This chapter presents a survey of the most important security and privacy issues related to large-scale data sharing and mining in big data with focus on differential privacy as a promising approach for achieving privacy especially in statistical databases often used in healthcare. A case study is presented utilizing differential privacy in healthcare domain, the chapter analyzes and compares the major differentially private data release strategies and noise mechanisms such as the Laplace and the exponential mechanisms. The background section discusses several security and privacy approaches in big data including authentication and encryption protocols, and privacy preserving techniques such as k-anonymity. Next, the chapter introduces the differential privacy concepts used in the interactive and non-interactive data sharing models and the various noise mechanisms used. An instrumental case study is then presented to examine the effect of applying differential privacy in analytics. The chapter then explores the future trends and finally, provides a conclusion.