://www.reddit.com/r/Bitcoin/comments/3u1m36/why_arent_we_as_a_community_talking_about/cxbamhn?context=3

The following was originally posted to reddit; I was asked to repost it here:

In a system where everyone mostly trusts each other, sharding works great! You
just split up the blockchain the same way you'd shard a database, assigning
miners/validators a subset of the txid space. Transaction validation would
assume that if you don't have the history for an input yourself, you assume
that history is valid. In a banking-like environment where there's a way to
conduct audits and punish those who lie, this could certainly be made to work.
(I myself have worked on and off on a scheme to do exactly that for a few
different clients: [Proofchains](https://github.com/proofchains))

But in a decentralized environment sharding is far, far, harder to
accomplish... There's an old idea we've been calling "fraud proofs", where you
design a system where for every way validation can fail, you can create a short
proof that part of the blockchain was invalid. Upon receiving that proof your
node would reject the invalid part of the chain and roll back the chain. In
fact, the original Satoshi whitepaper refers to fraud proofs, using the term
"alerts", and assumed SPV nodes would use them to get better guarantees they're
using a valid chain. (SPV as implemented by bitcoinj is sometimes referred to
as "non-validating SPV") The problem is, how do you guarantee that the fraud
will get detected? And How do you guarantee that fraud that is detected
actually gets propagated around the network? And if all that fails... then
what?

The nightmare scenario in that kind of system is some miner successfully gets
away with fraud for awhile, possibly creating hundreds of millions of dollars
worth of bitcoins out of thin air. Those fake coins could easily "taint" a
significant fraction of the economy, making rollback impossible and shaking
faith in the value of the currency. Right now in Bitcoin this is pretty much
impossible because everyone can run a full node to validate the chain for
themselves, but in a sharded system that's far harder to guarantee.

Now, suppose we *can* guarantee validity. zk-SNARKS are basically a way of
mathematically proving that you ran a certain computer program on some data,
and that program returned true. *Recursive* zk-SNARKS are simply zk-SNARKS
where the program can also recursively evaluate that another zk-SNARK is true.
With this technology a miner could *prove* that the shard they're working on is
valid, solving the problem of fake coins. Unfortunately, zk-SNARKS are bleeding
edge crypto, (if zerocoin had been deployed a the entire system would have been
destroyed by a recently found bug that allowed fake proofs to be created) and
recursive zk-SNARKS don't exist yet.

The closest thing I know of to recrusive zk-SNARKS that actually does work
without "moon-math" is an idea I came up with for treechains called coin
history linearization. Basically, if you allow transactions to have multiple
inputs and outputs, proving that a given coin is valid requires the entire coin
history, which has quasi-exponential scaling - in the Bitcoin economy coins are
very quickly mixed such that all coins have pretty much all other coins in
their history.

Now suppose that rather than proving that all inputs are valid for a
transaction, what if you only had to prove that *one* was valid? This would
linearize the coin history as you only have to prove a single branch of the
transaction DAG, resulting in O(n) scaling. (with n <= total length of the
blockchain chain)

Let's assume Alice is trying to pay Bob with a transaction with two inputs each
of equal value. For each input she irrevocable records it as spent, permanently
committing that input's funds to Bob. (e.g. in an irrevocable ledger!) Next she
makes use of a random beacon - a source of publicly known random numbers that
no-one can influence - to chose which of the two inputs' coin history's she'll
give to Bob as proof that the transaction is real. (both the irrevocable ledger
and random beacon can be implemented with treechains, for example)

If Alice is being honest and both inputs are real, there's a 100% chance that
she'll be able to successfully convince Bob that the funds are real. Similarly,
if Alice is dishonest and neither input is real, it'll be impossible for her
convince prove to Bob that the funds are real.

