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

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-qu...

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Main Authors: Siddhartha Siddhiprada Bhoi, Arathi Arakala, Amy Beth Corman, Asha Rao
Format: Article
Language:English
Published: MDPI AG 2025-05-01
Series:Cryptography
Subjects:
Online Access:https://www.mdpi.com/2410-387X/9/2/31
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author Siddhartha Siddhiprada Bhoi
Arathi Arakala
Amy Beth Corman
Asha Rao
author_facet Siddhartha Siddhiprada Bhoi
Arathi Arakala
Amy Beth Corman
Asha Rao
author_sort Siddhartha Siddhiprada Bhoi
collection DOAJ
description 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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spelling doaj-art-634d7aa3beb64e3d945849fc4858d49a2025-08-20T03:24:32ZengMDPI AGCryptography2410-387X2025-05-01923110.3390/cryptography9020031Post-Quantum Homomorphic Encryption: A Case for Code-Based AlternativesSiddhartha Siddhiprada Bhoi0Arathi Arakala1Amy Beth Corman2Asha Rao3Department of Mathematical Sciences, RMIT University, Melbourne, VIC 3000, AustraliaDepartment of Mathematical Sciences, RMIT University, Melbourne, VIC 3000, AustraliaDepartment of Mathematical Sciences, RMIT University, Melbourne, VIC 3000, AustraliaDepartment of Mathematical Sciences, RMIT University, Melbourne, VIC 3000, AustraliaHomomorphic 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.https://www.mdpi.com/2410-387X/9/2/31homomorphic encryptioncode-based encryptionpost-quantum cryptographyreview
spellingShingle Siddhartha Siddhiprada Bhoi
Arathi Arakala
Amy Beth Corman
Asha Rao
Post-Quantum Homomorphic Encryption: A Case for Code-Based Alternatives
Cryptography
homomorphic encryption
code-based encryption
post-quantum cryptography
review
title Post-Quantum Homomorphic Encryption: A Case for Code-Based Alternatives
title_full Post-Quantum Homomorphic Encryption: A Case for Code-Based Alternatives
title_fullStr Post-Quantum Homomorphic Encryption: A Case for Code-Based Alternatives
title_full_unstemmed Post-Quantum Homomorphic Encryption: A Case for Code-Based Alternatives
title_short Post-Quantum Homomorphic Encryption: A Case for Code-Based Alternatives
title_sort post quantum homomorphic encryption a case for code based alternatives
topic homomorphic encryption
code-based encryption
post-quantum cryptography
review
url https://www.mdpi.com/2410-387X/9/2/31
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