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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 equations system, whe...

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Main Authors: T.J, Wong, L.F, Koo, M.H.A., Sathar, A.F.N., Rasedee, Izzatul Nabila, Sarbini
Format: Article
Language:English
Published: Lviv Polytechnic National University 2024
Subjects:
QA Mathematics
Online Access:http://ir.unimas.my/id/eprint/47124/1/202411411351140.pdf
http://ir.unimas.my/id/eprint/47124/
https://science.lpnu.ua/sites/default/files/journal-paper/2024/dec/36889/202411411351140.pdf
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spelling my.unimas.ir-471242024-12-30T07:43:08Z http://ir.unimas.my/id/eprint/47124/ An attack on ELG-LUC3-ECC cryptosystem using Hastad’s and Julta’s theorem T.J, Wong L.F, Koo M.H.A., Sathar A.F.N., Rasedee Izzatul Nabila, Sarbini QA Mathematics 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 2024-11 Article PeerReviewed text en http://ir.unimas.my/id/eprint/47124/1/202411411351140.pdf T.J, Wong and L.F, Koo and M.H.A., Sathar and A.F.N., Rasedee and Izzatul Nabila, 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 https://science.lpnu.ua/sites/default/files/journal-paper/2024/dec/36889/202411411351140.pdf 10.23939/mmc2024.04.1135
institution Universiti Malaysia Sarawak
building Centre for Academic Information Services (CAIS)
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaysia Sarawak
content_source UNIMAS Institutional Repository
url_provider http://ir.unimas.my/
language English
topic QA Mathematics
spellingShingle QA Mathematics
T.J, Wong
L.F, Koo
M.H.A., Sathar
A.F.N., Rasedee
Izzatul Nabila, Sarbini
An attack on ELG-LUC3-ECC cryptosystem using Hastad’s and Julta’s theorem
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.
format Article
author T.J, Wong
L.F, Koo
M.H.A., Sathar
A.F.N., Rasedee
Izzatul Nabila, Sarbini
author_facet T.J, Wong
L.F, Koo
M.H.A., Sathar
A.F.N., Rasedee
Izzatul Nabila, Sarbini
author_sort T.J, Wong
title 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_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_sort attack on elg-luc3-ecc cryptosystem using hastad’s and julta’s theorem
publisher Lviv Polytechnic National University
publishDate 2024
url http://ir.unimas.my/id/eprint/47124/1/202411411351140.pdf
http://ir.unimas.my/id/eprint/47124/
https://science.lpnu.ua/sites/default/files/journal-paper/2024/dec/36889/202411411351140.pdf
_version_ 1819914989611253760
score 13.223943

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