Fraud proof is a way of validating data published by Optimistic Rollups. During the synchronization of data from Layer 2 networks to the Ethereum mainnet, one can initiate a challenge in the challenge period if he thinks the data is not correct, or there is fraud. After that, calculation will be done by Layer1 smart contracts to decide who is fraudulent to be penalized.

Currently, fraud proof can be categorized into single-round interactive proving and multi-round interactive proving.

**Single-Round Interactive Proving**

Single-round interactive proving is to replay the disputed transactions on Layer 1 to detect whether there is an invalid state or not before those transactions are submitted to the mainnet.

For example, as a validator, Alice synchronizes the data compressed by Rollup to Layer 1 while staking her bond. Bob needs to initiate a challenge during the challenge period by staking his bond if he thinks the data is disputable. In this case, the rollup protocol will recompute the disputed transaction on Layer1 to determine who wins the challenge. In the end, the winner will be rewarded while the loser’s bond will be slashed.

However, due to relatively high on-chain computing costs, this proving method may be limited to the Layer1 block size if there is an excessive amount of transaction data to be recomputed.

**Multi-Round Interactive Proving**

Under such a proving method, Alice needs to divide her synchronized data regarded as disputable by Bob into two equal halves. Bob, as a challenger, will then choose the half he wants to challenge. The half will be divided into another two equal halves by Alice. This process will repeat until both parties are disputing a single step of execution. At this point, the Layer1 smart contract will catch the fraudulent party through computation.

Therefore, compared with single-round interactive proving, multi-round interactive proving is a more cost-effective way to resolve disputes. Also, it is more applicable for complex smart contracts and disputes with higher requirements.

Nevertheless, for multi-round interactive proving, its challenge period may be longer as the number of interactions grows.