Stubborn Mining: Generalizing Selfish Mining and Combining with an Eclipse Attack With Srijan Kumar, Andrew Miller and Elaine Shi 1 Kartik Nayak

2 Alice Bob Charlie Emily Blockchain Bitcoin Mining Dave Fairness: If Alice has 1/4 th computation power, she gets 1/4 th of the total reward

3 Selfish Mining [ES’14] If Alice deviates from the protocol, can she gain more? Yes! Computation power > 0.33 Alice Emily Charlie Bob Dave

4 Prior work: Selfish Mining One way of deviating so that one miner earns more revenue at the expense of others Stubborn Mining We show other attacks in the same model that perform better than selfish mining Earn ~$137,000 / day more than by Selfish Mining attack 1 Our Contribution: All miners earn ~$1.5 M / day

5 Eclipse Attacks [HKZG’15] World 1 World 2 Alice can double-spend Compose Stubborn Mining and Eclipse Attacks Alic e Bob Charlie Emily Dave 2 Our Contribution:

6 1 2 Compose Stubborn Mining and Eclipse Attacks Stubborn Mining Key Contributions Sometimes, the best strategies benefit the “victim” Both of these attacks are better than were previously known for the attacker

7 Selfish Mining (in more detail) Alice Emily Charlie Bob Dave Alic e (α) Publi c (β) γ: Alice’s ability to win race conditions (α, γ): network model parameters 40%: Ghash.IO largest pool in 2014 α 41%: two largest mining pools 21%: largest mining pool γ : depending on attacker’s influence - May 16, 2015

8 Selfish Mining (in more detail) Public’s view 0 1 α 2 α 3 α β β Alice’s private chain Alic e (α) Publi c (β) γ: Alice’s ability to win race conditions (α, γ): network model parameters

9 Selfish Mining (in more detail) Alic e (α) Publi c (β) Public’s view 0 1 α 2 α 3 α β β

10 Selfish Mining (in more detail) Alic e (α) Publi c (β) Public’s view 0 1 α 2 α 3 α β β 0’ β α γβ (1-γ)β γ: Fraction of public mining on Alice’s block Alice’s private chain A strategy where Alice reveals blocks under certain conditions

11 Our Contribution: Stubborn Mining Intuition: A selfish miner gives up too easily Three stubborn mining strategies: 1.Lead Stubborn Mining 2.Equal-Fork Stubborn Mining 3.Trail Stubborn Mining

12 Lead Stubborn Mining Alic e (α) Publi c (β) 0 1 α 2 α 3 α β β 0’ β α γβ (1-γ)β Public’s view 2’ α 1’ β Alice’s private chain

13 Equal-Fork Stubborn Mining Alic e (α) Publi c (β) 0 1 α 2 α 3 α β β 0’ β α γβ (1-γ)β Public’s view Alice’s private chain

14 Trail Stubborn Mining Alic e (α) Publi c (β) 0 1 α 2 α 3 α β β 0’ β α γβ (1-γ)β Public’s view (1-γ)β Alice’s private chain

15 Hybrid Stubborn Mining Strategies S L F T1T1 Lead Stubbornness Equal-Fork Stubbornness Trail Stubbornness LF T2T2 LT 1 FT 1 LFT 1

16 There is no one-size-fits-all dominant strategy. γ: Alice’s network influence (fraction of public mining on Alice’s chain in case of a fork) Results MonteCarlo simulations Multiple samples and report mean

17 For a large parameter space, Stubborn Mining strategies perform better than Selfish Mining.

18 Trail stubborn strategies perform better than non-trail- stubborn counterparts when α > 0.33

19 Attacker’s Revenue: Compared to Honest Mining α = 0.4, γ = % higher revenue Increase in revenue: ~$375,000 / day

20 Attacker’s Revenue: Compared to Selfish Mining α = 0.4, γ = % higher revenue Increase in revenue: ~$137,000 / day

21 Eclipse Attacks (reminder) World 1 World 2 Alic e Bob Lucy Emily Dave

22 Eclipse Attacks (reminder) World 1 World 2 Alic e Bob Lucy Emily Dave Alic e (α) Publi c (β) Luc y (λ) λ < β

23 Exploiting Eclipse Attack Victims Alic e (α) Publi c (β) Luc y (λ) 1. Forward all messages – no eclipsing 2. Partition all messages – waste Lucy’s computation power 3. Collude with Lucy 4. Destroy if no stake (DNS) No Eclipsing Partition all messages Collude with Lucy Destroy if no stake Eclipsin g degree

24 Non-trivial compositions of Stubborn Mining + Eclipsing outperform naïve strategies 8% gain Alice’s relative gain wrt naïve Dominant Strategies Naïve: Honest/Selfish Mining – Stubbornness, Collude/Destroy Lucy - Eclipsing

25 Gain compared to Selfish Mining 25% gain Alice’s relative gain wrt Selfish Mining

26 The attack may benefit Lucy Lucy’s relative gain:

27 Detecting and inferring attacks Are these attacks likely to occur? Discussed in the paper Countermeasures? Dispersed mining power Selfish Mining not observed until now ~$375,000 / day Other cryptocurrencies

28 Conclusion 1 2 Compose Stubborn Mining and Eclipse Attacks Stubborn Mining Thank You! Dominant Strategies