Scott Roberts via bitcoin-dev

2017-10-09 21:26:50 UTC

Background:

The bitcoin difficulty algorithm does not seem to be a good one.Â If there is a fork due to miners seeking maximum profit without due regard to security, users, and nodes, the "better" coin could end up being the minority chain. If 90% of hashrate is really going to at least initially go towards using SegWit2x, BTC would face 10x delays in confirmations until the next difficulty adjustment, negatively affecting its price relative to BTC1, causing further delays from even more miner abandonment (until the next adjustment). The 10% miners remaining on BTC do not inevitably lose by staying to endure 10x delays because they have 10x less competition, and the same situation applies to BTC1 miners. If the prices are the same and stable, all seems well for everyone, other things aside.Â But if the BTC price does not fall to reflect the decreased hashrate, the situation seems to be a big problem for both coins: BTC1 miners will jump back to BTC when the difficulty adjustment occurs, initiating a potentially never-ending oscillation between the two coins, potentially worse than what BCH is experiencing.Â They will not issue coins too fast like BCH because that is a side effect of the asymmetry in BCH's rise and fall algorithm.

Solution:

Hard fork to implement a new difficulty algorithm that uses a simple rolling average with a much smaller window.Â Many small coins have done this as a way to stop big miners from coming on and then suddenly leaving, leaving constant miners stuck with a high difficulty for the rest of a (long) averaging window.Â Even better, adjust the reward based on recent solvetimes to motivate more mining (or less) if the solvetimes are too slow (or too fast).Â This will keep keep the coin issuance rate perfectly on schedule with real time.Â

I recommend the following for Bitcoin, as fast, simple, and better than any other difficulty algorithm I'm aware of.Â This is the result of a lot of work the past year.

=== Begin difficulty algorithm ===# Zawy v6 difficulty algorithm (modified for bitcoin)# Unmodified Zawy v6 for alt coins:Â # http://zawy1.blogspot.com/2017/07/best-difficulty-algorithm-zawy-v1b.html# My failed attempts at something better:# https://github.com/seredat/karbowanec/commit/231db5270acb2e673a641a1800be910ce345668a## Keep negative solvetimes to correct bad timestamps.# Do not be tempted to use:# next_D = sum(last N Ds) * T / [max(last N TSs) - min(last N TSs];# D=difficulty, ST= Solvetime, TS = timestamp, T=TargetSolveTime

# set constants until next hard fork:

T=600;Â N=30; # Averaging window. Smoother than N=15, faster response than N=60.X=5; # size of sudden hashrate changes expected as multiple of base hashrate.limit = X^(2/N); # limit rise and fall to protect against timestamp errors & manipulationadjust = 1/(1+0.67/N);Â # keeps avg solvetime on track for small N.

# begin difficulty algorithmÂ

avg_ST=0; # avg SolveTimeavg_D=0;for ( i=height;Â i > height-N;Â i--) {Â # go through N most recent blocksÂ Â avg_ST += (TS[i] - TS[i-1]) / N; # TS=timestampsÂ Â avg_D += D[i]/N;}avg_ST = T*limit if avg_ST > T*limit;Â avg_ST = T/limit if avg_ST < T/limit;Â

next_D = avg_D * T / avg_ST * adjust;Â

# Tim Olsen suggested changing coin reward to protect against hash attacks.# Karbowanek coin suggested something similar.# After testing many ideas, I could not find anything better than the simplest idea below.# It was a surprise that coin issuance rate came out perfect.# BaseReward = coins per block

next_reward = BaseReward * avg_ST / T;

======= end algo ====

Due to the limit and keeping negative solvetimes in a true average, timestamp errors resulting in negative solvetimes are corrected in the next block. Otherwise, one would need to do like Zcash and cause a 5-block delay in the response by resorting to the median of past 11 blocks (MTP) as the most recent timestamp, offsetting the timestamps from their corresponding difficulties by 5 blocks. (it does not cause an averaging problem, but it does cause a 5-block delay in the response.)

Small N windows like keep the correct median, but cause avg solvetime to be above the target. The "adjust" constant (empirically determined) fixes this, but it causes the median to be that same percentage too low, below the ideal Poisson median which is 0.693 of the mean. I was not able to find a fix to this that did not slow down the response to hashrate changes.

