Abstract: A method and apparatus for the distributed, privacy preserving and integrity preserving technical implementation of an order book where a group of computing devices belonging to agents (traders, brokers, or groups thereof) wishing to engage in distributed double auctions and markets can (1) keep private the information about the solvency of the individual agent owing the trader's computer; (2) publicly register the values of buy and sell orders while (a) maintaining confidential the information about the owner of the buy (resp. sell) order and (b) still having the possibility to accrue matched buy/sell transactions to the accounts of the computing devices of the individual agents owing those orders; (3) maintain the financial integrity of the market as implemented by a distributed systems of computing devices; and (4) keep private the possible exit from the market by computing devices operated by agents who could no longer meet their contractual obligations.