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Abstract In this paper, we propose a framework for lightning-fast privacy-preserving outsourced computation framework in the cloud, which we refer to as LightCom. Using LightCom, a user can securely achieve the outsource data storage and fast, secure data processing in a single cloud server different from the existing multi-server outsourced computation model. Specifically, we first present a general secure computation framework for LightCom under the cloud server equipped with multiple Trusted Processing Units (TPUs), which face the side-channel attack. Under the LightCom, we design two specified fast processing toolkits, which allow the user to achieve the commonly-used secure integer computation and secure floating-point computation against the side-channel information leakage of TPUs, respectively. Furthermore, our LightCom can also guarantee access pattern protection during the data processing and achieve private user information retrieve after the computation. We prove that the proposed LightCom can successfully achieve the goal of single cloud outsourced data processing to avoid the extra computation server and trusted computation server, and demonstrate the utility and the efficiency of LightCom using simulations.