Advances in cloud computing have greatly motivated data owners to outsource their huge amount of personal multimedia data and/or computationally expensive tasks onto the cloud by leveraging its abundant resources for cost saving and flexibility. Despite the tremendous benefits, the outsourced multimedia data and its originated applications may reveal the data owner's private information, such as the personal identity, locations, or even financial profiles. This observation has recently aroused new research interest on privacy-preserving computations over outsourced multimedia data. In this paper, we propose an effective and practical privacy-preserving computation outsourcing protocol for the prevailing scale-invariant feature transform (SIFT) over massive encrypted image data. We first show that the previous solutions to this problem have either efficiency/security or practicality issues, and none can well preserve the important characteristics of the original SIFT in terms of distinctiveness and robustness. We then present a new scheme design that achieves efficiency and security requirements simultaneously with the preservation of its key characteristics, by randomly splitting the original image data, designing two novel efficient protocols for secure multiplication and comparison, and carefully distributing the feature extraction computations onto two independent cloud servers. We both carefully analyze and extensively evaluate the security and effectiveness of our design. The results show that our solution is practically secure, outperforms the state-of-the-art, and performs comparably with the original SIFT in terms of various characteristics, including rotation invariance, image scale invariance, robust matching across affine distortion, and addition of noise and change in 3D viewpoint and illumination.