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In the era of cloud computing, the cloud server always plays a significant role to carry the heavy tasks of computation. As for storage services, it provides an efficient manner for accessing data. For data privacy, encryption is usually referred to as a simple approach, but in fact cloud services cannot work with the traditional encryption. Therefore, outsourced computing over encrypted data receives attention of preserving privacy in the cloud setting. The notion, privacy-preserving outsourced similarity test (PPOS) over encrypted data, is introduced to capture the following scenario. The cloud stores encrypted data with the encrypted feature vector and then picks up the target data by testing similarity between those vectors and the search query. Recently, Zhang et al. proposed a PPOS scheme based on additive homomorphic encryption, garbled circuits, and ciphertext-policy attribute-based encryption. In this paper, we aim for presenting the formal security model and new scheme of PPOS. We use as few primitives as possible to minimize cryptographic building blocks. Our solution avoids using homomorphic encryption and constructs the PPOS scheme simply from garbled circuits and ciphertext-policy attribute-based encryption.