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arXiv · 2504.16091

Post-Quantum Homomorphic Encryption: A Case for Code-Based Alternatives

Siddhartha Siddhiprada Bhoi·Arathi Arakala·Amy Beth Corman·Asha Rao
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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.

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Siddhartha Siddhiprada Bhoi, Arathi Arakala, Amy Beth Corman, Asha Rao. 2025-03-28. Post-Quantum Homomorphic Encryption: A Case for Code-Based Alternatives. https://arxiv.org/abs/2504.16091

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