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

• URL: http://arxiv.org/abs/2504.16091v1
• Date: Fri, 28 Mar 2025 06:49:22 GMT
• Title: Post-Quantum Homomorphic Encryption: A Case for Code-Based Alternatives
• Authors: Siddhartha Siddhiprada Bhoi, Arathi Arakala, Amy Beth Corman, Asha Rao,
• Abstract summary: Homomorphic Encryption (HE) allows secure and privacy-protected computation on encrypted data without the need to decrypt it.<n>Most of the current PQHE algorithms are secured by lattice-based problems.<n>Code-based encryption is a novel way to diversify post-quantum algorithms.
• Score: 0.6749750044497732
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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