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

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 equatio...

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Main Authors: Wong, Tze Jin, Abdul Sathar, Mohammad Hasan, Koo, Lee Feng, A. F. N, Rasedee, I. N., Sarbini
Format: Article
Language:English
Published: Lviv Polytechnic National University 2024
Online Access:http://psasir.upm.edu.my/id/eprint/117657/
http://psasir.upm.edu.my/id/eprint/117657/1/117657.pdf
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author Wong, Tze Jin
Abdul Sathar, Mohammad Hasan
Koo, Lee Feng
A. F. N, Rasedee
I. N., Sarbini
author_facet Wong, Tze Jin
Abdul Sathar, Mohammad Hasan
Koo, Lee Feng
A. F. N, Rasedee
I. N., Sarbini
author_sort Wong, Tze Jin
building UPM Institutional Repository
collection Online Access
description 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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format Article
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institution Universiti Putra Malaysia
institution_category Local University
language English
last_indexed 2025-11-15T14:34:24Z
publishDate 2024
publisher Lviv Polytechnic National University
recordtype eprints
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spelling upm-1176572025-06-05T01:16:40Z http://psasir.upm.edu.my/id/eprint/117657/ An attack on ELG-LUC3-ECC cryptosystem using Hastad’s and Julta’s theorem Wong, Tze Jin Abdul Sathar, Mohammad Hasan Koo, Lee Feng A. F. N, Rasedee I. N., Sarbini 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. Lviv Polytechnic National University 2024 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/117657/1/117657.pdf Wong, Tze Jin and Abdul Sathar, Mohammad Hasan and Koo, Lee Feng and A. F. N, Rasedee and I. N., Sarbini (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 https://science.lpnu.ua/mmc/all-volumes-and-issues/volume-11-number-4-2024/attack-elg-luc3-ecc-cryptosystem-using-hastads
spellingShingle Wong, Tze Jin
Abdul Sathar, Mohammad Hasan
Koo, Lee Feng
A. F. N, Rasedee
I. N., Sarbini
An attack on ELG-LUC3-ECC cryptosystem using Hastad’s and Julta’s theorem
title An attack on ELG-LUC3-ECC cryptosystem using Hastad’s and Julta’s theorem
title_full An attack on ELG-LUC3-ECC cryptosystem using Hastad’s and Julta’s theorem
title_fullStr An attack on ELG-LUC3-ECC cryptosystem using Hastad’s and Julta’s theorem
title_full_unstemmed An attack on ELG-LUC3-ECC cryptosystem using Hastad’s and Julta’s theorem
title_short An attack on ELG-LUC3-ECC cryptosystem using Hastad’s and Julta’s theorem
title_sort attack on elg-luc3-ecc cryptosystem using hastad’s and julta’s theorem
url http://psasir.upm.edu.my/id/eprint/117657/
http://psasir.upm.edu.my/id/eprint/117657/
http://psasir.upm.edu.my/id/eprint/117657/1/117657.pdf