Post-Quantum Homomorphic Encryption: A Case for Code-Based Alternatives
Abstract
Homomorphic Encryption (HE) allows secure and privacy-protected computation on encrypted data without the need to decrypt it. Since Shor's algorithm rendered prime factorisation and discrete logarithm-based ciphers insecure with quantum computations, researchers have been working on building post-quantum homomorphic encryption (PQHE) algorithms. Most of the current PQHE algorithms are secured by Lattice-based problems and there have been limited attempts to build ciphers based on error-correcting code-based problems. This review presents an overview of the current approaches to building PQHE schemes and justifies code-based encryption as a novel way to diversify post-quantum algorithms. We present the mathematical underpinnings of existing code-based cryptographic frameworks and their security and efficiency guarantees. We compare lattice-based and code-based homomorphic encryption solutions identifying challenges that have inhibited the progress of code-based schemes. We finally propose five new research directions to advance post-quantum code-based homomorphic encryption.
Cite
@article{arxiv.2504.16091,
title = {Post-Quantum Homomorphic Encryption: A Case for Code-Based Alternatives},
author = {Siddhartha Siddhiprada Bhoi and Arathi Arakala and Amy Beth Corman and Asha Rao},
journal= {arXiv preprint arXiv:2504.16091},
year = {2025}
}