Subject: [bitcoin-dev] Bitcoin Cash's new difficulty algorithm

From: Scott Roberts <[email-masked]>
Date: Thu, 2 Nov 2017 19:31:55 -0400

Bitcoin cash will hard fork on Nov 13 to implement a new difficulty
algorithm.  Bitcoin itself might need to hard fork to employ a similar
algorithm. It's about as good as they come because it followed the
"simplest is best" route. Their averaging window is probably
significantly too long (N=144). It's:

next_D = sum (past 144 D's) * T / sum(past 144 solvetimes)

They correctly did not use max(timestamp) - min(timestamp) in the
denominator like others do.

They've written the code and they're about to use it live, so Bitcoin
will have a clear, simple, and tested path if it suddenly needs to
hard fork due to having 20x delays for the next 2000 blocks (taking it
a year to get unstuck).

Details on it and the decision process:
https://www.bitcoinabc.org/november

It uses a nice median of 3 for the beginning and end of the window to
help alleviate bad timestamp problems. It's nice, helps a little, but
will also slow its response by 1 block.  They also have 2x and 1/2
limits on the adjustment per block, which is a lot more than they will
ever need.

I recommend bitcoin consider using it and making it N=50 instead of 144.

I have seen that any attempts to modify the above with things like a
low pass filter, starting the window at MTP, or preventing negative
timestamps will only reduce its effectiveness. Bitcoin's +12 and -6
limits on the timestamps are sufficient and well chosen, although
something a bit smaller than the +12 might have been better.

One of the contenders to the above is new and actually better, devised
by Degnr8 and they call it D622 or wt-144.It's a little better than
they realize. It's the only real improvement in difficulty algorithms
since the rolling average.  It gives a linearly higher weight to the
more recent timestamps. Otherwise it is the same. Others have probably
come across it, but there is too much noise in difficulty algorithms
to find the good ones.

# Degnr8's D622 difficulty algorithm
# T=TargetTime, S=Solvetime
# modified by zawy
for i = 1 to N  (from oldest to most recent block)
    t += T[i] / D[i] * i
    j += i
next i
next_D = j / t * T

I believe any modification to the above strict mathematical weighted
average will reduce it's effectiveness. It does not oscillate anymore
than regular algos and rises faster and drops faster, when needed.