The integrity of information systems is predicated on the integrity of processes that manipulate data. Processes are conventionally executed using the conventional von Neumann (VN) architecture. The VN computation model is plagued by a large trusted computing base (TCB), due to the need to include memory and input/output devices inside the TCB. This situation is becoming increasingly unjustifiable due to the steady addition of complex features such as platform virtualization, hyper-threading, etc. In this research work, we propose a new model of computation - TCB minimizing model of computation (TMMC) - which explicitly seeks to minimize the TCB, viz., hardware and software that need to be trusted to guarantee the integrity of execution of a process. More specifically, in one realization of the model, the TCB can be shrunk to include only a low complexity module; in a second realization, the TCB can be shrunk to include nothing, by executing processes in a blockchain network. The practical utilization of TMMC using a low complexity trusted module, as well as a blockchain network, is detailed in this research work. The utility of the TMMC model in guaranteeing the integrity of execution of a wide range of useful algorithms (graph algorithms, computational geometric algorithms, NP algorithms, etc.), and complex large-scale processes composed of such algorithms, are investigated.