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To date, increasing number of entities on the smart grid begin to establish their local energy generator for ensuring reliability and resilience of power supply. These 'microgrids' can either connect to the power grid or isolate themselves from the grid by consuming their locally generated or stored energy. In reality, some microgrids may have excessive energy while the others may have to request extra energy from the main grid. To better balance the demand and supply of the distributed smart microgrids, it is desired to develop peer-to-peer (P2P) energy exchange models that enable microgrids to interactively exchange their local energy instead of consuming energy delivered from the main grid. However, in this scenario, all the microgrids have to disclose their private information (e.g., demand load and energy storage amount) to each other in the exchange. To tackle these issues, in this paper, we first formulate several novel energy exchange optimization problems that minimize the global energy loss during the exchange in different scenarios, and then develop an efficient and privacy-preserving scheme to solve the energy exchange optimization problems without private information disclosure. We also extend the privacy-preserving scheme to a collusion-resistant scheme in which all the microgrids cannot learn any additional information through colluding with each other. The performance of our proposed approaches is experimentally validated on real microgrid data. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]