Lee Feng Koo and Tze Jin Wong and Pang Hung Yiu and Nik Mohd Asri Nik Long
An Attack on the Lucas Based ElGamal Cryptosystem in the Elliptic Curve Group Over Finite Field Using Greater Common Divisor
80 - 83
2019
13
4
International Journal of Mathematical and Computational Sciences
https://publications.waset.org/pdf/10010260
https://publications.waset.org/vol/148
World Academy of Science, Engineering and Technology
Greater common divisor (GCD) attack is an attack that relies on the polynomial structure of the cryptosystem. This attack required two plaintexts differ from a fixed number and encrypted under same modulus. This paper reports a security reaction of Lucas Based ElGamal Cryptosystem in the Elliptic Curve group over finite field under GCD attack. Lucas Based ElGamal Cryptosystem in the Elliptic Curve group over finite field was exposed mathematically to the GCD attack using GCD and Dickson polynomial. The result shows that the cryptanalyst is able to get the plaintext without decryption by using GCD attack. Thus, the study concluded that it is highly perilous when two plaintexts have a slight difference from a fixed number in the same Elliptic curve group over finite field.
Open Science Index 148, 2019