The stock markets have two primary functions, that of providing liquidity and price discovery. While the market micro-structure was mostly ignored or assumed to function ideally for the purpose of asset pricing, M. O'Hara (Journal of Finance, 2003) has established that both liquidity and price discovery affect asset pricing, and in particular asset returns. While the cost of liquidity provision is borne by investors, and is clearly detrimental to asset returns, periodic price discovery has both positive and negative consequences for asset pricing. In this work we propose using cryptography, and in particular multi-party secure computation and zero-knowledge proofs, to setup 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 distributed computing where no individual party (or small coalition) gets to know the order book.