Collection and analysis of various logs (e.g., process logs, network logs) are fundamental activities in computer forensics. Ensuring the security of the activity logs is therefore crucial to ensure reliable forensics investigations. However, because of the black-box nature of clouds and the volatility and co-mingling of cloud data, providing the cloud logs to investigators while preserving users' privacy and the integrity of logs is challenging. The current secure logging schemes, which consider the logger as trusted cannot be applied in clouds since there is a chance that cloud providers (logger) collude with malicious users or investigators to alter the logs. In this paper, we analyze the threats on cloud users' activity logs considering the collusion between cloud users, providers, and investigators. Based on the threat model, we propose Secure-Logging-as-a-Service ( SecLaaS), which preserves various logs generated for the activity of virtual machines running in clouds and ensures the confidentiality and integrity of such logs. Investigators or the court authority can only access these logs by the RESTful APIs provided by SecLaaS, which ensures confidentiality of logs. The integrity of the logs is ensured by hash-chain scheme and proofs of past logs published periodically by the cloud providers. In prior research, we used two accumulator schemes Bloom filter and RSA accumulator to build the proofs of past logs. In this paper, we propose a new accumulator scheme-Bloom-Tree, which performs better than the other two accumulators in terms of time and space requirement.