But what if one of the two inputs is real and the other is actually fake? Half
the time the transaction will succeed - the random beacon will select the real
input and Bob won't know that the other input is fake. However, half the time
the *fake* input will be selected, and Alice won't be able to prove anything.
Yet, the real input has irrevocably been spent anyway, destroying the funds! If
the process by which funds are spent really is irrevocable, and Alice has
absolutely no way to influence the random beacon, the two cases cancel out.
While she can get away with fraud, there's no economic benefit for her to do
so. On a macro level, this means that fraud won't result in inflation of the
currency. (in fact, we want a system that institutionalizes this so-called
"fraud" - creating false proofs is a great way to make your coins more private)
(FWIW the way zk-SNARKS actually work is similar to this simple linearization
scheme, but with a lot of very clever error correction math, and the hash of
the data itself as the random beacon)

An actual implementation would be extended to handle multiple transaction
inputs of different sizes by weighing the probability that an input will be
selected by it's value - merkle-sum-trees work well for this. We still have the
problem that O(n) scaling kinda sucks; can we do better?

Yes! Remember that a genesis transaction output has no history - the coins are
created out of thin air and its validity is proven by the proof of work itself.
So every time you make a transaction that spends a genesis output you have a
chance of reducing the length of the coin validity proof back to zero. Better
yet, we can design a system where every transaction is associated with a bit of
proof-of-work, and thus every transaction has a chance of resetting the length
of the validity proof back to zero. In such a system you might do the PoW on a
per-transaction basis; you could outsource the task to miners with a special
output that only the miner can spend. Now we have O(1) scaling, with a k that
depends on the inflation rate. I'd have to dig up the calculations again, but
IIRC I sketched out a design for the above that resulted in something like 10MB
or 100MB coin validity proofs, assuming 1% inflation a year. (equally you can
describe that 1% inflation as a coin security tax) Certainly not small, but
compared to running a full node right now that's still a *huge* reduction in
storage space. (recursive zk-SNARKS might reduce that proof to something like
1kB of data)

Regardless of whether you have lightweight zk-SNARKS, heavyweight linearized
coin history proofs, or something else entirely, the key advantage is that
validation can become entirely client side. Miners don't even need to care
whether or not their *own* blocks are "valid", let alone other miners' blocks.
Invalid transactions in the chain are just garbage data, which gets rejected by
wallet software as invalid. So long as the protocol itself  works and is
implemented correctly it's impossible for fraud to go undetected and destroy
the economy the way it can in a sharded system.

However we still have a problem: censorship. This one is pretty subtle, and
gets to the heart of how these systems actually work. How do you prove that a
coin has validly been spent? First, prove that it hasn't already been spent!
How do you do that if you don't have the blockchain data? You can't, and no
amount of fancy math can change that.

In Bitcoin if everyone runs full nodes censorship can't happen: you either have
the full blockchain and thus can spend your money and help mine new blocks, or
that alternate fork might as well not exist. SPV breaks this as it allows funds
to be spent without also having the ability to mine - with SPV a cartel of
miners can prevent anyone else from getting access to the blockchain data
required to mine, while still allowing commerce to happen. In reality, this
type of cartel would be more subtle, and can even happen by accident; just
delaying other miners getting blockchain data by a few seconds harms those
non-cartel miners' profitability, without being obvious censorship. Equally, so
long as the cartel has [>30% of hashing power it's profitable in the long run
for the cartel if this
happens](http://www.mail-archive.com/[email-masked]/msg03200.html).

In sharded systems the "full node defense" doesn't work, at least directly. The
whole point is that not everyone has all the data, so you have to decide what
happens when it's not available.

Altcoins provide one model, albeit a pretty terrible one: taken as a whole you
can imagine the entire space of altcoins as a series of cryptocurrency shards
for moving funds around. The problem is each individual shard - each altcoin -
is weak and can be 51% attacked. Since they can be attacked so easily, if you
designed a system where funds could be moved from one shard to another through
coin history proofs every time a chain was 51% attacked and reorged you'd be
creating coins out of thin air, destroying digital scarcity and risking the
whole economy with uncontrolled inflation. You can instead design a system
where coins can't move between shards - basically what the altcoin space looks
like now - but that means actually paying someone on another "shard" requires
you to sell your coins and buy their coins - a inefficient and expensive
logistical headache. (there's a reason the Eurozone was created!)

