A Practical Exercise in Adapting SIFT Using FHE Primitives

TL;DR

This paper explores implementing SIFT with CKKS Fully Homomorphic Encryption, highlighting current limitations, proposing adaptations, and introducing deferred computations to enable practical encrypted image processing.

Contribution

It presents methods for adapting algorithms to FHE, alternative implementations to reduce depth, and a novel deferred computation approach for comparisons.

Findings

Identified key limitations in current FHE for image processing.

Proposed alternative algorithms to lower multiplicative depth.

Introduced deferred computations to avoid costly encrypted comparisons.

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