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: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Lviv Polytechnic National University
2024
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| Subjects: | |
| 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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| Summary: | 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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