Big data analytics has been regarded as a promising technology to yield better insights into future development by government and industry. Data collection and aggregation are necessary steps to enable data analysis. However, data may be dispersed across multiple places and in different formats. Even worse, data can be encrypted under different encryption mechanisms when different data owners try to secure their data. This makes data aggregation very difficult, if not impossible, especially when the encryption keys cannot be shared for various reasons. In this paper, we take the first step in addressing this problem. More specifically, we propose a new notion of cross-domain encryption switching that bridges two well-studied encryption mechanisms, namely traditional public key encryption and identity-based encryption. As of independent interest, our notion supports keyword search over encrypted data. We provide a provably-secure instantiation satisfying the notion, and further present the efficiency analysis to show the scalability. Our proposed scheme is applicable in multi-domain cloud storage system.