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, where...
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| Format: | Article |
| Language: | English |
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Lviv Polytechnic National University
2024
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| Online Access: | http://psasir.upm.edu.my/id/eprint/114785/ http://psasir.upm.edu.my/id/eprint/114785/1/114785.pdf |
| _version_ | 1848866595019948032 |
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| author | Wong, T.J. Koo, L.F. A. Sathar, M.H. Rasedee, A.F.N. Sarbini, I. N. |
| author_facet | Wong, T.J. Koo, L.F. A. Sathar, M.H. Rasedee, A.F.N. Sarbini, I. N. |
| author_sort | Wong, T.J. |
| 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. |
| first_indexed | 2025-11-15T14:23:06Z |
| format | Article |
| id | upm-114785 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T14:23:06Z |
| publishDate | 2024 |
| publisher | Lviv Polytechnic National University |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1147852025-03-10T02:08:25Z http://psasir.upm.edu.my/id/eprint/114785/ An attack on ELG-LUC3-ECC cryptosystem using Hastad’s and Julta’s theorem Wong, T.J. Koo, L.F. A. Sathar, M.H. Rasedee, A.F.N. Sarbini, I. N. 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/114785/1/114785.pdf 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 https://science.lpnu.ua/mmc/all-volumes-and-issues/volume-11-number-4-2024/attack-elg-luc3-ecc-cryptosystem-using-hastads 10.23939/mmc2024.04.1135 |
| spellingShingle | Wong, T.J. Koo, L.F. A. Sathar, M.H. Rasedee, A.F.N. Sarbini, I. N. 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/114785/ http://psasir.upm.edu.my/id/eprint/114785/ http://psasir.upm.edu.my/id/eprint/114785/ http://psasir.upm.edu.my/id/eprint/114785/1/114785.pdf |