A statistical consensus rule for reducing 0-conf double-spend risk

This idea was suggested by "Joe" on 2011-02-14 https://bitcointalk.org/index.php?topic=3441.msg48484#msg48484 . It deserves another look.

Nodes today make a judgment regarding which of several conflicting spends to accept, and which is a double-spend. But there is no incorporation of these collective judgments into the blockchain. So today, it's the wild west, right up until the next block. To address this:

  - Using its own clock, node associates a timestamp with every
transaction upon first seeing its tx hash (at inv, in a block, or when
created)
  - Node relays respend attempts (subject to anti-DOS rules, see github
PR #3883)
  - Eventually, node adds a consensus rule:
     Do not accept blocks containing a transaction tx2 where
         - tx2 respends an output spent by another locally accepted
transaction tx1, and
         - timestamp(tx2) - timestamp(tx1) > T

What is T?

According to http://bitcoinstats.com/network/propagation/ recent tx propagation has a median of 1.3 seconds. If double-spender introduces both transactions from the same node, assuming propagation times distributed exponentially with median 1.3 seconds, the above consensus rule with reject threshold T = 7.4 seconds would result in mis-identification of the second-spend by less than 1% of nodes.*

If tx1 and tx2 are introduced in mutually time-distant parts of the network, a population of nodes in between would be able to accept either transaction, as they can today. But the attacker still has to introduce them at close to the same time, or the majority of the network will confirm the one introduced earlier.

Merchant is watching also, and these dynamics mean he will not have to watch for very long to gain confidence if he was going to get double-spent, he would have learned it by now. The consensus rule also makes mining a never-broadcast double-spend quite difficult, because the network assigns it very late timestamps. Miner has to get lucky and find the block very quickly. In other words, it converges to a Finney attack.

This would be the first consensus rule that anticipated less than 100% agreement. But the parameters could be chosen so that it was still extremely conservative. Joe also suggested a fail-safe condition: drop this rule if block has 6 confirmations, to prevent a fork in unusual network circumstances.

We can't move toward this, or any, solution without more data. Today, the network is not transparent to double-spend attempts, so we mostly have to guess what the quantitative effects would be. The first step is to share the data broadly by relaying first double-spend attempts as in github PR #3883.

*Calcs: For Exp(lambda), median ln(2)/lambda = 1.3 ==> lambda = .533 Laplace(0,1/lambda) < .01 ==> T = 7.34 seconds

Unfortunately this could fork the network permanently, which is much worse than a double spend. There's no magic way to have a consensus, so it becomes trivial with a few tries to split the network into two halves: (tx1 before tx2, tx2 before tx1). Some nodes in the middle will accept either block, but you've still forked off some non-zero number of nodes.

At a minimum, you'd need a way to reconcile the split (Accept the offending block once it's 2+ deep). The problem is that since the rule isn't enforceable, no miner will wait before mining on the longest chain (which is the rational move), and you're back to where we are now.

On Sat, May 3, 2014 at 8:29 PM, Tom Harding <tomh@thinlink•com> wrote:

