In the design of Bitcoin mining serves two fundemental purposes:
proof-of-publication and order consensus.  Bitcoin's design entangles
these fundemental purposes with other goals, such as validation and
initial coin distribution. This leads to a design that is fundementally
unscalable, albeit effective on a small scale. Here we show how these
purposes do not need to be entangled together, and how by disentangling
them we can achieve better scalability and validation of the system as a

Let's first look at what role each of those purposes plays:

* Proof-of-publication

The fundemental problem Bitcoin solves is the double-spend problem.
Alice has some Bitcoins, and she wants to give them to Bob. She does
this by signing a digital message, a transaction, authorizing her coins
to be assigned to Bob. However, Bob has no way of knowing if Alice has
signed a conflicting digital message assigning her coins to Charlie

Bitcoin solves this problem by providing a way for Alice and Bob to
agree on a common place where *all* transactions will be published, the
blockchain. Because the definition of a valid transaction is that it has
been published in the blockchain, Bob can examine the contents of it,
and be confident that no conflicting transaction exists.

* Order consensus

Due to the constraints of physics no decentralized system can provide
instantaneous and reliable proof of publication; for a non-ideal
proof-of-publication system to be useful to solve the double-spend
problem we need to come to a consensus about the order in which data was
published. Once an order has been established, subsequent
double-spending transactions can be declared invalid.

Note that time itself isn't directly required, only the order of
transactions needs to be agreed upon.

* Why validation is an optional optimization

Given only proof-of-publication, and a consensus on the order of
transactions, can we make a succesful crypto-coin system? Surprisingly,
the answere is yes!

Suppose the rules of Bitcoin allowed blocks to contain invalid
transactions, in fact, suppose miners did no verification what-so-ever
of the contents of the blocks they mined. Could Bob still be confident
in the coins he received? Absolutely. There is consensus that the
transaction sending coins to Bob's came first and all prior transactions
can be verified as valid by checking the entire blockchain. In Bitcoin
all full nodes do this and Bitcoin could succesfully operate on that

What can't be supported in this model is SPV clients: the existance of a
transaction in a block tells you nothing about its validity, so no
compact proof can be made.

Real-world examples of this issue can be found in the parasitic
consensus system Mastercoin, and to a lesser extent Colored Coins: the
former uses Bitcoin as a proof-of-publication, applying it's own
independent set of rules to that published data. The latter tracks the
transfer of assets in a way that takes advantage of the Bitcoin
validation rules, but any given txout can only be proven to represent a
particular asset with a full chain of transfers back to the asset
genesis. It's notable that proponents of colored coins have proposed
that rules to validate colored coins be added to Bitcoin to make such
lengthy proofs not required.(1)

* What is the minimum domain for anti-double-spend proof-of-publication?

Answer: a single txout.

So what do we mean by "domain" here? In the existing Bitcoin system,
modulo validation, what Alice has proven to Bob is that an entire
transaction has been published. But that's not actually what Bob wants
to know: he only wants to be sure that no transaction inputs, that is
the CTxIn data structure containing a valid scriptSig and reference to a
previous output, have been published that spend outputs of the
transaction he is accepting from Alice. Put more simply, he doesn't care
where a double-spending transaction sends the money, he only cares that
it exists at all.

Suppose the blockchain consisted of blocks that only contained
information on the transaction outputs spent by that block; essentially
a block is a list of CTxIn's. We also, add a third field to the existing
CTxIn structure, hashTx, which commits to the rest of the transaction
spending that txout.

If we sort the CTxIn's in each block by the hash of the *transaction
output being spent* and commit to them with a merkle tree, Bob can now
determine if Alice's transaction is valid by checking the blockchain for
blocks that contain a conflicting spend of any of the inputs to that
transaction. For each block the proof that the block does not contain a
given spend is log2(n) in size.

Put another way, Bob needs proof that some data, a valid CTxIn spending
some CTxOut, has never been published before. He only cares about that
particular CTxOut, so the "publication domain" he is interested in is
that single CTxOut. (note that we are considering a CTxIn as valid if
its scriptSig satisfies the prevout's scriptPubKey; the rest of the
transaction may be invalid for other reasons)

Conversely a transaction is only considered to be valid if all CTxIn's
in that transaction have been succesfully committed to the blockchain
proper; there must be proof that every CTxIn has been published.

Note the parallels to the authors TXO commitments proposal: where TXO
commitments commit to the outputs of every transaction in each block,
here we are committing to the inputs of all transactions.

* Transaction validation

Miners still are doing almost no validation in this scheme, other than
the fact that a block is only valid if the data in it follows some
order. Bob still needs to examine the chain of of all transactions to
determine if Alice's payment was valid. However, the information he
needs to do this is greatly diminished: log(n) * m per txout in that
history, with n as the average number of spends in a block, and m the
number of blocks each txout was in existance for.

Of course, a practical implementation of this concept will have to rely
heavily on direct transfer of proof data from payor to payee.

