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Survey | Open Access

For what algebraic systems does a useful privacy homomorphism exist?

Valentina Grazian1, Antonio Tortora2( ), Maria Tota3
Dipartimento di Matematica "Tullio Levi-Civita", Università di Padova, Via Trieste 63 - 35121 - Padova, Italy
Dipartimento di Matematica e Fisica, Università della Campania "Luigi Vanvitelli", Viale Lincoln 5 - 81100 - Caserta, Italy
Dipartimento di Matematica, Università di Salerno, Via Giovanni Paolo II, 132 - 84084 - Fisciano (SA), Italy
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Abstract

Homomorphic encryption plays a crucial role in the challenging problem of privacy preservation. In this survey, we describe a number of homomorphic schemes providing the relevant definitions to make the topic accessible to both cryptographers and mathematicians. We classify the schemes according to the timeline of appearance and, for some of them, we verify that they are correct with respect to decryption and evaluation, providing proofs or references. Recent research directions are also briefly discussed in this context.

Keywords

fully homomorphic encryptionprivacy preservationcloud computing
CLC number: 94A60, 08A99

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AIMS Mathematics
Volume 10 Issue 4,
April 2025
Pages 9539-9562
DOI: 10.3934/math.2025440

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Cite this article:
Grazian V, Tortora A, Tota M. For what algebraic systems does a useful privacy homomorphism exist?. AIMS Mathematics, 2025, 10(4): 9539-9562. https://doi.org/10.3934/math.2025440

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Received: 23 December 2024
Revised: 31 March 2025
Accepted: 15 April 2025
Published: 15 April 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)