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...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Lviv Polytechnic National University
2024
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| Online Access: | http://psasir.upm.edu.my/id/eprint/117657/ http://psasir.upm.edu.my/id/eprint/117657/1/117657.pdf |
| _version_ | 1848867306792288256 |
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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. |
| first_indexed | 2025-11-15T14:34:24Z |
| format | Article |
| id | upm-117657 |
| 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 |
| repository_type | Digital Repository |
| 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 |