A Practical Exercise in Adapting SIFT Using FHE Primitives

Abstract: An exercise in implementing Scale Invariant Feature Transform using CKKS Fully Homomorphic encryption quickly reveals some glaring limitations in the current FHE paradigm. These limitations include the lack of a standard comparison operator and certain operations that depend on it (like array max, histogram binning etc). We also observe that the existing solutions are either too low level or do not have proper abstractions to implement algorithms like SIFT. In this work, we demonstrate: 1. Methods of adapting regular code to the FHE setting. 2. Alternate implementations of standard algorithms (like array max, histogram binning, etc.) to reduce the multiplicative depth. 3. A novel method of using deferred computations to avoid performing expensive operations such as comparisons in the encrypted domain. Through this exercise, we hope this work acts as a practical guide on how one can adapt algorithms to FHE