The bitcoin difficulty algorithm does not seem to be a good one.Â If there is a fork due to miners seeking maximum profit without due regard to security, users, and nodes, the "better" coin could end up being the minority chain. If 90% of hashrate is really going to at least initially go towards using SegWit2x, BTC would face 10x delays in confirmations until the next difficulty adjustment, negatively affecting its price relative to BTC1, causing further delays from even more miner abandonment (until the next adjustment). The 10% miners remaining on BTC do not inevitably lose by staying to endure 10x delays because they have 10x less competition, and the same situation applies to BTC1 miners. If the prices are the same and stable, all seems well for everyone, other things aside.Â But if the BTC price does not fall to reflect the decreased hashrate, the situation seems to be a big problem for both coins: BTC1 miners will jump back to BTC when the difficulty adjustment occurs, initiating a potentially never-ending oscillation between the two coins, potentially worse than what BCH is experiencing.Â They will not issue coins too fast like BCH because that is a side effect of the asymmetry in BCH's rise and fall algorithm.

Solution:

Hard fork to implement a new difficulty algorithm that uses a simple rolling average with a much smaller window.Â Many small coins have done this as a way to stop big miners from coming on and then suddenly leaving, leaving constant miners stuck with a high difficulty for the rest of a (long) averaging window.Â Even better, adjust the reward based on recent solvetimes to motivate more mining (or less) if the solvetimes are too slow (or too fast).Â This will keep keep the coin issuance rate perfectly on schedule with real time.Â

I recommend the following for Bitcoin, as fast, simple, and better than any other difficulty algorithm I'm aware of.Â This is the result of a lot of work the past year.

=== Begin difficulty algorithm ===# Zawy v6 difficulty algorithm (modified for bitcoin)# Unmodified Zawy v6 for alt coins:Â # http://zawy1.blogspot.com/2017/07/best-difficulty-algorithm-zawy-v1b.html# My failed attempts at something better:# https://github.com/seredat/karbowanec/commit/231db5270acb2e673a641a1800be910ce345668a## Keep negative solvetimes to correct bad timestamps.# Do not be tempted to use:# next_D = sum(last N Ds) * T / [max(last N TSs) - min(last N TSs];# D=difficulty, ST= Solvetime, TS = timestamp, T=TargetSolveTime

# set constants until next hard fork:

T=600;Â N=30; # Averaging window. Smoother than N=15, faster response than N=60.X=5; # size of sudden hashrate changes expected as multiple of base hashrate.limit = X^(2/N); # limit rise and fall to protect against timestamp errors & manipulationadjust = 1/(1+0.67/N);Â # keeps avg solvetime on track for small N.

# begin difficulty algorithmÂ

avg_ST=0; # avg SolveTimeavg_D=0;for ( i=height;Â i > height-N;Â i--) {Â # go through N most recent blocksÂ Â avg_ST += (TS[i] - TS[i-1]) / N; # TS=timestampsÂ Â avg_D += D[i]/N;}avg_ST = T*limit if avg_ST > T*limit;Â avg_ST = T/limit if avg_ST < T/limit;Â

next_D = avg_D * T / avg_ST * adjust;Â

# Tim Olsen suggested changing coin reward to protect against hash attacks.# Karbowanek coin suggested something similar.# After testing many ideas, I could not find anything better than the simplest idea below.# It was a surprise that coin issuance rate came out perfect.# BaseReward = coins per block

next_reward = BaseReward * avg_ST / T;

======= end algo ====

Due to the limit and keeping negative solvetimes in a true average, timestamp errors resulting in negative solvetimes are corrected in the next block. Otherwise, one would need to do like Zcash and cause a 5-block delay in the response by resorting to the median of past 11 blocks (MTP) as the most recent timestamp, offsetting the timestamps from their corresponding difficulties by 5 blocks. (it does not cause an averaging problem, but it does cause a 5-block delay in the response.)

Small N windows like keep the correct median, but cause avg solvetime to be above the target. The "adjust" constant (empirically determined) fixes this, but it causes the median to be that same percentage too low, below the ideal Poisson median which is 0.693 of the mean. I was not able to find a fix to this that did not slow down the response to hashrate changes.