Running Compression Algorithms in the Encrypted Domain: A Case-Study on the Homomorphic Execution of RLE

Abstract

This paper is devoted to the study of the problem of running compression algorithms in the encrypted domain, using a (somewhat) fully homomorphic encryption (FHE) scheme. We do so with a particular focus on conservative compression algorithms. Despite of the encrypted domain Turingcompleteness which comes with the magic of FHE operators, we show that a number of subtleties crop up when it comes to running compression algorithms and, in particular, that guaranteed conservative compression is not possible to achieve in the FHE setting. To illustrate these points, we analyze the most elementary conservative compression algorithm of all, namely Run-Length Encoding (RLE). We first study the way to regularize this algorithm in order to make it (meaningfully) fit within the constraints of a FHE execution. Secondly, we analyze it from the angle of optimizing the resulting structure towards (as much as possible) FHE execution efficiency. The paper is concluded by concrete experimental results obtained using the Fan-Vercauteren cryptosystem as well as the Armadillo FHE compiler. It is also this paper intent to share the concrete return on experience we gained in attempting to run a simple yet practically significant algorithm over FHE.