> This idea was suggested by "Joe" on 2011-02-14
> https://bitcointalk.org/index.php?topic=3441.msg48484#msg48484 .  It
> deserves another look.
>
> Nodes today make a judgment regarding which of several conflicting
> spends to accept, and which is a double-spend.  But there is no
> incorporation of these collective judgments into the blockchain.  So
> today, it's the wild west, right up until the next block.  To address this:
>
>   - Using its own clock, node associates a timestamp with every
> transaction upon first seeing its tx hash (at inv, in a block, or when
> created)
>   - Node relays respend attempts (subject to anti-DOS rules, see github
> PR #3883)
>   - Eventually, node adds a consensus rule:
>      Do not accept blocks containing a transaction tx2 where
>          - tx2 respends an output spent by another locally accepted
> transaction tx1, and
>          - timestamp(tx2) - timestamp(tx1) > T
>
> What is T?
>
> According to http://bitcoinstats.com/network/propagation/ recent tx
> propagation has a median of 1.3 seconds.  If double-spender introduces
> both transactions from the same node, assuming propagation times
> distributed exponentially with median 1.3 seconds, the above consensus
> rule with reject threshold T = 7.4 seconds would result in
> mis-identification of the second-spend by less than 1% of nodes.*
>
> If tx1 and tx2 are introduced in mutually time-distant parts of the
> network, a population of nodes in between would be able to accept either
> transaction, as they can today.  But the attacker still has to introduce
> them at close to the same time, or the majority of the network will
> confirm the one introduced earlier.
>
> Merchant is watching also, and these dynamics mean he will not have to
> watch for very long to gain confidence if he was going to get
> double-spent, he would have learned it by now.  The consensus rule also
> makes mining a never-broadcast double-spend quite difficult, because the
> network assigns it very late timestamps.  Miner has to get lucky and
> find the block very quickly.  In other words, it converges to a Finney
> attack.
>
> This would be the first consensus rule that anticipated less than 100%
> agreement.  But the parameters could be chosen so that it was still
> extremely conservative.  Joe also suggested a fail-safe condition: drop
> this rule if block has 6 confirmations, to prevent a fork in unusual
> network circumstances.
>
> We can't move toward this, or any, solution without more data. Today,
> the network is not transparent to double-spend attempts, so we mostly
> have to guess what the quantitative effects would be.  The first step is
> to share the data broadly by relaying first double-spend attempts as in
> github PR #3883.
>
>
> *Calcs:
> For Exp(lambda), median ln(2)/lambda = 1.3 ==> lambda = .533
> Laplace(0,1/lambda) < .01 ==> T = 7.34 seconds
>
>
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Christophe Biocca wrote:

> it becomes trivial with a few tries to split the network into two
> halves: (tx1 before tx2, tx2 before tx1).

"before" implies T=0. That is a much too optimistic choice for T; 50% of nodes would misidentify the respend.

> Tom Harding <tomh@thinlink•com> wrote:
>>    - Eventually, node adds a consensus rule:
>>       Do not accept blocks containing a transaction tx2 where
>>           - tx2 respends an output spent by another locally accepted
>> transaction tx1, and
>>           - timestamp(tx2) - timestamp(tx1) > T

Christophe Biocca wrote:

> The problem is that since the rule
> isn't enforceable, no miner will wait before mining on the longest
> chain (which is the rational move), and you're back to where we are
> now.

Back up to the miner who decided to include a "seasoned" double-spend in his block. Let's say he saw it 21 seconds after he saw an earlier spend, and included it, despite the rule.

The expected cost of including the respend is any revenue loss from doing so: (total miner revenue of block)*(fraction of hashpower following the rule). So today, if only 1% of hashpower follows the rule (ie a near total failure of consensus implementation), he still loses at least .25 BTC.

.25 BTC is about 1000x the typical "double-spend premium" I'm seeing right now. Wouldn't the greedy-rational miner just decide to include the earlier spend instead?

Sorry to run on, a correction is needed. A much better approximation requires that the rule-following minority finds the next TWO blocks, so the cost is

(total miner revenue of block)*(fraction of hashpower following the rule)^2

So the lower bound cost in this very pessimistic scenario is .0025 BTC, still quite high for one transaction. I guess miner could try to make a business out of mining double-spends, to defray that cost.

On 5/11/2014 9:41 PM, Tom Harding wrote:

> Back up to the miner who decided to include a "seasoned" double-spend
> in his block.  Let's say he saw it 21 seconds after he saw an earlier
> spend, and included it, despite the rule.
>
> The expected cost of including the respend is any revenue loss from
> doing so: (total miner revenue of block)*(fraction of hashpower
> following the rule).  So today, if only 1% of hashpower follows the
> rule (ie a near total failure of consensus implementation), he still
> loses at least .25 BTC.
>
> .25 BTC is about 1000x the typical "double-spend premium" I'm seeing
> right now.  Wouldn't the greedy-rational miner just decide to include
> the earlier spend instead