Privacy-Preserving String Edit Distance with Moves

We propose the first two-party protocol for securely computing an extended edit distance. The parties possessing their respective strings x and y want to securely compute the edit distance with move operations (EDM), that is, the minimum number of insertions, deletions, renaming of symbols, or substring moves required to transform x to y. Although computing the exact EDM is NP-hard, there exits an almost linear-time algorithm within the approximation ratio O(lg* N lgN) for N = max{vertical bar x vertical bar, vertical bar y vertical bar}. We extend this algorithm to the privacy-preserving computation enlisting the homomorphic encryption scheme so that the party can obtain the approximate EDM without revealing their privacy under the semi-honest model.