A game theoretic perspective on the block size limit debate, Bitcoins long term security and 51% attacks.

1. 51% ATTACKS
– POOLS AND
GAME THEORY
GAME THEORETIC PERSPECTIVE ON THE
BLOCK SIZE LIMIT AND THE SECURITY OF
THE BITCOIN NETWORK

2. STATEMENTS
• Gavin’s proposal (50% block size
increase/ year) would break the
mining incentive scheme
• (some) 51% attacks cannot be
detected and are very likely
• Bitcoin will naturally without a
hardfork evolve to a POW/POS
mixture

3. MINING REWARD &
BLOCK SIZE LIMIT (1/4)

4. MINING REWARD &
BLOCK SIZE LIMIT (2/4)
- Nash equilibrium
- Real „Transaction Fee Death Spiral“
- Your pool always performs better if it accepts lower fees
 Mining fees will converge to the cost of including a
transaction vs. not including a transaction

5. MINING REWARD &
BLOCK SIZE LIMIT (3/4)
X | 25 BTC X+1 | 25 BTC
X+1 | 25 BTC
10% * 25 = 2.5
X+2 | 25 BTC
99% * 25 = 24.75

6. MINING REWARD &
BLOCK SIZE LIMIT (4/4)
Empty mempool problem
X | 5 BTC X+1 | 5 BTC
X+1 | 5 BTC
10% * 5 = 0.5
X+2 | 0.1 BTC
99% * 0.1 =
0.099

7. THE BLOCK SIZE LIMIT HAS
TO MAKE TRANSACTIONS
SCARCE AND THEREFORE
VALUABLE
Proposal: dynamic block size limit based
on transactions and transaction fees of
the last 2016 blocks

8. BITCOIN WITH CLOSE
TO 0 MINING SUBSIDY
Assumption:
The avarge Bitcoin user holds $100,000 in Bitcoin
What would they be willing to pay in fees in total in
one year?
=> SAME RATIO AS MARKETCAP/ COST OF ATTACKING

9. Bitcoin market cap
mining reward
money into mining
cost of acquiring
51%

10. INCENTIVE
CHALLENGES TODAY

11. 30% HR = 30% MR = 0.3
Adding 1% HR
= 31% MR / 0.31
= 31/101 = 30,69% = 0.3069 (diff =
0.0069)
Cannibalizing pools:
1/71* 0,7 = 0,0098
POOL – WARS
ADDING 1% HASH RATE

12. POOL – WARS
WORTH OF AN ORPHANED
BLOCK
Worth of orphaned block in other pools = HR share * block
reward
Cost of orphaned block in your pool = % of pool HR * block
reward
“parasitizing pools”
Parasitizing cont.
Regular reward
Mining contribution
Reward of mining
pool
Full reward

13. POTENTIAL SOLUTION
• Increase reward for a block
significantly compared to a
share
• Closed pools

14. VALUE OF A 51%
ATTACK
Big attacks:
•Shorting: value of destroying the
value
•Value of getting 100% of the miners
reward
Undetectable attacks:
•Selfish mining
•Increasing the share of participants

15. Bitcoin market cap
mining reward
money into mining
cost of acquiring
51%

16. NUMBERS
1) Mining reward ≈ money into mining
2) Cost of acquiring 51% < money into mining
3) Worth of a 51% attack ≥ mining reward
4) Worth of a 51% attack > cost of acquiring
51%

17. POOL – WARS
LIKELY ATTACK
• Three pools colluding:
• Ignoring every 10th block of
another pool

18. HISTORICAL
CENTRALIZATION OF POOLS

19. POOL – WARS
LIKELY ATTACK
THE UNWANTED COALITION
• Create a block with a
timestamp 2h+epsilon in the
future

20. POOL – WARS
LIKELY ATTACK – GOLDFINGER
REWARD
X | 25 BTC
X+2 B | 25 BTC
X+2 A | 25 BTC
+ 1 from A
X +1 A | 25 BTC
X +1 B | 25 BTC

21. MEMBERS ONLY
MINING
1. To increase earnings someone needs to be excluded
2. Let hashrate join until 80% of the network is in
3. As soon as >55% of blocks are created by members –
start giving none-member blocks a higher diff.
1. Overall difficulty will go down
2. Every participating miner/pool will become its own
difficulty (minimum the network diff) -> HR increase will
have smaller effect
-> Mixture of POW and POW share in the past

22. 5 STEPS TO DO A 51%
ATTACK
1. Publish mining software with higher EV
1. Mine on new headers (but validate it asap)
2. More „flexible“ 2 hours rule
3. Decide for fork with own block version number
4. Make miner aware of „Goldfinger“ reward
5. „Members only“ functionality
2. Create a pool with stickiness
1. New members will receive only 90% for shares in the first
2 weeks, after 2 weeks 110% (ponzi scheme)
3. Create unwanted coalitions (timestamp attack)
4. Atack other pools with cannibalizing pools
5. Eventually switch to members only

23. STATEMENTS
• Hashrate/POW does NOT secure
Bitcoin/transactions – full nodes
do! POW only distributes votes.
• Other mechanics for vote
distribution are maybe fine

24. FUNDING MINERS:
INSURANCE CONTRACT
BOUND TO % OF ORPHANED
BLOCKS

25. RANDOM THOUGHTS
• Make transactions only valid after a
specific block (proof of activity)
• Pools and pool members establish a trust
relation (not possible for small members)
• Change to a mix of proof of stake and
POW
• Block chain limit debate – in case of a
hard fork not the majority of hashrate
decides but merchants and exchanges