Secure computation of functionalities based on Hamming distance and its application to computing document similarity

This paper examines secure two-party computation of functions which depend only on the Hammingdistance 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 maliciousadversaries.We then show applications of HDOT. These include protocols for checking similarity between docu-ments without disclosing additional information about them (these protocols are based on algorithms ofBroder et. al. for computing document similarity based on the Jaccard measure). Another application isa variant of symmetric private information retrieval (SPIR), which can be used if the server’s databasecontains N entries, at most N/ logN of which have individual values, and the rest are set to some defaultvalue. The receiver does not learn whether it receives an individual value or the default value. Thisvariant of PIR is unique since it can be based on the existence of OT alone.