Homomorphic Cryptographic Algorithms for Edge Computing Security: A Mathematical Model Review

R. S. S. Raju Battula, Lubna Ansari

2025

Abstract

Edge computing has been one of the transformative paradigms in distributed systems, requiring security mechanisms to be robust for the protection of data at the periphery of a network. This review is hence an all-embracing discussion on the mathematical basis of homomorphic cryptographic algorithms and their application in edge computing scenarios. It is an in-depth investigation into the ways algebraic structures, especially polynomial rings and lattice-based constructions, can be used to devise secure homomorphic encryption schemes. The review comprises recent advances in homomorphic encryption (FHE) and semi-homomorphic encryption (SHE), emphasis on mathematical models, high computational efficiency, and practical challenges of implementing fully homomorphic encryption within resource-constrained Edge environments. Based on a detailed analysis of Ring Learning with Errors (RLWE) and related mathematical problems, we shall evaluate the security parameters and performance metrics that are critical for edge computing applications. Our results show that although the currently available homomorphic encryption schemes offer strong security guarantees, they suffer from important challenges in computational overhead and resource optimization. We present a novel framework for assessing the trade-off between security strength and computational efficiency, which is particularly relevant in the context of edge computing constraints. Further on, we are discussing emerging mathematical approaches to noise management and parameter optimization, which also gives some insight into further research directions. This review therefore contributes to the field by synthesizing current mathematical approaches, identification of critical challenges, and a proposal of possible solutions for moving forward with homomorphic cryptography applications in edge computing.

Paper Citation

in Harvard Style

Battula R. and Ansari L. (2025). Homomorphic Cryptographic Algorithms for Edge Computing Security: A Mathematical Model Review. In Proceedings of the 1st International Conference on Research and Development in Information, Communication, and Computing Technologies - ICRDICCT`25; ISBN 978-989-758-777-1, SciTePress, pages 534-540. DOI: 10.5220/0013916200004919

in Bibtex Style

@conference{icrdicct`2525,
author={R. S. S. Battula and Lubna Ansari},
title={Homomorphic Cryptographic Algorithms for Edge Computing Security: A Mathematical Model Review},
booktitle={Proceedings of the 1st International Conference on Research and Development in Information, Communication, and Computing Technologies - ICRDICCT`25},
year={2025},
pages={534-540},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0013916200004919},
isbn={978-989-758-777-1},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 1st International Conference on Research and Development in Information, Communication, and Computing Technologies - ICRDICCT`25
TI - Homomorphic Cryptographic Algorithms for Edge Computing Security: A Mathematical Model Review
SN - 978-989-758-777-1
AU - Battula R.
AU - Ansari L.
PY - 2025
SP - 534
EP - 540
DO - 10.5220/0013916200004919
PB - SciTePress