A validation-cost metric for aggregate limits and fee determination

At the first Scaling Bitcoin workshop in Montreal I presented on the topic of "bad blocks" that take an excessive amount of time to validate. You can read a transcript of this talk here:

http://diyhpl.us/wiki/transcripts/scalingbitcoin/alternatives-to-block-size-as-aggregate-resource-limits/

The core message was that the assumption made by the design parameters of the system, namely that validation costs scale linearly with transaction or block size, is wrong. In particular, in certain kinds of transactions there are validation costs which scale quadraticly with size. For example, the construction of SIGHASH_ALL results in each input signing a different message digest, meaning that the entire transaction (minus the scriptSigs) is rehashed for each input. As another example, the number of signature operation performed during block validation is unlimited if the validations are contained within the scriptPubKey (this scales linearly but with a very large constant factor). The severity of these issues increase as the aggregate limits in place on maximum transaction and block size increase.

There have been various solutions suggested, and I would like to start a public discussion to see if consensus can be reached over a viable approach.

Gavin, for example, has written code that tracks the number of bytes hashed and enforces a separate limit for a block over this aggregate value. Other costs could be constrained in a similar whack-a-mole way. I have two concerns with this approach:

1. There would still exist a gap between the average-case validation cost of a full block and the worst case validation cost of a block that was specifically constructed to hit every limit.

2. Transaction selection and by extension fee determination would become much more complicated multi-dimensional optimization problems. Since fee management in particular is code replicated in a lot of infrastructure, I would be very concerned over making optimal behavior greatly more difficult.

My own suggestion, which I submit for consideration, is to use a linear function of the various costs involved (signatures verified, bytes hashed, inputs consumed, script opcodes executed, etc.). The various algorithms used for transaction selection and fee determination can then be reused, using the output of this new linear function as the "size" of the transaction.

Separately, many others including Greg Maxwell have advocated for a "net-UTXO" metric instead of, or in combination with a validation-cost metric. In the pure form the block size limit would be replaced with a maximum UTXO set increase, thereby applying a cost in extra fee required to create unspent outputs. This has the distinct advantage of making dust outputs considerably more expensive than regular spend outputs.

For myself, I remain open to the possibility of adding a UTXO set size corrective factor to a chiefly validation-cost metric. It would be nice to reward users for cleaning up scattered small output, reward miners for including dust-be-gone outputs, and make spam attacks more costly. But doing so requires setting aside some unused validation resources in order to reward miners who clean up the UTXO, which means it widens the gap between average and worst case block validation times. Also, worry over the size of the UTXO database is only a concern for how Bitcoin Core is currently structured -- with e.g. UTXO or STXO commitments it could be the case that in the future full nodes do not store the UTXO and instead carry proofs of their inputs as prunable witness data. If we choose a net-UTXO metric however, we will be stuck with it for some time.

I will be submitting a talk proposal for Scaling Bitcoin on this topic, but I would like to get some feedback from the developer community first. Anyone have any thoughts to add?

I have several thoughts:

Weighing CPU validation cost should be reasonably straightforward-- just pick some arbitrary, commonly-available, recent hardware and then benchmark the two things that take the bulk of validation time (hashing to create the signature hash, then ECDSA validation), and weigh the terms in the validation cost equation appropriately (e.g. hashing X GB of data takes the same amount of CPU time as one libsecp256k1 validation, so count cpu cost of an OP_CHECKSIG as 1 + X/actual_bytes_hashed).

But how should bandwidth cost be counted? There isn't an obvious "Y GB of bandwidth-per-month equals 1 ECDSA validation. We need to find common units for the terms in the validation cost equation for it to make sense, otherwise we're adding apples and oranges.

I think the only units that will work is "percentage of maximum validation ability for some reference hardware running with a network connection capable of some reference bandwidth."

For example, imagine the reference was the typical home computer being sold today running with some multiple or fraction of the average global broadband connection speed of 5Mbps. CPU cost to validate a block can then be expressed as a percentage of maximum capacity, as can bandwidth-- hooray, two metrics with the same units, so they can be added up. If the result is less than 100%, then the block is valid-- it can be received and validated in a reasonable amount of time.

Rolling in UTXO growth is harder, for two reasons: 1) UTXO changes per block can be negative or positive, as opposed to bandwidth/CPU costs. 2) It is not clear how to choose or benchmark "reference UTXO growth"

(1) could be finessed to just treat UTXO shrinkage as zero. (2) could just be decided by picking a reasonable growth number. Since we want the UTXO set to fit into main memory, something a bit below the long-ish term price/performance trend of main memory would be a good target.

So, starting with that growth rate and an initial UTXO size in bytes, divide by the number of blocks in a year to get a maximum UTXO growth in bytes per block.

When validating a block, take the actual UTXO growth, express it as a percentage of the maximum allowed (make it zero if it is negative), and combine with the CPU and bandwidth percentages.

If the total is less than 100%, block is valid. Otherwise, invalid.

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Now.... all of that worked through, I'm not 100% sure it solves the "do miners or wallet have to solve a bin-packing problem to determine which transactions to put into their blocks or what fees to attach."

I think it mostly works out-- instead of fee-per-kilobyte, it would be fee-per-validation-cost (which is in the weird units "fraction of 100% validation cost").

But the UTXO term might be a problem-- transactions that create more UTXOs than they spend might end up being costly. I'm traveling right now, perhaps somebody could pick some arbitrary reference points and try to get a rough idea of what different transactions might pay in fees (e.g. if a one-input-two-output had a cost of X, two-output-one-input would have a cost of X/something).

I'm not convinced that a single validation cost metric is the best approach-- it might be better to break the cost into three (UTXO growth, CPU, and bandwidth) and just let miners set reasonable transaction selection policies that keep each of the three under whatever caps are imposed on each. If a miner comes up with a clever algorithm that lets them pack in more transactions and get more fees, good for them!

But I do like the simplicity of a single validation cost metric.