If you want to transfer value between shards with coin history proofs, without
risking inflation, you need all the shards to share some type of global
consensus. This is the idea behind treechains: every part of the tree is linked
to a top-level timestamp chain, which means we have global consensus on the
contents of all chains, and thus spending a coin really is an immutable
one-time act.

Let's go into a bit more detail. So what is a coin in a treechains system?
First and foremost it's a *starting point* in some part of the tree, a specific
subchain. When Alice wants to prove to Bob that she spent a coin, giving it to
Bob, she inserts into that subchain the data that proves that someone *could
have* spent that coin - a valid signature and the hash of the transaction
output it was spending. But the actual proof that she gives to Bob isn't just
that spend data, but rather proof that all the blocks in that chain between the
starting point and the spend did *not* have a valid spend in them. (easiest way
to do that? give Bob those blocks) That proof must link back to the top-level
chain; if it doesn't the proof is simply not valid.

Now suppose Alice can't get that part of the subchain, perhaps because a cartel
of miners is mining it and won't give anyone else the data, or perhaps because
everyone with the data suffered a simultaneous harddrive crash. We'll also say
that higher up in the tree the data is available, at minimum the top-level
chain. As with Bitcoin, as long as that cartel has 51% of the hashing power,
Alice is screwed and can't spend her money.

What's interesting is what happens after that cartel disbands: how does mining
restart? It's easy to design a system where the creation of a block doesn't
require the knowledge of previous blocks, so new blocks can be added to extend
the subchain. But Alice is still screwed: she can't prove to Bob that the
missing blocks in the subchain didn't contain a valid spend of her coin. This
is pretty bad, on the other hand the damage is limited to just that one
subchain, and the system as a whole is unaffected.

There's a tricky incentives problem here though: if a miner can extend a
subchain without actually having previous blocks in that chain, where's the
incentive for that miner to give anyone else the blocks they create? Remember
that exclusive knowledge of a block is potentially valuable if you can extort
coin owners for it. (Bitcoin suffers from this problem right now with
validationless "SPV" mining, though the fact that a block can be invalid in
Bitcoin helps limit its effects)

Part of the solution could be mining reward; in Bitcoin, coinbase outputs can't
be spent for 100 blocks. A similar scheme could require that a spend of a
coinbase output in a subchain include proof that the next X blocks in that
subchain were in fact linked together. Secondly make block creation dependent
on actually having that data to ensure the linkage actually means something,
e.g. by introducing some validity rules so blocks can be invalid, and/or using
a PoW function that requires hashers to have a copy of that data.

Ultimately though this isn't magic: like it or not lower subchains in such a
system are inherently weaker and more dangerous than higher ones, and this is
equally true of any sharded system. However a hierarchically sharded system
like treechains can give users options: higher subchains are safer, but
transactions will expensive. The hierarchy does combine the PoW security of all
subchains together for the thing you can easily combine: timestamping security.

There's a big problem though: holy !@#$ is the above complex compared to
Bitcoin! Even the "kiddy" version of sharding - my linearization scheme rather
than zk-SNARKS - is probably one or two orders of magnitude more complex than
using the Bitcoin protocol is right now, yet right now a huge % of the
companies in this space seem to have thrown their hands up and used centralized
API providers instead. Actually implementing the above and getting it into the
hands of end-users won't be easy.

On the other hand, decentralization isn't cheap: using PayPal is one or two
orders of magnitude simpler than the Bitcoin protocol.

-- 
'peter'[:-1]@petertodd.org
0000000000000000061df93abb76cdc4b1617bb097b4cab90f3f1ca5ae0a0df5