Dark markets for share trading provide an important function in the financial services industry, however the operators of such markets are not operating in the dark; leaving the possibility open for the market operator to gain a market advantage. Multi-Party Computation (MPC) is a method to remove the need for such trusted third parties. In this paper we show how MPC can be used to implement such a dark market. Importantly we base our solution on the throughputs and algorithms needed in real markets. In particular we base our implementation on the Turquoise Plato market used by the London Stock Exchange.