Security violations are becoming more common in real-time systems - an area that was considered to be invulnerable in the past - as evidenced by the recent W32.Stuxnet and Duqu worms. A failure to protect such systems from malicious entities could result in significant harm to both humans as well as the environment. The increasing use of multicore architectures in such systems exacerbates the problem since shared resources on these processors increase the risk of being compromised. In this paper, we present the SecureCore framework that, coupled with novel monitoring techniques, is able to improve the security of realtime embedded systems. We aim to detect malicious activities by analyzing and observing the inherent properties of the real-time system using statistical analyses of their execution profiles. With careful analysis based on these profiles, we are able to detect malicious code execution as soon as it happens and also ensure that the physical system remains safe.