Analysis of the complexity of Homomorphic Encryption algorithms

Authors

DOI:

https://doi.org/10.5902/2179460X87825

Keywords:

Partially Homomorphic Cryptography, Computational complexity, Privacy, Security

Abstract

Partially Homomorphic Cryptography plays a crucial role in preserving privacy during the processing of sensitive information. This work presents partially homomorphic encryption schemes applied to integers, which support only one homomorphic operation, either additive or multiplicative. We analyze the computational time complexities associated with encryption, decryption, homomorphic computation, and potential attacks on each scheme. Additionally, we compare the studied schemes, detailing their algorithms and highlighting their key efficiency and security characteristics.

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Author Biographies

Aline De Lurdes Zuliani Lunkes, Laboratório Nacional de Computação Científica

Holds a teaching degree in Mathematics from the Federal University of Santa Maria (2015), a Master's degree in Computational Modeling from the Federal University of Rio Grande (2018), and a Ph.D. in Computational Modeling from the National Laboratory for Scientific Computing (2023). 

Fábio Borges de Oliveira, Laboratório Nacional de Computação Científica

He holds a Ph.D. degree in Doctor of Engineering in the Department of Computer Science at Technological University of Darmstadt - Germany (TU Darmstadt), a Master of Computational Modeling at Brazilian National Laboratory for Scientific Computing (LNCC in Portuguese), and a Bachelor of Mathematics at State University of Londrina - Brazil (UEL in Portuguese). Currently, he is developing research at the LNCC.

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Published

2025-04-11

How to Cite

Lunkes, A. D. L. Z., & Oliveira, F. B. de. (2025). Analysis of the complexity of Homomorphic Encryption algorithms. Ciência E Natura, 47, e87825 . https://doi.org/10.5902/2179460X87825