Security is emerging as an essential issue in the design of infrastructure-as-a-service (IaaS) cloud environment applications, which are broadly used in micro-system reliability, transaction processing system, e-commerce services, digital computers for government and medical electronics. Here, the security-driven allocation of Batch of Tasks (BoT) in cloud system is a challenging issue and has been reported as a well-known NP-complete problem. So, many models have been developed, however, existing trust-based models do not factor in security demand properly when making the decision and assigning the cloudlets/tasks. To design a trust-based task allocation model, evaluation and computation of security overhead are needed. The proposed model is negotiating the cipher suite between the task and computing resource in the form of security demand. Furthermore, this paper proposes Security Aware Efficient Static Task Allocation (SA-ESTA) and Security Prioritized Efficient Static Task Allocation (SP-ESTA) algorithms which integrate security demands and trust level into allocation for the IaaS Cloud environment. The proposed algorithms schedule a BoT, on virtual machines (VMs) in order to optimize the flowtime, security overhead, and system failure probability. To evaluate the performance of SA-ESTA and SP-ESTA, the experimental study based on random test-bed trace has been conducted and compared with four other existing baselines and three traditional algorithms on account of flowtime, security overhead and failure probability. Our meticulous performance simulation results clearly show that the proposed algorithms perform better than the peer algorithms under various test conditions.