Notes on non-interactive secure comparison in "image feature extraction in the encrypted domain with privacy-preserving SIFT"

Protocols for secure comparison are a fundamental building block of many privacy-preserving protocols such as privacy-preserving face recognition or privacy-preserving fingerprint authentication. So far, all existing secure comparison protocols that have been used in practical implementations require interaction. In recent work, Hsu et al. (IEEE Transactions on Image Processing 2012) propose protocols for privacy-preserving computation of the scale-invariant feature transform (SIFT) in the encrypted domain. Their fundamental building block is a new protocol for performing secure comparisons under additively homomorphic encryption that requires no interaction. In this paper we present potential for optimization and shortcomings of their secure comparison protocol. More specifically, we show that it 1) allows optimizations by shifting computation from the server to the user, 2) removes the gain that the user has in outsourcing computations to the server, and most importantly is 3) either computationally intractable for the server or insecure. As alternatives we propose to use either interactive comparison protocols or non-interactive somewhat or fully homomorphic encryption.