In this paper, an efficient log authentication scheme for Forensic Computing is proposed. To conduct reliable Forensic Computing, it is required that the logs as digital evidences be verified. To verify them, digital signatures issued by authorities are needed. However, if many logging hosts connect to the server that issues the signatures, the traffic of the server will increase. Therefore, we propose an efficient log authentication scheme for Forensic Computing. Our scheme reduces the traffic of the Sign Server, which signs the logs of the logging hosts, by using distributed Merkle Tree Algorithm among the logging hosts. We show our scheme's effectiveness through evaluation experiments.