Similar document detection is a well-studied problem with important application domains, such as plagiarism detection, document archiving, and patent/copyright protection. Recently, the research focus has shifted towards the privacy-preserving version of the problem, in which two parties want to identify similar documents within their respective datasets. These methods apply to scenarios such as patent protection or intelligence collaboration, where the contents of the documents at both parties should be kept secret. Nevertheless, existing protocols on secure similar document detection suffer from high computational and/or communication costs, which renders them impractical for large datasets. In this work, we introduce a solution based on simhash document fingerprints, which essentially reduce the problem to a secure XOR computation between two bit vectors. Our experimental results demonstrate that the proposed method improves the computational and communication costs by at least one order of magnitude compared to the current state-of-the-art protocol. Moreover, it achieves a high level of precision and recall.