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An attack on ELG-LUC3-ECC cryptosystem using Hastad’s and Julta’s theorem


Citation

Wong, T.J. and Koo, L.F. and A. Sathar, M.H. and Rasedee, A.F.N. and Sarbini, I. N. (2024) An attack on ELG-LUC3-ECC cryptosystem using Hastad’s and Julta’s theorem. Mathematical Modeling and Computing, 11 (4). pp. 1135-1140. ISSN 2312-9794; eISSN: 2415-3788

Abstract

In this study, an attack on the El-Gamal encryption scheme ELG-LUC3-ECC is proposed, which is based on a third-order Lucas sequence over an elliptic curve finite field, using Hastad’s and Julta’s theorems. Hastad’s theorem was used to solve the problem of multivariate modular equations system, whereas Julta’s theorem was used to find the solutions of multivariable modular equation. As a result, the minimum amount of plaintext required for a successful attack may be determined. Thus, similar attacks can be prevented if the quantity of plaintext remains within the appropriate range.


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Additional Metadata

Item Type: Article
Divisions: Universiti Putra Malaysia
UPM Kampus Bintulu
DOI Number: https://doi.org/10.23939/mmc2024.04.1135
Publisher: Lviv Polytechnic National University
Keywords: Cubic; El-Gamal; Hastad’s theorem; Julta’s theorem; Lucas sequence
Depositing User: Ms. Che Wa Zakaria
Date Deposited: 10 Mar 2025 02:08
Last Modified: 10 Mar 2025 02:08
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.23939/mmc2024.04.1135
URI: http://psasir.upm.edu.my/id/eprint/114785
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