Abstract— For many evolving application scenarios like ubiquitous and autonomic computing systems, trustworthy computing solutions are essential. However the fact that the autonomic elements that may take part in such networks may be 1) severely resource constrained, and that 2) the sheer scale of such devices may also place constraints on their cost, calls for inexpensive, low complexity (but nevertheless trustworthy) computing modules, or secure co-processors (ScP). We propose two synergistic strategies for the realization of very low complexity, inexpensive ScPs. The first is a simple security policy, decrypt only when necessary (DOWN). The second is the utilization of untrusted external resources to improve the security of very low complexity ScPs. We point out some very desirable properties of probabilistic key pre-distribution schemes (PKPS) that can take good advantage of the DOWN policy and simultaneously make use of external resources, to render the problem of their suscept...