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This paper examines secure two-party computation of functions, which depend only on the Hamming distance of the inputs of the two parties. We present efficient protocols for computing these functions. In particular, we present protocols which are secure in the sense of full simulatability against malicious adversaries. We then show applications of HDOT. These include protocols for checking similarity between documents without disclosing additional information about them these protocols are based on algorithms of Broder et al. for computing document similarity based on the Jaccard measure. Another application is a variant of symmetric private information retrieval SPIR, which can be used if the server's database contains N entries, at most N / logN of which have individual values, and the rest are set to some default value. The receiver does not learn whether it receives an individual value or the default value. This variant of PIR is unique since it can be based on the existence of OT alone.