We consider the issue of securing dark pools/markets in thefinancial services sector. Currently, these markets are executed via trusted third parties, which opens potential for market operators to conduct fraud. We present a potential solution to this problem by using Multi-Party Computation (MPC) to enable a trusted third party to be emulated in software for three popular market mechanisms: continuous double auction (CDA), periodic auction (PA), and scheduled volume matching (SVM). Our experiments show that whilst the predominate market clearing mechanism of CDA is not currently viable when executed using MPC, SVM (a popular market mechanism for dark pools) is viable. We present experimental validation of this conclusion by presenting the expected throughputs for such markets in two popular MPC paradigms: the two party dishonest majority setting, and the honest majority three party setting.