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The physical security of application-specific embedded processors such as those found in smart-cards has become increasingly important since they are used more and more as conduits for sensitive financial and identity information. The advent of side-channel attacks has meant that a combination of algorithm, software, and hardware defense is required. In this paper, we reexamine the issue of nondeterministic processors, simplifying previous designs using a multithreaded architecture. From this simplification, we are able to construct a formally reasoned assessment of the security level offered by such a device.