{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T19:50:45Z","timestamp":1771703445627,"version":"3.50.1"},"reference-count":66,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,5,12]],"date-time":"2025-05-12T00:00:00Z","timestamp":1747008000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Cryptography"],"abstract":"<jats:p>Homomorphic Encryption (HE) allows secure and privacy-protected computation on encrypted data without the need to decrypt it. Since Shor\u2019s 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.<\/jats:p>","DOI":"10.3390\/cryptography9020031","type":"journal-article","created":{"date-parts":[[2025,5,12]],"date-time":"2025-05-12T09:13:38Z","timestamp":1747041218000},"page":"31","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Post-Quantum Homomorphic Encryption: A Case for Code-Based Alternatives"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-6099-9707","authenticated-orcid":false,"given":"Siddhartha Siddhiprada","family":"Bhoi","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, RMIT University, Melbourne, VIC 3000, Australia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5515-175X","authenticated-orcid":false,"given":"Arathi","family":"Arakala","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, RMIT University, Melbourne, VIC 3000, Australia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3542-3807","authenticated-orcid":false,"given":"Amy Beth","family":"Corman","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, RMIT University, Melbourne, VIC 3000, Australia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6222-282X","authenticated-orcid":false,"given":"Asha","family":"Rao","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, RMIT University, Melbourne, VIC 3000, Australia"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3477139","article-title":"Computing blindfolded on data homomorphically encrypted under multiple keys: A survey","volume":"54","author":"Aloufi","year":"2021","journal-title":"ACM Comput. 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