Exclusive-or computation on reconciled data

Abstract

Assume there are two users. They both have some sets of binary vectors of length n and want to compute jointly exclusive-or on the union of their sets. In the proof, we use the method of monochromatic rectangles, which was proposed in A.C. Yao, STOC, 1979. In addition, we establish a connection between the codewords of the Hamming code and sets that determine different monochromatic rectangles.