** Privacy

The increased validation effort required on the part of Bob has an
important privacy advantage: whole transactions need never appear in the
blockchain at all. By incorporating a simple nonce into every
transaction blinding the miners have no way of linking CTxIn's to
CTxOut's. This achieves the end goal of Adam Back's blind symmetric
commitments(3) but by leaving data out of the blockchain entirely rather
than blinding it.

* The incentive to share blockchain data

What is the incentive for miners have in the Bitcoin system to share
their blocks? Why not just share the block header? Of course, the
incentive is that unless they share their block data, all other miners
in the system won't build upon their blocks because they have no idea if
they are valid or not.

But here there is no such thing as an invalid block! Blocks are just
arbitrary data with no specific meaning; whether or not the data is
valid in some sense is of no importance to the miner.

We can re-introduce this incentive by using a proof-of-work scheme that
has the requirement of posession of blockchain data. For instance we
could make the underlying computation be simply H(header + all previous
blocks) - without the entire blockchain you would be unable to mine, or
even validate the work done.

Of course this is impractical for a number of reasons. But it's
important to recognize that this simple scheme doesn't make any
compromises about the continual availability of blockchain data, and
thus the ability for users to validate history. Any lesser scheme will
be a trade-off between that guarantee and other objectives.

** Full TxIn set commitments

Since we have to require miners to posess blockchain data, we might as
well make a simple optimization: rather than commit to the CTxIn's in a
single block, commit to multiple blocks.

First, let's require that every CTxIn present in a block be have a valid
scriptSig for the corresponding scriptPubKey. To do this we need for
CTxIn's to commit to the H(txout) they are spending, and include the
CTxOut itself alongside the CTxIn in the block. Our hash commitments are
now chained as follows:

    CTxIn -> CTxOut -> <merkle path> -> CTransaction -> <merkle path> -> CTxIn

Now that we have valid and invalid CTxIn's, we might as well state that
only one valid CTxIn is allowed for a given CTxOut per block; proof that
a transaction is valid now doesn't have to take into account the problem
of an *invalid* CTxIn that you need to prove is invalid and thus can be
ignored. This validation is stateless, requiring only local data, and
still provides for strong privacy.(a) A fraud proof in this scheme is
simply the CTxIn and CTxOut and merkle path, and the code required to
evaluate it is the same code required to evaluate the data in a block.

a) Remember the mention of a per transaction nonce? It can be used
   between the CTxOut and the rest of the CTransaction so that even if
   every CTxIn and CTxOut is known, the actual transactions can't be

Now that we have a definition of a valid CTxIn, we can naturally extend
this to define the set of all valid *oldest* CTxIn's. That is for any
given CTxOut, we include the first valid CTxIn found in any block in
this set. This is analogous to the concept of the UTXO set, except that
items can only ever be added to the TxIn set.

As with UTXO commitments we can commit to the state of the TxIn set
using a merkelized radix tree whose tip is committed to by the block

Of course because a block can manipulate the contents of this set in an
invalid way, we've strongly reintroduced the notion of an invalid block,
we've re-introduced the incentive to share blockchain data, and we've
re-introduced the requirement to have the full set of blockchain data to

*** Mining with incomplete blockchain data

Or have we? This requirement isn't particularly strong as all: if other
miners are usually honest we'll get away with just trusting them to mine
only valid blocks. Meanwhile the TxIn set in merkelized radix tree form
can have items added to it with only the subset of internal nodes
modified by your additions. A miner can easily produce blocks only
containing CTxIn's spending CTxOuts from a subset of the possible
values. Multiple such miners can even co-operate to produce blocks, with
each handling a specific subset, as multiple radix trees are easily

Note that Bitcoin is even worse in this regard: you don't need any
previous blockchain data at all to create a new block. For instance the
authors proof-of-tx-propagation concept(5) has the serious flaw that
unscrupulous miners can use the proof that other miners are mining
certain transactions as a way to avoid doing any validation themselves.

*** The deletion problem

What happens if a copy of some of the txin set can't be found? With
Bitcoin this isn't an issue in theory - the miners are supposed to never
extend blocks they haven't verified in full and they are supposed to
distribute blocks freely. Not necessarily a perfect assumption(6) but it
mostly holds true.

With any type of sharded blockchain, it is easy to see that assumption
may not hold true. Now rather than a 51% attack in terms of total
hashing power, you could have a "local" attack on some portion of the
commitment set. On the other hand, with the right set of incentives, the
existance of such an attack can be made to imply actual consent by those
owning the coins involved, e.g. through proof-of-stake combined with the
proof-of-work. (perhaps better described as proof-of-consent with

1) OP_CHECKCOLORVERIFY: soft-fork for native color coin support,,

2) Merkle tree of open transactions for lite mode?,
   Gregory Maxwell

3) Ultimate blockchain compression w/ trust-free lite nodes
   Alan C. Reiner

4) blind symmetric commitment for stronger byzantine voting resilience,,
   Adam Back

5) Near-block broadcasts for proof of tx propagation,,
   Peter Todd

6) Perverse incentives to withhold blocks
   Peter Todd


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