Today's cyber-physical systems face various impediments to achieving their intended goals, namely, communication uncertainties and faults, relative to the increased integration of networked and wireless devices, hinder the synchronism needed to meet real-time deadlines. Moreover, being critical, these systems are also exposed to significant security threats. This threat combination increases the risk of physical damage. This paper addresses these problems by studying how to build the first real-time Byzantine reliable broadcast protocol (RTBRB) tolerating network uncertainties, faults, and attacks. Previous literature describes either real-time reliable broadcast protocols, or asynchronous (non real-time) Byzantine~ones. We first prove that it is impossible to implement RTBRB using traditional distributed computing paradigms, e.g., where the error/failure detection mechanisms of processes are decoupled from the broadcast algorithm itself, even with the help of the most powerful failure detectors. We circumvent this impossibility by proposing RT-ByzCast, an algorithm based on aggregating digital signatures in a sliding time-window and on empowering processes with self-crashing capabilities to mask and bound losses. We show that RT-ByzCast (i) operates in real-time by proving that messages broadcast by correct processes are delivered within a known bounded delay, and (ii) is reliable by demonstrating that correct processes using our algorithm crash themselves with a negligible probability, even with message loss rates as high as 60%.