An attack on ELG-LUC3-ECC cryptosystem using Hastad's and Julta's theorem
Universiti Putra Malaysia, Bintulu Campus, T. J. Wong, L. F. Koo, Universiti Putra Malaysia, Bintulu Campus, Mohammad Hasan Abdul Sathar, Universiti Putra Malaysia, Ahmad Fadly Nurullah Rasedee, Universiti Sains Islam Malaysia, Izzatul Nabila Sarbini, Universiti Malaysia Sarawak · Mathematical Modeling and Computing · 2024
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.