Big Data provides a tremendous amount of detailed data for improved decision making, from overall strategic decisions, to automated operational micro-decisions. Directly, or with the right analytical methods, these data may reveal private information such as preferences and choices, as well as bargaining positions. Therefore, these data may be both personal or of strategic importance to companies, which may distort the value of Big Data. Consequently, privacy-preserving use of such data has been a long-standing challenge, but today this can be effectively addressed by modern cryptography. One class of solutions makes data itself anonymous, although this degrades the value of the data. Another class allows confidential use of the actual data by Computation on Encrypted Data (CoED). This chapter describes how CoED can be used for privacy-preserving statistics and how it may distort existing trustee institutions and foster new types of data collaborations and business models. The chapter provides an introduction to CoED, and presents CoED applications for collaborative statistics when applied to financial risk assessment in banks and directly to the banks’ customers. Another application shows how MPC can be used to gather high quality data from, for example,. national statistics into online services without compromising confidentiality.