In recent years collaborative editing systems such as wikis, GoogleDocs and version control systems became very popular. In order to improve reliability, fault-tolerance and availability shared data is replicated in these systems. User misbehaviors can make the system inconsistent or bring corrupted updates to replicated data. Solutions to secure data history of state-based replication exist, however they are hardly applied to operation-based replication. In this paper we propose an approach to secure log in operation-based optimistic replication system. authenticators based on hash values and digital signatures are generated each time a site shares or receives new updates on replicas. authenticators secure logs with security properties of integrity and authenticity. We present in detail algorithms to construct and verify authenticators and we analyse their complexities.