of the Bitcoin System Yoshinori Hashimoto BUIDL Ltd Shunya Noda University of British Columbia Kyohei Okumura The University of Tokyo Scaling Bitcoin September 2019 BUIDL as a blockchain service provider ID: 810512
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A Lucas Critique to the Difficulty Adjustment Algorithm of the Bitcoin System
Yoshinori Hashimoto (BUIDL, Ltd.)Shunya Noda (University of British Columbia)Kyohei Okumura (The University of Tokyo)
@Scaling Bitcoin
September 2019
Slide2BUIDL as a blockchain service provider
Consulting & DevelopmentResearch & Development
Slide3Yoshinori Hashimoto
BUIDL, Ltd.(Researcher)Shunya NodaUBC EconKyohei OkumuraU Tokyo Econ(Ph.D. Student)
Slide4Design Issue of the Bitcoin SystemThe Bitcoin community agreed to aim at generating blocks every 10 minutes
(on average).Need to adjust the “difficulty target”.Difficulty Adjustment Algorithm (DAA)How should we design it?
Slide5Policy Goal: winning rate Probability of {hash value < difficulty target}
Proportional to the reciprocal of “difficulty”.: (global) hash rateBlock time Exponential dist. with intensity . Average block time: . By controlling , we want to satisfy
Slide6Current Bitcoin DAAPeriodic adjustment (every 2016 blocks 2 weeks)
=Ideal block time (= 10 minutes)
Average
block time in previous 2016 blocks
Too slow
Increase the winning rate
Too fast
Decrease the winning rate
More justification?
Slide7Sample AnalogueMaximum likelihood estimate of the hash rate in previous 2016 blocks:
Bitcoin DAA can be interpreted as
Sample Analogue:
Bitcoin DAA achieves the policy goal by using the (estimated)
historical hash rate
.
=
Average
block time in previous 2016 blocks
-1
Slide8Miners’ IncentiveLarger winning rate Mining more
profitable!More likely to win the prize.More miners enter the market.Turn on/off mining ASIC Small switching costChange in winning rate also changes the hash rate.does NOT guarantee
Slide90
Winning Rate Hash Rate
Slide100
Policy Curve
Winning Rate
Hash Rate
Slide110
Policy Curve
Winning Rate
Hash Rate
Supply
Curve
(Hash rate is increasing in winning rate)
Slide120
Policy Curve
Winning Rate
Hash Rate
Supply
Curve
(Hash rate is increasing in winning rate)
Slide130
Policy Curve
Winning Rate
Hash Rate
Supply
Curve
(Hash rate is increasing in winning rate)
Slide140
Policy Curve
Winning Rate
Hash Rate
Want to choose
to achieve this point!
Slide150
Policy Curve
Winning Rate
Hash Rate
Supply
Curve
(Hash rate is increasing in winning rate)
Slide160
Policy Curve
Winning Rate
Hash Rate
Supply
Curve
(Hash rate is increasing in winning rate)
Slide170
Policy Curve
Winning Rate
Hash Rate
Too slow block generation!
Supply
Curve
(Hash rate is increasing in winning rate)
Slide180
Policy Curve
Winning Rate
Hash Rate
Supply
Curve
(Hash rate is increasing in winning rate)
Slide190
Policy Curve
Winning Rate
Hash Rate
Supply
Curve
(Hash rate is increasing in winning rate)
Slide200
Policy Curve
Winning Rate
Hash Rate
Overshoot.
Fails to select the
ideal winning rate (
).
Supply
Curve
(Hash rate is increasing in winning rate)
Slide210
Winning Rate
Hash Rate
Slide220
Winning Rate
Hash Rate
Elastic hash supply
The winning rate
never
converges to the policy goal.
Slide23SimulationReplicate the situation of late 2018.Per hash reward attained the historical minimum.
Slide24We were about to face a crisis in November 2018!
Blue line: IdealRed line: Under Bitcoin DAABitcoin DAA fails to “trace” the ideal outcome.Block time is
highly unstable
.
Slide25In contrast, the DAA of
Bitcoin Cash is shown to be very robust. (See the paper)
Slide26Policy Suggestion:(1) We must upgrade Bitcoin DAA. (2) The current DAA of the Bitcoin Cash
system is a good candidate for it.
Slide27Thank you!Original paper download link:https://ssrn.com/abstract=3410460
Slide28Alternative: Bcash DAABitcoin Cash (Bcash) is another blockchain platform.Hardforked from Bitcoin
Share many structures.Bcash updates the winning rate continually (every period).Look at the total block time of previous 144 blocks.
If
and
were constant, this DAA also achieves
.
Replace DAA equation
Obtain economy under new DAA.
Slide29Supply Curve
0
Policy Curve
Intuition (Bitcoin DAA)
During the period of observation,
an identical winning rate
is used.
DAA estimates
.
Data point
Updated
Slide30Supply Curve
0
Policy Curve
Intuition (Bitcoin cash DAA)
is updated every period.
Historical hash rate
fluctuates around
.
Take average
Closer to
!
Data points vary!!
Updated point is closer to the steady state.
Slide31Local (In)Stability (Bitcoin DAA)Theorem 1:Under the Bitcoin DAA,
iff .Where
If
, the winning rate oscillates and diverges.
Slide32Local Stability (Bitcoin cash DAA)Theorem 2:Under the Bcash DAA,
iff .Proof: Evaluate eigenvalues of the characteristic equation.Much weaker than the hypothesis of Theorem 1.