Note: This was originally published to the Bitcoin Development mailing list.

In the design of Bitcoin mining serves two fundamental purposes: proof-of-publication and order consensus. Bitcoin’s design entangles these fundamental purposes with other goals, such as validation and initial coin distribution. This leads to a design that is fundamentally 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 whole.

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

## Proof-of-publication

The fundamental 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 instead.

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 model.

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> -> CT= xIn


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 derived.

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 header.

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 mine.

#### 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 composed.(b)

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 proof-of-work)

## References

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

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

6) Perverse incentives to withhold blocks Peter Todd