Paper 2026/504

Compression And Decompression Under FHE Using Error-Correcting Codes and Copy-And-Recurse

Abstract

Compression has been a fundamental problem in computer science for decades. Simply put, we want to represent a low-entropy vector $v$ of size $n$ with less than $n$ elements so that $v$ can be reconstructed (decompressed) from the shorter representation. Since compressed vectors require less storage and less communication, compression algorithms are part of almost every digital system. When the vector is encrypted with fully homomorphic encryption (FHE) the problem becomes significantly harder. Some research (e.g., [TCHES'19, CCS'21, EuroCrypt'23 ,USENIX'24]) have considered the problem of compressing an encrypted vector but they all assumed the decompression step happens in cleartext. This is a significant restriction. For example, any system with an untrusted agent that needs to receive data and analyze it cannot use existing compression algorithms. In this paper, we give the first (to the best of our knowledge) non-trivial compression-decompression algorithms that are both FHE-friendly. Our algorithms use the copy-and-recurse technique together with the known duality between compression and error-correcting codes. Our experiments show that our decompression algorithm is faster than the folklore decompression algorithm. This is useful in systems with an agent-in-the-middle that is bounded by communication and by computation.