SecureMR is a system that provides integrity assurance for MapReduce jobs running in open systems. It uses a replication-based scheme to decentralize integrity verification across mappers and reducers. Key components include commitment protocols where mappers sign hash commitments of intermediate data, and verification protocols where reducers verify the integrity of received data by comparing hashes. The system is implemented on Hadoop and evaluation shows it can detect misbehavior with high detection rates while imposing reasonable performance overhead.