Satoshi's white paper argues that Bitcoin is secure as long as honest nodes control more CPU power than any group of attackers. It also argues that a large miner would earn more by playing by the rules than by attacking. In 2013, Ittay Eyal and Emin Gün Sirer challenged the second idea in "Majority is not Enough".
The attack
In selfish mining, a pool that finds a block keeps it secret and continues mining on it.
- If the pool finds a second block first, it is ahead. It releases blocks in a way that always keeps the public chain behind, so honest miners waste their work on blocks that become stale.
- If honest miners find a block while the pool is one block ahead, the pool releases its block immediately and starts a race. The share of honest miners that build on the pool's block is called γ (gamma).
The pool loses some blocks itself, but honest miners lose more. Since rewards are shared out by blocks in the final chain, the pool's share can exceed its share of hash power.
The thresholds
- With γ = 0 (the pool never wins a tie), selfish mining pays above about 1/3 of total hash power.
- With γ = 1, it pays at any size.
- The authors proposed that miners choose randomly between competing blocks, which would raise the threshold to 1/4.
Their warning was that rational miners might join the selfish pool until it becomes a majority.
Has it happened?
There is no publicly confirmed case of large-scale selfish mining on Bitcoin. That does not prove it is impossible. It is hard to detect with certainty, and pools also care about their reputation and the price of bitcoin.
Security models
- Honest majority: the white paper's model. With an attacker holding 10% of hash power, the chance of catching up from 5 blocks behind is about 0.09%.
- Rational miners: miners maximise profit. Selfish mining shows that protocol rules and incentives do not always line up.
- Majority attacker: with over 50%, an attacker can reverse its own recent payments or block transactions. It still cannot steal coins or break the consensus rules that nodes enforce.
Why propagation matters
Fast block relay, such as compact blocks, reduces stale blocks and limits the advantage of a well-connected attacker.