Arbitrum derives its security from the Ethereum network, which provides consensus and finality for Arbitrum transactions. In other words, Ethereum guarantees the validity of the rollup’s off-chain computation and data availability behind the computation.
The use of optimistic rollups means Arbitrum executes transactions on the rollup outside of Ethereum, and bundle multiple transactions in a batch before submitting it to mainnet. As the term “optimistic” suggests, the off-chain transactions are assumed to be valid and no proof-of-validity is submitted. In case of a dispute, there is a time period after the rollup is submitted where anyone can challenge the transaction by submitting a fraud proof.