Arguments Against the Viability of a Block-stuffing Attack Under a l-Smoothed Base-fee Award

The primary motive and threat of a block-stuffing attack is that it could increase the base-fee which would artificially increase miner income. A secondary concern is the ease with which the attack could be obscured.

The Natural Base-fee

The uninfluenced base-fee in EIP-1559 seeks to find an equilibrium such that it is equal to the lowest fee-cap that a user in a full block is willing to pay. In other words, the basefee targets the maximum price the last transaction in a full block is willing to pay. If there was another transaction with a higher fee-cap, then miners would include that transaction and the base-fee would rise until it reached the target level. If miners are unable to construct a full-block since the base-fee is higher than the lowest fee-cap in a full-block, then the base-fee would fall to include it.

What is a Block-Stuffing Attack.

A block-stuffing attack involves a group of miners or pools colluding to double-fill a block in order to raise the base-fee. The colluding pools will then reclaim the money spent raising the base-fee and award an off-chain compensation in order to reimburse the money spent by pools double-stuffing the block. This is concerning because it is less detectable than other forms of attack that seek to raise transaction fees such as censorship attacks. #3# The Profit-Motive Argument Miners participating in a block-stuffing attack hope that raising the base-fee will allow them to harvest more rewards than they spend raising the block limit. If they harvest more money than they spent, then it is profitable to perform. The first issue is that they only recover a proportion of the money spent raising the base-fee equal to the proportion of the hash-rate which they control. Miners have a profit incentive to avoid joining the coalition since they can increase their profits by keeping the money that the attackers spent

The second issue is that Ethereum's fee demand elasticity is approximately greater than or equal to 1 as shown by V. Buterin in his work computing demand elasticity. Since demand elasticity is greater than or equal to 1, we are currently in a situation where the monoply quantity is greater than the current supply of gas. This means that decreasing the available supply of gas by 50% through stuffing fake transactions will only increase the price by at most 100%, which leaves overall revenue the same. Since there is no way to increase revenue by decreasing the block size due to the current demand elasticity, we can combine it with the knowledge that it is, at best, not unprofitable to attack the network.

We can continue to show that it is unprofitable to attack the network since there are incentives for defection, which means that the attack cannot be both undetectable and game-theoretically stable. Since members inside the coalition are required to return the money spent stuffing the block to the individual who spend it, they make on average, the same amount as if they had been mining before the attack. In the event that they decide to defect from the coalition they get to keep the money spent stuffing the block. When a member defects from the coalition and begins siphoning funds spent stuffing the blocks, members of the coalition end up losing part of the money spent stuffing the blocks, which brings their total profits below the level of mining before the attack. This leads to a cycle where miners leave the coalition because it is now less profitable than having. Eventually, the coalition will become one member who is subsidizing increased profits for the rest of the network until they run out of money.

In the Event That Fee Demand Becomes Inelastic, What Proportion of Miners Must Collude in Order to Make the Attack Viable.

If demand elasticity should drop below 1, then we can calulate the proportion of miners required to subsidize the increase in transaction fee. There remain the same incentives for defection, but it does become profitable for the attack to occur. The demand elasticity shows how many miners are required to collude in order to support that level of increased base fee. For example, if fee elasticity reaches .4 (the lowest estimated demand elasticity of bitcoin by Vitalik), then it becomes profitable to raise the base-fee as long as you can gather more than 40% of the hash-rate in a coalition. As you approach the monoply quantity, the fee elasticity will approach 1 since the fee demand elasticity at the monoply quantity is 1. This means that increasing the base-fee becomes less appealing as you reach the monoply quantity, and defection becomes even more rewarding.

Tim Roughgarden's paper provides additional information about a proportional fee-burn. Since fee demand elasticity is an indication of the magnitude of the difference between the current supply and the monoply quantity, the lowest fee demand elasticity will be before a block-stuffing attack begins. We can make it unprofitable to perform the attack at different demand elasticities by burning a proportion of the l-smoothed reward equal to the complement of the demand elasticity. For example, if Ethereum opted to burn 60% of an l-smoothed reward, they would be protected from fee demand elasticity of .4 and above. This provides an immense window of security that is greatly in excess of the observed fee demand elasticity.