Stock markets have two primary functions: providing liquidity and price discovery. While the market micro-structure was mostly ignored or assumed to function ideally for the purpose of asset pricing, O'Hara (Journal of Finance, 2003) has established that both liquidity provision and price discovery negatively affect asset pricing and returns. In this talk we propose using cryptography, and in particular secure multi-party computation (MPC), to set up a novel stock-market structure that, to a large extent, removes the negative consequences of liquidity costs and periodic price discovery. Interestingly, the proposed market structure takes us back to the early days of stock markets, i.e., periodic-call markets, but with the not-so-trusted auctioneer replaced by multiple parties running MPC with no individual party (or minor coalition) learning the order-book.