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Security is increasingly becoming an important issue in the design of real-time parallel applications, which are widely used in the industry and academic organizations. However, existing resource allocation schemes for real-time parallel jobs on clusters generally do not factor in security requirements when making allocation and scheduling decisions. In this paper, we develop two resource allocation schemes, called task allocation for parallel applications with deadline and security constraints (TAPADS) and security-aware and heterogeneity-aware resource allocation for parallel jobs (SHARP), by taking into account applications' timing and security requirements in addition to precedence constraints. We consider two types of computing platforms: homogeneous clusters and heterogeneous clusters. To facilitate the presentation of the new schemes, we build mathematical models to describe a system framework, security overhead, and parallel applications with deadline and security constraints. The proposed schemes are applied to heuristically find resource allocations that maximize the quality of security and the probability of meeting deadlines for parallel applications running on clusters. Extensive experiments using real-world applications and traces, as well as synthetic benchmarks, demonstrate the effectiveness and practicality of the proposed schemes.