Big data is a type of data set with rich information and significant value. To avoid leakage of user privacy during big data mining, some necessary measures on big data need to be placed. Since big data has huger volume, more complex structure and less tolerance of delays, traditional privacy preserving technologies are mostly unsuitable for preserving privacy of big data. From a cryptographic perspective, this paper surveys the recent progress on privacy preserving technologies for big data. Three basic problems in big data, namely storage, search and computation, are investigated, and their research background and main research directions are elaborated. The latest research progress of privacy preserving technologies for these problems is also presented. Finally, some important directions of privacy preserving technologies for big data are suggested.